@Book{Petris-DLM,
    title = {Dynamic Linear Models with R},
    author = {Giovanni Petris and Sonia Petrone and Patrizia
      Campagnoli},
    year = {2009},
    series = {useR!},
    publisher = {Springer-Verlag, New York},
  }

@book{WestHarr-DLM,
  added-at = {2009-10-28T04:42:52.000+0100},
  author = {West, Mike and Harrison, Jeff},
  biburl = {https://www.bibsonomy.org/bibtex/291bc168235af168280eb3558ca6dcdbc/jwbowers},
  citeulike-article-id = {111604},
  date-added = {2007-09-03 22:45:16 -0500},
  date-modified = {2007-09-03 22:45:16 -0500},
  howpublished = {Hardcover},
  interhash = {7a4066d39c9fa325dfddacb1264c79e9},
  intrahash = {91bc168235af168280eb3558ca6dcdbc},
  isbn = {0387947256},
  keywords = {bayesian statistics},
  month = {February},
  opturl = {http://www.amazon.fr/exec/obidos/ASIN/0387947256/citeulike04-21},
  publisher = {Springer-Verlag},
  timestamp = {2009-10-28T04:43:02.000+0100},
  title = {Bayesian Forecasting and Dynamic Models (Springer Series in Statistics)},
  year = 1997
}

@article{WestHarrMigon,
author = { Mike   West  and  P.   Jeff   Harrison  and  Helio S.   Migon },
title = {Dynamic Generalized Linear Models and Bayesian Forecasting},
journal = {Journal of the American Statistical Association},
volume = {80},
number = {389},
pages = {73-83},
year  = {1985},
publisher = {Taylor \& Francis},
doi = {10.1080/01621459.1985.10477131},

URL = {
        https://www.tandfonline.com/doi/abs/10.1080/01621459.1985.10477131

},
eprint = {
        https://www.tandfonline.com/doi/pdf/10.1080/01621459.1985.10477131

}

}

@book{AmariGeomInfo,
author = {Amari, Shun-ichi},
title = {Information Geometry and Its Applications},
year = {2016},
isbn = {4431559779},
publisher = {Springer Publishing Company, Incorporated},
edition = {1st},
abstract = {This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the NeymanScott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.}
}

@article{TierneyKadane1,
author = { Luke   Tierney  and  Joseph B.   Kadane },
title = {Accurate Approximations for Posterior Moments and Marginal Densities},
journal = {Journal of the American Statistical Association},
volume = {81},
number = {393},
pages = {82-86},
year  = {1986},
publisher = {Taylor \& Francis},
doi = {10.1080/01621459.1986.10478240},
URL = {
        https://www.tandfonline.com/doi/abs/10.1080/01621459.1986.10478240
},
eprint = {
        https://www.tandfonline.com/doi/pdf/10.1080/01621459.1986.10478240
}
}

@article{TierneyKadane2,
author = { Luke   Tierney  and  Robert E.   Kass  and  Joseph B.   Kadane },
title = {Fully Exponential Laplace Approximations to Expectations and Variances of Nonpositive Functions},
journal = {Journal of the American Statistical Association},
volume = {84},
number = {407},
pages = {710-716},
year  = {1989},
publisher = {Taylor \& Francis},
doi = {10.1080/01621459.1989.10478824},
URL = {

        https://doi.org/10.1080/01621459.1989.10478824
},
eprint = {

        https://doi.org/10.1080/01621459.1989.10478824
}
}

@article{Kalman_filter_origins,
    Author = {Kalman, Rudolph Emil},
    Title = {A New Approach to Linear Filtering and Prediction Problems},
    Journal = {Transactions of the ASME--Journal of Basic Engineering},
    Volume = {82},
    Number = {Series D},
    Pages = {35--45},
    Year = {1960}
}

@ARTICLE{nelder1972generalized,
  AUTHOR = {Nelder, J. A.  and Wedderburn, R. W. M.},
  TITLE = {Generalized linear models},
  YEAR = {1972},
  JOURNAL = {Journal of the Royal Statistical Society, Series A, General},
  VOLUME = {135},
  PAGES = {370--384},
}

@article{harrison1976bayesian,
  title={Bayesian forecasting},
  author={Harrison, P Jeffrey  and Stevens, Colin F},
  journal={Journal of the Royal Statistical Society. Series B (Methodological)},
  volume={38(3)},
  pages={205--247},
  year={1976},
  publisher={JSTOR},
}

@article{gamerman1998markov,
  title={Markov chain {M}onte {C}arlo for dynamic generalised linear models},
  author={Gamerman, Dani},
  journal={Biometrika},
  volume={85},
  number={1},
  pages={215--227},
  year={1998},
  publisher={Oxford University Press}
}

@article{Durbin2002,
  title={ A simple and efficient simulation smoother for state space
time series analysis},
  author={Durbin, J. and Koopman, S. J.},
  journal={Biometrika},
    number = 3,
    volume=89,
  pages = {603--15},
  year={2002}
}

@mastersthesis{marotta2018,
author = {Marotta, R.},
title = {Revisiting DLM for $P$-dimensional Exponential Family},
school = {Universidade Federal do Rio de Janeiro},
address = {RJ BR},
year = {2018}
}

@book{DurbinKoopman2001,
  title     = {Time Series Analysis by State Space Methods},
  author    = {James Durbin and Siem Jan Koopman},
  year      = {2001},
  publisher = {Oxford University Press}
}

@article{CarterKohn1994,
  title   = {On Gibbs Sampling for State Space Models},
  author  = {Chris Carter and Robert Kohn},
  journal = {Biometrika},
  year    = {1994},
  volume  = {81},
  number  = {3},
  pages   = {541-553}
}

@article{FearnheadKunsch2018,
  title   = {Particle Filters for High-Dimensional Time Series Models},
  author  = {Paul Fearnhead and Hans R. Künsch},
  journal = {Statistical Science},
  year    = {2018},
  volume  = {33},
  number  = {3},
  pages   = {357-378}
}

@article{Blei2017,
   title={Variational Inference: A Review for Statisticians},
   volume={112},
   ISSN={1537-274X},
   url={http://dx.doi.org/10.1080/01621459.2017.1285773},
   DOI={10.1080/01621459.2017.1285773},
   number={518},
   journal={Journal of the American Statistical Association},
   publisher={Informa UK Limited},
   author={Blei, David M. and Kucukelbir, Alp and McAuliffe, Jon D.},
   year={2017},
   month=apr, pages={859–877} }

@article{koop2023,
author = {Koop, Gary and Korobilis, Dimitris},
title = {BAYESIAN DYNAMIC VARIABLE SELECTION IN HIGH DIMENSIONS},
journal = {International Economic Review},
volume = {64},
number = {3},
pages = {1047-1074},
year={2023}
}

@article{DelMoral2006,
  title={Sequential Monte Carlo samplers},
  author={Del Moral, Pierre and Doucet, Arnaud and Jasra, Ajay},
  journal={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  volume={68},
  number={3},
  pages={411--436},
  year={2006},
  publisher={Wiley Online Library}
}

@article{Andrieu2010,
  title={Particle Markov chain Monte Carlo methods},
  author={Andrieu, Christophe and Doucet, Arnaud and Holenstein, Roman},
  journal={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  volume={72},
  number={3},
  pages={269--342},
  year={2010},
  publisher={Wiley Online Library}
}


@Book{tsay2005analysis,
  title={Analysis of financial time series},
  author={Tsay, Ruey S.},
  year={2005},
  publisher={John Wiley \& Sons},
}

@article{BeareBrendanK,
issn = {0012-9682},
abstract = {An emerging literature in time series econometrics concerns the modeling of potentially nonlinear temporal dependence in stationary Markov chains using copula functions. We obtain sufficient conditions for a geometric rate of mixing in models of this kind. Geometric β-mixing is established under a rather strong sufficient condition that rules out asymmetry and tail dependence in the copula function. Geometric ρ-mixing is obtained under a weaker condition that permits both asymmetry and tail dependence. We verify one or both of these conditions for a range of parametric copula functions that are popular in applied work.},
journal = {Econometrica},
pages = {395--410},
volume = {78},
publisher = {Blackwell Publishing Ltd},
number = {1},
year = {2010},
title = {Copulas and Temporal Dependence},
copyright = {Copyright 2010 The Econometric Society},
language = {eng},
address = {Oxford, UK},
author = {Beare, Brendan K.},
keywords = {Applications ; Asymmetry ; Autocorrelation ; Business \& Economics ; canonical correlation ; Coefficients ; Copula ; Copula (probability theory) ; Copula functions ; Correlation coefficients ; Density ; Econometrics ; Economic theory ; Economics ; Exact sciences and technology ; Inference from stochastic processes; time series analysis ; Insurance economics finance ; Markov analysis ; Markov chain ; Markov chains ; Markov processes ; Markovian processes ; Mathematical Methods In Social Sciences ; Mathematical theorems ; Mathematics ; Mathematics Interdisciplinary Applications ; maximal correlation ; mean square contingency ; mixing ; Nonlinear system ; Notes and Comments ; Numerical analysis ; Numerical analysis. Scientific computation ; Numerical methods in probability and statistics ; Parametric statistics ; Physical Sciences ; Probability and statistics ; Probability theory and stochastic processes ; Random variables ; Science \& Technology ; Sciences and techniques of general use ; Social Sciences ; Social Sciences Mathematical Methods ; Stationarity ; Statistical physics ; Statistics ; Statistics \& Probability ; Stochastic process ; Studies ; Tail dependence ; Time dependence ; Time series},
}

@article{ChenXiaohong2009Cnqa,
issn = {1368-4221},
abstract = {Parametric copulas are shown to be attractive devices for specifying quantile autoregressive models for nonlinear time-series. Estimation of local, quantile-specific copula-based time series models offers some salient advantages over classical global parametric approaches. Consistency and asymptotic normality of the proposed quantile estimators are established under mild conditions, allowing for global misspecification of parametric copulas and marginals, and without assuming any mixing rate condition. These results lead to a general framework for inference and model specification testing of extreme conditional value-at-risk for financial time series data.},
journal = {The econometrics journal},
pages = {S50--S67},
volume = {12},
publisher = {Blackwell Publishing Ltd},
number = {s1},
year = {2009},
title = {Copula-based nonlinear quantile autoregression},
copyright = {2009 Royal Economic Society},
language = {eng},
address = {Oxford, UK},
author = {Chen, Xiaohong and Koenker, Roger and Xiao, Zhijie},
keywords = {Business \& Economics ; Copula ; Copula functions ; Econometrics ; Economic models ; Economic theory ; Economics ; Ergodic nonlinear Markov models ; Estimating techniques ; Estimation ; Estimators ; Inference ; Markov analysis ; Markov models ; Mathematical independent variables ; Mathematical Methods In Social Sciences ; Mathematics ; Mathematics Interdisciplinary Applications ; Maximum likelihood estimation ; Non-linear models ; Parametric models ; Physical Sciences ; Quantile autoregression ; Science \& Technology ; Social Sciences ; Social Sciences Mathematical Methods ; Statistics \& Probability ; Studies ; Time series ; Time series models ; Vector-autoregressive models},
}




@article{HeinenAndréas2007Mamo,
issn = {0927-5398},
abstract = {We introduce the Multivariate Autoregressive Conditional Double Poisson model to deal with discreteness, overdispersion and both auto and cross-correlation, arising with multivariate counts. We model counts with a double Poisson and assume that conditionally on past observations the means follow a Vector Autoregression. We resort to copulas to introduce contemporaneous correlation. We apply it to the study of sector and stock-specific news related to the comovements in the number of trades per unit of time of the most important US department stores traded on the NYSE. We show that the market leaders inside a specific sector are related to their size measured by their market capitalization.},
journal = {Journal of empirical finance},
pages = {564--583},
volume = {14},
publisher = {Elsevier B.V},
number = {4},
year = {2007},
title = {Multivariate autoregressive modeling of time series count data using copulas},
copyright = {2007 Elsevier B.V.},
language = {eng},
author = {Heinen, Andréas and Rengifo, Erick},
keywords = {Autoregressive model ; Copula continued extension ; Correlation ; Count data ; Counts ; Econometrics ; Economic models ; Economics ; Factor model ; Humanities and Social Sciences ; Market microstructure ; Multivariate analysis ; Multivariate statistics ; Overdispersion ; Poisson distribution ; Poisson regression ; STAR model ; Statistics ; Time series ; U.S.A ; Vector autoregression ; Vector-autoregressive models},
}

@article{BrechmannEikeChristian2015Ctsm,
issn = {1524-1904},
abstract = {The analysis of multivariate time series is a common problem in areas like finance and economics. The classical tools for this purpose are vector autoregressive models. These however are limited to the modeling of linear and symmetric dependence. We propose a novel copula‐based model that allows for the non‐linear and non‐symmetric modeling of serial as well as between‐series dependencies. The model exploits the flexibility of vine copulas, which are built up by bivariate copulas only. We describe statistical inference techniques for the new model and discuss how it can be used for testing Granger causality. Finally, we use the model to investigate inflation effects on industrial production, stock returns and interest rates. In addition, the out‐of‐sample predictive ability is compared with relevant benchmark models. Copyright © 2014 John Wiley \& Sons, Ltd.},
journal = {Applied stochastic models in business and industry},
pages = {495--514},
volume = {31},
publisher = {Blackwell Publishing Ltd},
number = {4},
year = {2015},
title = {COPAR-multivariate time series modeling using the copula autoregressive model},
copyright = {Copyright © 2014 John Wiley \& Sons, Ltd.},
language = {eng},
author = {Brechmann, Eike Christian and Czado, Claudia},
keywords = {Autoregressive model ; Autoregressive processes ; Bivariate analysis ; Business ; Copula (linguistics) ; copula autoregression ; Econometrics ; Economics ; forecasting time series ; Granger causality ; Inference ; Mathematical models ; Methodology ; multivariate time series ; Nonlinearity ; Raw materials ; STAR model ; Statistical inference ; Statistics ; Time series ; Vector autoregression ; Vine copula},
}

@article{Barrera-GómezJose2023CPRw,
issn = {1044-3983},
abstract = {The analysis of time series studies linking daily counts of a health indicator with environmental variables (e.g., mortality or hospital admissions with air pollution concentrations or temperature; or motor vehicle crashes with temperature) is usually conducted with Poisson regression models controlling for long-term and seasonal trends using temporal strata. When the study includes multiple zones, analysts usually apply a two-stage approach: first, each zone is analyzed separately, and the resulting zone-specific estimates are then combined using meta-analysis. This approach allows zone-specific control for trends. A one-stage approach uses spatio-temporal strata and could be seen as a particular case of the case–time series framework recently proposed. However, the number of strata can escalate very rapidly in a long time series with many zones. A computationally efficient alternative is to fit a conditional Poisson regression model, avoiding the estimation of the nuisance strata. To allow for zone-specific effects, we propose a conditional Poisson regression model with a random slope, although available frequentist software does not implement this model. Here, we implement our approach in the Bayesian paradigm, which also facilitates the inclusion of spatial patterns in the effect of interest. We also provide a possible extension to deal with overdispersed data. We first introduce the equations of the framework and then illustrate their application to data from a previously published study on the effects of temperature on the risk of motor vehicle crashes. We provide R code and a semi-synthetic dataset to reproduce all analyses presented.},
journal = {Epidemiology (Cambridge, Mass.)},
pages = {873--878},
volume = {34},
publisher = {Lippincott Williams \& Wilkins},
number = {6},
year = {2023},
title = {Conditional Poisson Regression with Random Effects for the Analysis of Multi-site Time Series Studies},
copyright = {Copyright © 2023 The Author(s). Published by Wolters Kluwer Health, Inc. 2023},
language = {eng},
address = {Hagerstown, MD},
author = {Barrera-Gómez, Jose and Puig, Xavier and Ginebra, Josep and Basagaña, Xavier},
keywords = {Methods},
}



@article{OmutoCT2010Mmot,
issn = {0140-1963},
abstract = {Many researchers have used time-series analysis of remotely sensed images to gain understanding of the dynamics of loss of vegetation cover in drylands. However, complex interactions between vegetation and climate still mask the potential of remote sensing signals to detect human-induced loss of vegetation cover. This paper presents mixed-effect modelling method for time-series NDVI-rainfall relationship to account for the complex interaction between vegetation and climate. Mixed-effects method is a form of statistical modelling that can simultaneously model environmental relationships for a population and for different groups within the population. In this study, it was used to model the NDVI-rainfall relationship in Somalia and for different vegetation types in the country. Its time-series application removed the interaction between vegetation and rainfall and identified areas experiencing human-induced loss of vegetation cover in the country. On average, it gave an accurate relationship between rainfall and NDVI (
r
2
>
60%) and detected areas with human-induced loss of vegetation cover (kappa
=
75%). Although the potential of mixed-effects was shown using vegetation types, other factors such as soil types and land use can also be included in the method to improve accuracy of time-series NDVI images in detecting human-induced loss of vegetation cover in the drylands.},
journal = {Journal of arid environments},
pages = {1552--1563},
volume = {74},
publisher = {Elsevier Ltd},
number = {11},
year = {2010},
title = {Mixed-effects modelling of time series NDVI-rainfall relationship for detecting human-induced loss of vegetation cover in drylands},
copyright = {2010 Elsevier Ltd},
language = {eng},
address = {LONDON},
author = {Omuto, C.T. and Vargas, R.R. and Alim, M.S. and Paron, P.},
keywords = {Animal and plant ecology ; Animal plant and microbial ecology ; arid lands ; Biological and medical sciences ; Climate ; Ecology ; Enhanced vegetation index ; Environmental science ; Environmental Sciences ; Environmental Sciences \& Ecology ; Fundamental and applied biological sciences. Psychology ; General aspects. Techniques ; Hydrology ; Land use ; Life Sciences \& Biomedicine ; Loss of vegetation ; Mathematical models ; Methods and techniques (sampling tagging trapping modelling...) ; Mixed-effects ; Modelling ; NDVI ; Normalized Difference Vegetation Index ; Physical geography ; Plant cover ; Population ; Population (statistical) ; rain ; Rainfall ; Remote sensing ; researchers ; Science \& Technology ; Soil classification ; soil types ; Statistical model ; Synecology ; Terrestrial ecosystems ; time series analysis ; Vegetation ; Vegetation (pathology) ; vegetation cover ; vegetation types},
}

@article{ZhangHeping2008JMoT,
issn = {0162-1459},
abstract = {Exposure to ambient pollutants at concentrations above defined standards is a risk factor for respiratory symptoms, especially in sensitive children. Many studies have been undertaken to monitor air quality and to assess its association with respiratory symptoms. We propose a joint mixed-effects regression model of time series measures and recurrent events to analyze the air quality and respiratory symptom data from the Yale Mothers and Infants Health Study. Three mothers' symptoms (runny nose, cough, and sore throat) and three infants' symptoms (runny nose, cough, and general sickness) were investigated. To alleviate the computational complexity, a two-stage maximum likelihood-based estimation procedure is introduced to estimate the parameters, and simulation studies are conducted to assess the validity of this estimation procedure. Our analysis reveals differences in the etiology of respiratory symptoms between mothers and infants. Most notably, coarse particles of mass between 2.5 and 10 μ in diameter increased the risks of mothers' runny nose and cough symptoms but had no significant effect on any of the three infants' symptoms. The sulfate level was negatively associated with the risk of infants' runny nose and cough symptoms but had no significant effect on any of the three mothers' symptoms. High level of humidity is negatively associated with the mothers' cough incidence but had no significant association with any of the three infants' symptoms. Such differences reveal not only the sensitivity of the mothers and infants to the air quality, but also call for further understanding of the differences. It is possible that actions taken to overcome humidity by mothers may inadvertently affect their infants.},
journal = {Journal of the American Statistical Association},
pages = {48--60},
volume = {103},
publisher = {Taylor \& Francis},
number = {481},
year = {2008},
title = {Joint Modeling of Time Series Measures and Recurrent Events and Analysis of the Effects of Air Quality on Respiratory Symptoms},
copyright = {American Statistical Association 2008},
language = {eng},
address = {ALEXANDRIA},
author = {Zhang, Heping and Ye, Yuanqing and Diggle, Peter and Shi, Jian},
keywords = {Air pollution ; Air quality ; Air quality assessment ; Applications ; Applications and Case Studies ; Censored data ; Cough ; El Niño ; Etiology ; Exact sciences and technology ; General topics ; Health ; Health risk assessment ; Humidity ; Infants ; Inference from stochastic processes; time series analysis ; Joint analysis ; Longitudinal data ; Mathematics ; Maximum likelihood estimation ; Maximum likelihood method ; Medical sciences ; Modeling ; Mothers ; Multivariate analysis ; Nose ; Outdoor air quality ; Parametric models ; Pediatrics ; Pets ; Physical Sciences ; Probability and statistics ; Recurrent event ; Regression analysis ; Respiratory care ; Respiratory diseases ; Respiratory symptoms ; Respiratory system ; Risk factor ; Risk factors ; Science \& Technology ; Sciences and techniques of general use ; Sore throat ; Standard error ; Statistical analysis ; Statistical data ; Statistical methods ; Statistical models ; Statistics ; Statistics \& Probability ; Time series ; Time series models},
}

@article{KlingenbergBernhard2008Rmfb,
issn = {0167-9473},
abstract = {Time series of discrete random variables present unique statistical challenges due to serial correlation and uneven sampling intervals. While regression models for a series of counts are well developed, only few methods are discussed for the analysis of moderate to long (e.g.Â from 20 to 152 observations) binary or binomial time series. This article suggests generalized linear mixed models with autocorrelated random effects for a parameter-driven approach to such series. We use a Monte Carlo EM algorithm to jointly obtain maximum likelihood estimates of regression parameters and variance components. The likelihood approach, although computationally extensive, allows estimation of marginal joint probabilities of two or more serial events. These are crucial in checking the goodness-of-fit, whether the model adequately captures the serial correlation and for predicting future responses. The model is flexible enough to allow for missing observations or unequally spaced time intervals. We illustrate our approach and model assessment tools with an analysis of the series of winners in the traditional boat race between the universities of Oxford and Cambridge, re-evaluating a long-held belief about the effect of the weight of the crew on the odds of winning. We also show how our methods are useful in modeling trends based on the General Social Survey database.},
journal = {Computational statistics \& data analysis},
pages = {4076--4090},
volume = {52},
publisher = {Elsevier B.V},
number = {8},
year = {2008},
title = {Regression models for binary time series with gaps},
copyright = {2008 Elsevier Ltd},
language = {eng},
address = {AMSTERDAM},
author = {Klingenberg, Bernhard},
keywords = {Autocorrelation ; Computer Science ; Computer Science Interdisciplinary Applications ; Econometrics ; Exact sciences and technology ; Expectationâ€“maximization algorithm ; General topics ; Generalized linear mixed model ; Likelihood function ; Linear inference regression ; Linear model ; Mathematics ; Mixed model ; Multivariate analysis ; Numerical analysis ; Numerical analysis. Scientific computation ; Numerical methods in probability and statistics ; Physical Sciences ; Probability and statistics ; Random effects model ; Regression analysis ; Science \& Technology ; Sciences and techniques of general use ; Statistics ; Statistics \& Probability ; Technology},
}

@article{LiJinglan2019Htmm,
issn = {1048-5252},
abstract = {We propose time-varying coefficient mixed-effects models for continuous multiple time series data and longitudinal data. The challenge is how to simultaneously display serial, clustering, and multivariate attributes of the data set, to which the routinely assumed two-level hierarchical model and univariate response models are not able to apply. Asymptotic properties of the proposed methods are established. We also conduct the model comparison, and find that the proposed methods outperform the traditional univariate response models, nonparametric models, and linear mixed effects models in both predicting the response and estimating the coefficient surface based on simulation studies. Finally, we have applied our methods to a real-world study on the price-volume relationship of NASDAQ stock market data.},
journal = {Journal of nonparametric statistics},
pages = {695--721},
volume = {31},
publisher = {Taylor \& Francis},
number = {3},
year = {2019},
title = {Hierarchical time-varying mixed-effects models in high-dimensional time series and longitudinal data studies},
copyright = {American Statistical Association and Taylor \& Francis 2019 2019},
language = {eng},
address = {Abingdon},
author = {Li, Jinglan and Zhang, Zhengjun},
keywords = {Asymptotic methods ; Asymptotic properties ; Clustering ; Computer simulation ; local linear regression ; mixed effects models ; Multivariate analysis ; profile likelihood ; Time series ; Varying coefficient models},
}

@article{ChoSun-Joo2018AGLM,
issn = {0033-3123},
abstract = {As a method to ascertain person and item effects in psycholinguistics, a generalized linear mixed effect model (GLMM) with crossed random effects has met limitations in handing serial dependence across persons and items. This paper presents an autoregressive GLMM with crossed random effects that accounts for variability in lag effects across persons and items. The model is shown to be applicable to intensive binary time series eye-tracking data when researchers are interested in detecting experimental condition effects while controlling for previous responses. In addition, a simulation study shows that ignoring lag effects can lead to biased estimates and underestimated standard errors for the experimental condition effects.},
journal = {Psychometrika},
pages = {751--771},
volume = {83},
publisher = {Springer US},
number = {3},
year = {2018},
title = {Autoregressive Generalized Linear Mixed Effect Models with Crossed Random Effects: An Application to Intensive Binary Time Series Eye-Tracking Data},
copyright = {The Psychometric Society 2018},
language = {eng},
address = {New York},
author = {Cho, Sun-Joo and Brown-Schmidt, Sarah and Lee, Woo-yeol},
keywords = {Assessment ; Autoregressive model ; Behavioral Science and Psychology ; Binary number ; Computer Simulation ; Data processing ; experimental psychology ; Eye Movement Measurements ; Eye tracking ; Generalized linear models ; Humanities ; Humans ; Lag ; Law ; Linear Models ; mathematics ; natural sciences ; Psycholinguistics ; Psychology ; psychology and cognitive sciences ; Psychometrics ; Random effects model ; Series (mathematics) ; social sciences ; Standard error ; Statistical Theory and Methods ; Statistics ; statistics \& probability ; Statistics for Social Sciences ; Testing and Evaluation ; Time Factors ; Time series},
}

@article{LiaoYu-Pin2017Aoms,
issn = {1848-0225},
abstract = {In the past few decades, demand forecasting has become relatively difficult due to rapid changes in the global environment. This research illustrates the use of the make-to-stock (MTS) production strategy in order to explain how forecasting plays an essential role in business management. The linear mixed-effect (LME) model has been extensively developed and is widely applied in various fields. However, no study has used the LME model for business forecasting. We suggest that the LME model be used as a tool for prediction and to overcome environment complexity. The data analysis is based on real data in an international display company, where the company needs accurate demand forecasting before adopting a MTS strategy. The forecasting result from the LME model is compared to the commonly used approaches, including the regression model, autoregressive model, times series model, and exponential smoothing model, with the results revealing that prediction performance provided by the LME model is more stable than using the other methods. Furthermore, product types in the data are regarded as a random effect in the LME model, hence demands of all types can be predicted simultaneously using a single LME model. However, some approaches require splitting the data into different type categories, and then predicting the type demand by establishing a model for each type. This feature also demonstrates the practicability of the LME model in real business operations.},
journal = {Croatian Operational Research Review},
pages = {357--376},
volume = {8},
publisher = {Hrvatsko društvo za operacijska istraživanja},
number = {2},
year = {2017},
title = {Advantage of make-to-stock strategy based on linear mixed-effect model: a comparison with regression, autoregressive, times series, and exponential smoothing models},
language = {eng},
author = {Liao, Yu-Pin and Chiu, Shin-Kuan},
keywords = {Applied mathematics. Quantitative methods ; Autoregressive model ; Build to stock ; Econometrics ; Exponential smoothing ; forecasting ; Linear mixed effect model ; make-to-stock ; Mathematics ; order demand ; Production strategy ; Regression ; Series (mathematics) ; T57-57.97},
organization = {Department of International Trade, Feng Chia University, Taichung, Taiwan},
}



@article{DavisRichardA2021CTSA,
issn = {0162-1459},
abstract = {A growing interest in non-Gaussian time series, particularly in series comprised of nonnegative integers (counts), is taking place in today's statistics literature. Count series naturally arise in fields, such as agriculture, economics, epidemiology, finance, geology, meteorology, and sports. Unlike stationary Gaussian series where autoregressive moving-averages are the primary modeling vehicle, no single class of models dominates the count landscape. As such, the literature has evolved somewhat ad-hocly, with different model classes being developed to tackle specific situations. This article is an attempt to summarize the current state of count time series modeling. The article first reviews models having prescribed marginal distributions, including some recent developments. This is followed by a discussion of state-space approaches. Multivariate extensions of the methods are then studied and Bayesian approaches to the problem are considered. The intent is to inform researchers and practitioners about the various types of count time series models arising in the modern literature. While estimation issues are not pursued in detail, reference to this literature is made.},
journal = {Journal of the American Statistical Association},
pages = {1533--1547},
volume = {116},
publisher = {Taylor \& Francis},
number = {535},
year = {2021},
title = {Count Time Series: A Methodological Review},
copyright = {2021 American Statistical Association 2021},
language = {eng},
address = {Alexandria},
author = {Davis, Richard A. and Fokianos, Konstantinos and Holan, Scott H. and Joe, Harry and Livsey, James and Lund, Robert and Pipiras, Vladas and Ravishanker, Nalini},
keywords = {Autocorrelation ; Averages ; Bayesian analysis ; Count Negative binomial distribution ; Discrete mathematics ; econometrics ; economics and business ; Epidemiology ; Finance ; Geology ; mathematics ; Meteorology ; Modelling ; natural sciences ; Poisson distribution ; Regression analysis ; Series (mathematics) ; social sciences ; Sports ; State-space models ; Statistical methods ; Statistics ; statistics \& probability ; Time series},
}

@article{NandaRatihOktri2022CMaC,
issn = {1660-4601},
abstract = {In response to the COVID-19 pandemic, mobile-phone data on population movement became publicly available, including Google Community Mobility Reports (CMR). This study explored the utilization of mobility data to predict COVID-19 dynamics in Jakarta, Indonesia. We acquired aggregated and anonymized mobility data sets from 15 February to 31 December 2020. Three statistical models were explored: Poisson Regression Generalized Linear Model (GLM), Negative Binomial Regression GLM, and Multiple Linear Regression (MLR). Due to multicollinearity, three categories were reduced into one single index using Principal Component Analysis (PCA). Multiple Linear Regression with variable adjustments using PCA was the best-fit model, explaining 52% of COVID-19 cases in Jakarta (R-Square: 0.52; p < 0.05). This study found that different types of mobility were significant predictors for COVID-19 cases and have different levels of impact on COVID-19 dynamics in Jakarta, with the highest observed in “grocery and pharmacy” (4.12%). This study demonstrates the practicality of using CMR data to help policymakers in decision making and policy formulation, especially when there are limited data available, and can be used to improve health system readiness by anticipating case surge, such as in the places with a high potential for transmission risk and during seasonal events.},
journal = {International journal of environmental research and public health},
pages = {6671},
volume = {19},
publisher = {MDPI AG},
number = {11},
year = {2022},
title = {Community Mobility and COVID-19 Dynamics in Jakarta, Indonesia},
copyright = {2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.},
language = {eng},
address = {Switzerland},
author = {Nanda, Ratih Oktri and Nursetyo, Aldilas Achmad and Ramadona, Aditya Lia and Imron, Muhammad Ali and Fuad, Anis and Setyawan, Althaf and Ahmad, Riris Andono},
keywords = {2019-20 coronavirus outbreak ; Cell Phone ; community mobility ; Coronavirus disease 2019 (COVID-19) ; Coronaviruses ; COVID-19 ; COVID-19 - epidemiology ; Datasets ; Decision making ; Drug stores ; Generalized linear model ; Geography ; Holidays \& special occasions ; Humans ; Indonesia - epidemiology ; Jakarta ; Linear regression ; Mathematical models ; Mean square errors ; Mobility ; Models Statistical ; National parks ; Negative binomial distribution ; Pandemics ; Pharmacy ; Poisson regression ; Population ; Principal components analysis ; Public transportation ; Recreation ; Regression analysis ; Regression models ; Regulation ; Restrictions ; Severe acute respiratory syndrome coronavirus 2 ; Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ; Statistical analysis ; Statistical model ; statistical modelling ; Statistical models ; Statistics ; Variables},
}

@article{WangEmilyT2022Scft,
issn = {0013-9580},
abstract = {Objective
Epilepsy monitoring unit (EMU) admissions are critical for presurgical evaluation of drug‐resistant epilepsy but may be nondiagnostic if an insufficient number of seizures are recorded. Seizure forecasting algorithms have shown promise for estimating the likelihood of seizures as a binary event in individual patients, but methods to predict how many seizures will occur remain elusive. Such methods could increase the diagnostic yield of EMU admissions and help patients mitigate seizure‐related morbidity. Here, we evaluated the performance of a state‐space method that uses prior seizure count data to predict future counts.
Methods
A Bayesian negative‐binomial dynamic linear model (DLM) was developed to forecast daily electrographic seizure counts in 19 patients implanted with a responsive neurostimulation (RNS) device. Holdout validation was used to evaluate performance in predicting the number of electrographic seizures for forecast horizons ranging 1–7 days ahead.
Results
One‐day‐ahead prediction of the number of electrographic seizures using a negative‐binomial DLM resulted in improvement over chance in 73.1% of time segments compared to a random chance forecaster and remained >50% for forecast horizons of up to 7 days. Superior performance (mean error = .99) was obtained in predicting the number of electrographic seizures in the next day compared to three traditional methods for count forecasting (integer‐valued generalized autoregressive conditional heteroskedasticity model or INGARCH, 1.10; Croston, 1.06; generalized linear autoregressive moving average model or GLARMA, 2.00). Number of electrographic seizures in the preceding day and laterality of electrographic pattern detections had highest predictive value, with greater number of electrographic seizures and RNS magnet swipes in the preceding day associated with a higher number of electrographic seizures the next day.
Significance
This study demonstrates that DLMs can predict the number of electrographic seizures a patient will experience days in advance with above chance accuracy. This study represents an important step toward the translation of seizure forecasting methods into the optimization of EMU admissions.},
journal = {Epilepsia (Copenhagen)},
pages = {3156--3167},
volume = {63},
publisher = {Wiley Subscription Services, Inc},
number = {12},
year = {2022},
title = {Seizure count forecasting to aid diagnostic testing in epilepsy},
copyright = {2022 International League Against Epilepsy.},
language = {eng},
address = {United States},
author = {Wang, Emily T. and Chiang, Sharon and Cleboski, Stephen and Rao, Vikram R. and Vannucci, Marina and Haneef, Zulfi},
keywords = {Bayes Theorem ; Bayesian analysis ; Bayesian inference ; Convulsions \& seizures ; count forecasting ; Diagnostic Techniques and Procedures ; Diagnostic tests ; Epilepsy ; Epilepsy - diagnosis ; epilepsy monitoring unit ; Humans ; Morbidity ; responsive neurostimulation ; seizure prediction ; Seizures ; Seizures - diagnosis},
}

@misc{macrotrends_data,
  title = {Macrotrends commodities data},
  howpublished = {\url{https://www.macrotrends.net/charts/commodities}},
  note = {Accessed: May 1, 2023},
  year = {2023},
  author = {Macrotrends}
}

@article{carpenter2017stan,
 title={Stan: A Probabilistic Programming Language},
 volume={76},
 url={https://www.jstatsoft.org/index.php/jss/article/view/v076i01},
 doi={10.18637/jss.v076.i01},
 abstract={Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectation propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.},
 number={1},
 journal={Journal of Statistical Software},
 author={Carpenter, Bob and Gelman, Andrew and Hoffman, Matthew D. and Lee, Daniel and Goodrich, Ben and Betancourt, Michael and Brubaker, Marcus and Guo, Jiqiang and Li, Peter and Riddell, Allen},
 year={2017},
 pages={1–32}
}

@book{Vaart_1998, place={Cambridge}, series={Cambridge Series in Statistical and Probabilistic Mathematics}, title={Asymptotic Statistics}, publisher={Cambridge University Press}, author={Vaart, A. W. van der}, year={1998}, collection={Cambridge Series in Statistical and Probabilistic Mathematics}}

@book{MacKay2003,
  added-at = {2007-05-24T14:43:04.000+0200},
  author = {MacKay, David J. C.},
  biburl = {https://www.bibsonomy.org/bibtex/24c23fea472f6e75c0964badd83883d77/tmalsburg},
  interhash = {86f621d9d6f9f159448f768d792d4511},
  intrahash = {4c23fea472f6e75c0964badd83883d77},
  keywords = {bayesianinference book informationtheory neuralnetworks patternrecognition probabilitytheory},
  publisher = {Copyright Cambridge University Press},
  timestamp = {2007-05-24T14:43:04.000+0200},
  title = {Information Theory, Inference, and Learning Algorithms},
  year = 2003
}
@book{gelman2013bayesian,
  title={Bayesian Data Analysis, Third Edition},
  author={Gelman, A. and Carlin, J.B. and Stern, H.S. and Dunson, D.B. and Vehtari, A. and Rubin, D.B.},
  isbn={9781439840955},
  lccn={2013039507},
  series={Chapman \& Hall/CRC Texts in Statistical Science},
  url={https://books.google.com.br/books?id=ZXL6AQAAQBAJ},
  year={2013},
  publisher={Taylor \& Francis}
}


@misc{ArtigokParametrico,
      title={k-parametric Dynamic Generalized Linear Models: a sequential approach via Information Geometry},
      author={Mariane Branco Alves and Helio S. Migon and Raíra Marotta and {dos Santos}, Junior, Silvaneo Vieira},
      year={2024},
      eprint={2201.05387},
      archivePrefix={arXiv},
      primaryClass={stat.ME}
}

@misc{ArtigoPacote,
  title={kDGLM: an R package for Bayesian analysis of Dynamic Generialized Linear Models},
  author={{dos Santos}, Junior, Silvaneo Vieira and Mariane Branco Alves and Helio S. Migon},
  year={2024}
}

@misc{ArtigoAltMethod,
  title={A More Efficient Sequential Approach for k-parametric Dynamic Generalized Linear Models},
  author={{dos Santos}, Junior, Silvaneo Vieira and Mariane Branco Alves and Helio S. Migon},
  year={2024}
}

@misc{ArtigoMultivar,
  title={An Efficient Sequential Approach for Joint Modelling of Multiple Time Series},
  author={{dos Santos}, Junior, Silvaneo Vieira and Mariane Branco Alves and Helio S. Migon},
  year={2024}
}

@article{daSilva2011,
  title={Dynamic Bayesian beta models},
  author={da Silva, C. Q. and Migon, H. S and Correia, L. T.},
  journal={Computational Statistics and Data Analysis},
   volume={55(6)},
   pages={2074--89},
  year={2011}
}




@article{Hartigan-LinearBayes,
 ISSN = {00359246},
 URL = {http://www.jstor.org/stable/2984348},
 abstract = {A method of linear prediction is proposed, which follows the Bayesian scheme in combining prior and present information, but which uses only the first two moments of the distribution of parameters and observations, rather than the complete probability model required of Bayesian techniques.},
 author = {J. A. Hartigan},
 journal = {Journal of the Royal Statistical Society. Series B (Methodological)},
 number = {3},
 pages = {446--454},
 publisher = {[Royal Statistical Society, Wiley]},
 title = {Linear Bayesian Methods},
 volume = {31},
 year = {1969}
}

@book{abramowitz_approx,
  added-at = {2008-06-25T06:25:58.000+0200},
  address = {New York},
  author = {Abramowitz, Milton and Stegun, Irene A.},
  biburl = {https://www.bibsonomy.org/bibtex/223ec744709b3a776a1af0a3fd65cd09f/a_olympia},
  description = {BibTeX - Wikipedia, the free encyclopedia},
  edition = {ninth Dover printing, tenth GPO printing},
  interhash = {d4914a420f489f7c5129ed01ec3cf80c},
  intrahash = {23ec744709b3a776a1af0a3fd65cd09f},
  keywords = {Handbook},
  publisher = {Dover},
  timestamp = {2008-06-25T06:25:58.000+0200},
  title = {Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables},
  year = 1964
}

@book{degroot86-Infer,
  added-at = {2009-10-28T04:42:52.000+0100},
  author = {DeGroot, Morris H.},
  biburl = {https://www.bibsonomy.org/bibtex/29166dd4bba0eb5ae538c622033f5f37f/jwbowers},
  citeulike-article-id = {106895},
  date-added = {2007-09-03 22:45:16 -0500},
  date-modified = {2007-09-03 22:45:16 -0500},
  interhash = {0506ce3e89f39df55b02cf75c280c518},
  intrahash = {9166dd4bba0eb5ae538c622033f5f37f},
  keywords = {statistics},
  timestamp = {2009-10-28T04:43:06.000+0100},
  title = {Probability and Statistics},
  publisher = {Pearson},
  year = 1986
}


  @Article{DLM-pkg,
    title = {An {R} Package for Dynamic Linear Models},
    author = {Giovanni Petris},
    journal = {Journal of Statistical Software},
    year = {2010},
    volume = {36},
    number = {12},
    pages = {1--16},
    url = {https://www.jstatsoft.org/v36/i12/},
  }


@book{hoff2009first,
  title={A First Course in Bayesian Statistical Methods},
  author={Hoff, P.D.},
  isbn={9780387924076},
  lccn={2009929120},
  series={Springer Texts in Statistics},
  url={https://books.google.com.br/books?id=V8jT2SimGR0C},
  year={2009},
  publisher={Springer New York}
}

@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2020},
    note={URL: \url{https://www.R-project.org/}},
}

@Misc{book-of-proofs,
  author       = {Joram Soch and
                  Thomas J. Faulkenberry and
                  Kenneth Petrykowski and
                  Carsten Allefeld},
  title        = {The Book of Statistical Proofs},
  month        = dec,
  year         = 2020,
  publisher    = {Zenodo},
  version      = 2020,
  doi          = {10.5281/zenodo.4305950}
}

@article{interval_score,
    doi = {10.1371/journal.pcbi.1008618},
    author = {Bracher, Johannes AND Ray, Evan L. AND Gneiting, Tilmann AND Reich, Nicholas G.},
    journal = {PLOS Computational Biology},
    publisher = {Public Library of Science},
    title = {Evaluating epidemic forecasts in an interval format},
    year = {2021},
    month = {02},
    volume = {17},
    url = {https://doi.org/10.1371/journal.pcbi.1008618},
    pages = {1-15},
    abstract = {For practical reasons, many forecasts of case, hospitalization, and death counts in the context of the current Coronavirus Disease 2019 (COVID-19) pandemic are issued in the form of central predictive intervals at various levels. This is also the case for the forecasts collected in the COVID-19 Forecast Hub (https://covid19forecasthub.org/). Forecast evaluation metrics like the logarithmic score, which has been applied in several infectious disease forecasting challenges, are then not available as they require full predictive distributions. This article provides an overview of how established methods for the evaluation of quantile and interval forecasts can be applied to epidemic forecasts in this format. Specifically, we discuss the computation and interpretation of the weighted interval score, which is a proper score that approximates the continuous ranked probability score. It can be interpreted as a generalization of the absolute error to probabilistic forecasts and allows for a decomposition into a measure of sharpness and penalties for over- and underprediction.},
    number = {2},

}


@article{mase,
title = {Another look at measures of forecast accuracy},
journal = {International Journal of Forecasting},
volume = {22},
number = {4},
pages = {679-688},
year = {2006},
issn = {0169-2070},
doi = {https://doi.org/10.1016/j.ijforecast.2006.03.001},
url = {https://www.sciencedirect.com/science/article/pii/S0169207006000239},
author = {Rob J. Hyndman and Anne B. Koehler},
keywords = {Forecast accuracy, Forecast evaluation, Forecast error measures, M-competition, Mean absolute scaled error},
abstract = {We discuss and compare measures of accuracy of univariate time series forecasts. The methods used in the M-competition as well as the M3-competition, and many of the measures recommended by previous authors on this topic, are found to be degenerate in commonly occurring situations. Instead, we propose that the mean absolute scaled error become the standard measure for comparing forecast accuracy across multiple time series.}
}

@Misc{RStan,
    title = {{RStan}: the {R} interface to {Stan}},
    author = {{Stan Development Team}},
    note = {R package version 2.32.3},
    year = {2023},
    url = {https://mc-stan.org/},
}

@Article{INLA,
    author ={Rue, Havard and Martino, Sara  and Chopin, Nicholas},
    title ={Approximate {Bayesian} Inference for Latent {Gaussian},
            Models Using Integrated Nested {Laplace} Approximations (with discussion))},
    journal = {Journal of the Royal Statistical Society B},
    year    = {2009},
    volume  = {71},
    pages   = {319--392}
}

@article{gamerman2013non,
  title={A non-{G}aussian family of state-space models with exact marginal likelihood},
  author={Gamerman, Dani and dos Santos, Thiago Rezende and Franco, Glaura C},
  journal={Journal of Time Series Analysis},
  volume={34},
  number={6},
  pages={625--645},
  year={2013},
  publisher={Wiley Online Library}
}

@article{fruhwirth1994data,
  title={Data augmentation and dynamic linear models},
  author={Fr{\"u}hwirth-Schnatter, Sylvia},
  journal={Journal of Time Series Analysis},
  volume={15},
  number={2},
  pages={183--202},
  year={1994},
  publisher={Wiley Online Library}
}


@article{Shephard1997,
  title={ Likelihood analysis of non-{G}aussian measurement time
series},
  author={Shephard, N. and Pitt, M. K.},
  journal={Biometrika},
    number =3,
    volume=84,
  pages = {653--67},
  year={1997}
}


@inbook{AlexCar,
author = {Schmidt, Alexandra M. and Nobre, Widemberg S.},
publisher = {John Wiley & Sons, Ltd},
isbn = {9781118445112},
title = {Conditional Autoregressive (CAR) Model},
booktitle = {Wiley StatsRef: Statistics Reference Online},
chapter = {Conditional Autoregressive (CAR) Model},
pages = {1-11},
doi = {https://doi.org/10.1002/9781118445112.stat08048},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118445112.stat08048},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118445112.stat08048},
year = {2018},
keywords = {areal data level, Bayesian inference, disease mapping, Gaussian Markov random fields, image analysis, lattice data, spatial statistics},
abstract = {Abstract Conditional autoregressive (CAR) models are useful to obtain a multivariate joint distributions of a random vector based on univariate conditional specifications. These conditional specifications are based on Markovian properties such that the conditional distribution of a component of the random vector depends only on a set of neighbors. Conditional autoregressive models are particular cases of Markov random fields. CAR models have been applied in different areas of science; some examples are image analysis, epidemiology, and agriculture. Typically, Gaussian CAR specifications are used as latent structures in hierarchical models for areal level data. In this case, the region of interest is divided into a set of disjoint areas and a CAR random effect is used to account for possible correlation among observations made across the different areas.}
}

  @Article{KFAS,
    title = {{KFAS}: Exponential Family State Space Models in {R}},
    author = {Jouni Helske},
    journal = {Journal of Statistical Software},
    year = {2017},
    volume = {78},
    number = {10},
    pages = {1--39},
    doi = {10.18637/jss.v078.i10}
  }

@Manual{FKF,
  title = {FKF: Fast Kalman Filter},
  author = {David Luethi and Philipp Erb and Simon Otziger and Daniel McDonald and Paul Smith},
  year = {2023},
  note = {https://waternumbers.github.io/FKF/, https://github.com/waternumbers/FKF}
}

@Manual{bsts,
    title = {bsts: Bayesian Structural Time Series},
    author = {Steven L. Scott},
    year = {2024},
    note = {R package version 0.9.10},
    url = {https://CRAN.R-project.org/package=bsts}
}
@Manual{rjags,
    title = {Bayesian Graphical Models using MCMC
},
    author = {Martyn Plummer and Alexey Stukalov and Matt Denwood},
    year = {2024},
    note = {R package version 4-15},
    url = {https://CRAN.R-project.org/package=rjags}
}

@Manual{RINLA,
    title = {R-INLA: The R-INLA package for approximate Bayesian inference using integrated nested Laplace approximation},
    author = {Havard Rue and Sara Martino and Finn Lindgren},
    year = {2024},
    note = {R package version 24.02.09},
    url = {http://www.r-inla.org}
}

@Book{banerjee2014hierarchical,
  title={Hierarchical modeling and analysis for spatial data},
  author={Banerjee, Sudipto and Carlin, Bradley P and Gelfand, Alan E},
  year={2014},
  publisher={Chapman and Hall/CRC}
}

@InCollection{ameen1985normal,
  author = {J.R.M. Ameen and P.J. Harrison},
  title = {Normal discount Bayesian models},
  booktitle = {Bayesian Statistics 2},
  publisher = {North-Holland, Amsterdam, and Valencia University Press},
  year = {1985},
  editor = {J.M. Bernardo and M.H. DeGroot and D.V. Lindley and A.F.M. Smith}
}

@InCollection{ameen1985discount,
  author = {J.R.M. Ameen and P.J. Harrison},
  title = {Discount Bayesian multiprocess modelling with cusums},
  booktitle = {Time Series Analysis: Theory and Practice 5},
  publisher = {North-Holland, Amsterdam},
  year = {1985},
  editor = {O.D. Anderson}
}

@article{AlexMP,
author = {Alexandra M. Schmidt and Laís P. Freitas and Oswaldo G. Cruz and Marilia S. Carvalho},
title ={A Poisson-multinomial spatial model for simultaneous outbreaks with application to arboviral diseases},
journal = {Statistical Methods in Medical Research},
volume = {31},
number = {8},
pages = {1590-1602},
year = {2022},
doi = {10.1177/09622802221102628},
    note ={PMID: 35658776},
URL = { https://doi.org/10.1177/09622802221102628},
eprint = {https://doi.org/10.1177/09622802221102628},
    abstract = { Dengue, Zika, and chikungunya are arboviral diseases (AVD) transmitted mainly by Aedes aegypti. Rio de Janeiro city, Brazil, has been endemic for dengue for over 30 years, and experienced the first joint epidemic of the three diseases between 2015-2016. They present similar symptoms and only a small proportion of cases are laboratory-confirmed. These facts lead to potential misdiagnosis and, consequently, uncertainty in the registration of the cases. We have available the number of cases of each disease for the n=160 neighborhoods of Rio de Janeiro. We propose a Poisson model for the total number of cases of Aedes-borne diseases and, conditioned on the total, we assume a multinomial model for the allocation of the number of cases of each of the diseases across the neighborhoods. This provides simultaneously the estimation of the associations of the relative risk of the total cases of AVD with environmental and socioeconomic variables; and the estimation of the probability of presence of each disease as a function of available covariates. Our findings suggest that a one standard deviation increase in the social development index decreases the relative risk of the total cases of AVD by 28\%. Neighborhoods with smaller proportion of green area had greater odds of having chikungunya in comparison to dengue and Zika. A one standard deviation increase in population density decreases the odds of a neighborhood having Zika instead of dengue by 18\% but increases the odds of chikungunya in comparison to dengue by 18\% and by 43\% in comparison to Zika. }
}


@misc{datasus_data,
  title = {{DATASUS} - Department of Informatics of the Unified Health System},
  howpublished = {\url{http://datasus.saude.gov.br}},
  note = {Accessed: June 9, 2023},
  year = {2023},
  author = {{Ministry of Health, Brazil}}
}

 @article{covid_reduc,  title={Impact of the COVID-19 pandemic on hospital admissions for cardiovascular diseases in a large Brazilian urban center},  volume={55},  ISSN={0037-8682},  url={https://doi.org/10.1590/0037-8682-0264-2021},  DOI={10.1590/0037-8682-0264-2021},  journal={Revista da Sociedade Brasileira de Medicina Tropical},  publisher={Sociedade Brasileira de Medicina Tropical - SBMT},  author={Ribeiro, Edmar Geraldo and Pinheiro, Pedro Cisalpino and Nascimento, Bruno Ramos and Cacique, João Pedro Pereira and Teixeira, Renato Azeredo and Nascimento, Jamil de Souza and Franco, Tulio Batista and Brant, Luisa Campos Caldeira and Malta, Deborah Carvalho},  year={2022},  pages={e0264–2021} }

@article{sari2021handling,
  title={The handling of overdispersion on Poisson regression model with the generalized Poisson regression model},
  author={Saputro, Dewi Retno Sari and Susanti, Ade and Pratiwi, Nafisa Berliana Indah},
  journal={AIP Conference Proceedings},
  volume={2326},
  number={1},
  pages={020026},
  year={2021},
  publisher={AIP Publishing},
  doi={10.1063/5.0040330}
}

 @article{cargnoni1997bayesian,
  title={Bayesian forecasting of multinomial time series through conditionally {G}aussian dynamic models},
  author={Cargnoni, Claudia and M{\"u}ller, Peter and West, Mike},
  journal={Journal of the American Statistical Association},
  volume={92},
  number={438},
  pages={640--647},
  year={1997},
  publisher={Taylor \& Francis}
}

@article{souza2016extended,
  title={Extended Dynamic Generalized Linear Models: {T}he two-parameter exponential family},
  author={Souza, Mariana Albi   Oliveira and Migon, Helio  S. and Pereira, JBM},
  journal={Computational Statistics \& Data Analysis},
  year={2016},
  volume={121},
  pages={164--179},
  publisher={Elsevier}
}


@article{Alves2010,
  title={Transfer functions in dynamic generalized linear models},
  author={Mariane B. Alves and Dani Gamerman and Marco A. R. Ferreira},
  journal={Statistical Modelling},
  year={2010},
  volume={10},
  pages={03 - 40}
}

@article{Migon2013,
  title={ An efficient sampling scheme for dynamic generalized models},
  author={Helio S. Migon and Alexandra M. Schmidt and Romy E. R. Ravines and João B. M. Pereira },
  journal={Computational Statistics},
  year={2013},
  volume={28},
  pages={2267 - 2293}
}

@InCollection{Migon2005,
title = "Dynamic Models",
author = "Migon, {Helio S.} and Dani Gamerman and Lopes, {Hedibert F.} and Ferreira, {Marco A.R.}",
year = "2005",
doi = "10.1016/S0169-7161(05)25019-8",
language = "English (US)",
isbn = "9780444515391",
series = "Handbook of Statistics",
pages = "553--588",
editor = "D.K. Dey and C.R. Rao",
publisher={Elsevier B.V.},
booktitle = "Bayesian Thinking Modeling and Computation",
}

@book{gamerman2006markov,
  title={Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition},
  author={Gamerman, D. and Lopes, H.F.},
  isbn={9781584885870},
  lccn={2006044491},
  series={Chapman \& Hall/CRC Texts in Statistical Science},
  url={https://books.google.com.br/books?id=yPvECi_L3bwC},
  year={2006},
  publisher={Taylor \& Francis}
}


@article{Abanto2012,
  author =       {Abanto-Valle, C. A.  and Migon H. S. and Lachos, V. H.},
  title =        {Stochastic volatility in mean models with
heavy-tailed distributions},
  journal =      {Brazilian Journal of Probability and Statistics},
year={2012},
  volume =       {26},
  number =       {4},
  pages =        {402 - 422}
}

@InCollection{chib2009mult,
author={Chib, Siddhartha
and Omori, Yasuhiro
and Asai, Manabu},
editor={Mikosch, Thomas
and Krei{\ss}, Jens-Peter
and Davis, Richard A.
and Andersen, Torben Gustav},
title={Multivariate Stochastic Volatility},
bookTitle={Handbook of Financial Time Series},
year={2009},
publisher={Springer Berlin Heidelberg},
address={Berlin, Heidelberg},
crossref =     {Mikosch2009},
pages={365--400},
isbn={978-3-540-71297-8},
doi={10.1007/978-3-540-71297-8_16},
url={https://doi.org/10.1007/978-3-540-71297-8_16}
}

@article{smith1979generalization,
  title={A generalization of the {B}ayesian steady forecasting model},
  author={Smith, JQ},
  journal={Journal of the Royal Statistical Society. Series B (Methodological)},
  volume={41},
  pages={375--387},
  year={1979},
  publisher={JSTOR}
}

@article{harvey1989time,
  title={Time series models for count or qualitative observations},
  author={Harvey, Andrew C  and Fernandes, Clara},
  journal={Journal of Business \& Economic Statistics},
  volume={7},
  number={4},
  pages={407--417},
  year={1989},
  publisher={Taylor \& Francis Group}
}

@article{grunwald1993time,
  title={Time series of continuous proportions},
  author={Grunwald, Gary K and Raftery, Adrian E and Guttorp, Peter},
  journal={Journal of the Royal Statistical Society: Series B (Methodological)},
  volume={55},
  number={1},
  pages={103--116},
  year={1993},
  publisher={Wiley Online Library}
}

@book{bernardo2001bayesian,
  title={Bayesian Theory},
  author={Bernardo, Jos{\'e} M and Smith, Adrian FM},
  volume={405},
  year={2009},
  publisher={John Wiley \& Sons}
}

@article{berry2020bayesian,
  title={Bayesian forecasting of many count-valued time series},
  author={Berry, Lindsay R and West, Mike},
  journal={Journal of Business \& Economic Statistics},
  volume={38},
  number={4},
  pages={872--887},
  year={2020},
  publisher={Taylor \& Francis}
}

@article{Terui2010,
  author={Terui, Nobuhiko and Ban, Masataka  and Maki, Toshihiko },
  title={{Finding market structure by sales count dynamics—Multivariate structural time series models with hierarchical structure for count data.}},
  journal={Annals of the Institute of Statistical Mathematics},
  year=2010,
  volume={62},
  number={1},
  pages={ 91-107}
  }

@article{santos2021,
  title={NGSSEML: Non-{G}aussian state space with exact marginal likelihood},
  author={Santos, T. R. and Franco, G. C. and Gamerman, D.},
  journal={R Journal},
  pages={111},
  volume={13},
  year={2021}
}

@article{plumber,
    title = {CODA: Convergence Diagnosis and Output Analysis for MCMC},
    author = {Martyn Plummer and Nicky Best and Kate Cowles and Karen Vines},
    journal = {R News},
    year = {2006},
    volume = {6},
    number = {1},
    pages = {7--11},
    url = {https://journal.r-project.org/archive/},
    pdf = {https://www.r-project.org/doc/Rnews/Rnews_2006-1.pdf},
  }

@article{smith1986non,
  title={A non-{G}aussian state space model e application to prediction of records},
  author={Smith, RL and Miller, JE},
  journal={Journal of the Royal Statistical Society. Series B (Methodological)},
  volume={48(1)},
  pages={79--88},
  year={1986},
  publisher={JSTOR}
}

@article{ambrosini2012,
  title={\it {I}mpacto da vacinação de rotavírus no {B}rasil},
  author={Ambrosini, Veronica A and Carraro, Emerson},
  journal={ Revista
Medicina Ribeirão Preto (Methodological Revision)},
 volume=45,
  number = 4,
  pages={411--18},
  year={2012}
}

@Book{Mikosch2009,
title =        {Handbook of Financial Time Series},
year =         {2009},
editor =       {Mikosch, Thomas
and Krei{\ss}, Jens-Peter
and Davis, Richard A.
and Andersen, Torben Gustav},
publisher =    {Springer},
location =     {Berlin Heidelberg}
}

@article{Linhares2013,
  title={Rotavirus vaccination in Brazil: effectiveness and health impact seven years post-introduction},
  author={Linhares, Alexandre C. and Justino, Cleonice A.},
  journal={Expert Rev Vaccines},
  volume=13,
  number = 1,
  pages = {43--57},
  year={2013}
}

@article{DuttaChiranjit2024Mmpt,
issn = {1524-1904},
abstract = {Abstract In this article, we describe fast Bayesian statistical analysis of vector positive‐valued time series, with application to interesting financial data streams. We discuss a flexible level correlated model (LCM) framework for building hierarchical models for vector positive‐valued time series. The LCM allows us to combine marginal gamma distributions for the positive‐valued component responses, while accounting for association among the components at a latent level. We introduce vector autoregression evolution of the latent states, deriving its precision matrix and enabling its estimation using integrated nested Laplace approximation (INLA) for fast approximate Bayesian modeling via the R‐INLA package, building custom functions to handle this setup. We use the proposed method to model interdependencies between intraday volatility measures from several stock indexes.},
journal = {Applied stochastic models in business and industry},
year = {2024},
title = {Modeling multivariate positive‐valued time series using R‐INLA},
language = {eng},
author = {Dutta, Chiranjit and Ravishanker, Nalini and Basu, Sumanta},
}

@misc{Copernicus_co2,
  author = {{Directorate Space, Security and Migration, European Commission Joint Research Centre}},
  shortauthor  = {{EC JRC}},
  title = {Copernicus Emergency Management Service},
  year = {2024},
  howpublished = {\url{https://emergency.copernicus.eu/}},
  note = {Accessed: April 9, 2024}
}


@misc{ibge_amazon,
  author = {Instituto Brasileiro de Geografia e Estatística},
  shortauthor = {IBGE},
  title = {Legal Amazon},
  year = {2022},
  howpublished = {\url{https://www.ibge.gov.br/en/geosciences/environmental-information/geomorphology/17927-legal-amazon.html?=&t=sobre/}},
  note = {Accessed: April 9, 2024}
}

@article{Monique2023CiCD,
issn = {2072-4292},
abstract = {The Amazon region comprises the largest tropical forest on the planet and is responsible for absorbing huge amounts of CO2 from the atmosphere. However, changes in land use and cover have contributed to an increase in greenhouse gas emissions, especially CO2, and in endangered indigenous lands and protected areas in the region. The objective of this study was to detect changes in CO2 emissions and removals associated with land use and land cover changes in the Brazilian Legal Amazon (BLA) through the analysis of multispectral satellite images from 2009 to 2019. The Gross Primary Production (GPP) and CO2Flux variables were estimated by the MODIS sensor onboard Terra and Aqua satellite, representing carbon absorption by vegetation during the photosynthesis process. Atmospheric CO2 concentration was estimated from the GOSAT satellite. The variables GPP and CO2Flux showed the effective flux of carbon in the BLA to atmosphere, which were weakly correlated with precipitation (r = 0.191 and 0.133). The forest absorbed 211.05 TgC annually but, due to its partial conversion to other land uses, the loss of 135,922.34 km2 of forest area resulted in 5.82 TgC less carbon being absorbed. Pasture and agriculture, which comprise the main land conversions, increased by 100,340.39 km2 and absorbed 1.32 and 3.19 TgC less, and emitted close to twice more, than forest in these areas. Atmospheric CO2 concentrations increased from 2.2 to 2.8 ppm annually in BLA, with hotspots observed in the southeast Amazonia, and CO2 capture by GPP showed an increase over the years, mainly after 2013, in the north and west of the BLA. This study brings to light the carbon dynamics, by GPP and CO2Flux models, as related to the land use and land cover in one of the biggest world carbon reservoirs, the Amazon, which is also important to fulfillment of international agreements signed by Brazil to reduce greenhouse gas emissions and for biodiversity conservation and other ecosystem services in the region.},
journal = {Remote sensing (Basel, Switzerland)},
pages = {2780},
volume = {15},
publisher = {MDPI AG},
number = {11},
year = {2023},
title = {Changes in Carbon Dioxide Balance Associated with Land Use and Land Cover in Brazilian Legal Amazon Based on Remotely Sensed Imagery},
copyright = {COPYRIGHT 2023 MDPI AG},
language = {eng},
address = {Basel},
author = {Crivelari-Costa, Patrícia Monique and Lima, Mendelson and La Scala Jr, Newton and Rossi, Fernando Saragosa and Della-Silva, João Lucas and Dalagnol, Ricardo and Teodoro, Paulo Eduardo and Teodoro, Larissa Pereira Ribeiro and Oliveira, Gabriel de and Junior, José Francisco de Oliveira and Silva Junior, Carlos Antonio da},
keywords = {Absorption ; Air pollution ; Atmosphere ; Atmospheric models ; Biodiversity ; Biological diversity conservation ; Brazil ; Carbon dioxide ; Carbon dioxide concentration ; Carbon dioxide emissions ; carbon dioxide flux ; Carbon sequestration ; Change detection ; Climate change ; Deforestation ; Ecosystem services ; Ecosystems ; Emissions ; Emissions control ; Farm buildings ; Global temperature changes ; google earth engine ; GOSAT ; Greenhouse effect ; Greenhouse gases ; gross primary production ; International agreements ; Land cover ; Land use ; Laws regulations and rules ; MODIS ; Pasture ; Photosynthesis ; Primary production ; Protected areas ; Protection and preservation ; Remote sensing ; Satellite imagery ; Tropical forests ; Wildlife conservation},
}

@article{CaetanoMarcoAntonioLeonel2011opft,
issn = {0304-3800},
abstract = {The Brazilian government has already acknowledged the importance of investing in the development and application of technologies to reduce or prevent CO₂ emissions resulting from human activities in the Legal Brazilian Amazon (BA). The BA corresponds to a total area of 5×10⁶km² from which 4×10⁶km² was originally covered by the rain forest. One way to interfere with the net balance of greenhouse gases (GHG) emissions is to increase the forest area to sequester CO₂ from the atmosphere. The single most important cause of depletion of the rain forest is cattle ranching. In this work, we present an effective policy to reduce the net balance of CO₂ emissions using optimal control theory to obtain a compromising partition of investments in reforestation and promotion of clear technology to achieve a CO₂ emission target for 2020. The simulation indicates that a CO₂ emission target for 2020 of 376 million tonnes requires an estimated forest area by 2020 of 3,708,000km², demanding a reforestation of 454,037km². Even though the regional economic growth can foster the necessary political environment for the commitment with optimal emission targets, the reduction of 38.9% of carbon emissions until 2020 proposed by Brazilian government seems too ambitious.},
journal = {Ecological modelling},
pages = {2835--2840},
volume = {222},
publisher = {Elsevier B.V},
number = {15},
year = {2011},
title = {optimized policy for the reduction of CO₂ emission in the Brazilian Legal Amazon},
copyright = {2015 INIST-CNRS},
language = {eng},
address = {AMSTERDAM},
author = {Caetano, Marco Antonio Leonel and Gherardi, Douglas Francisco Marcolino and Yoneyama, Takashi},
keywords = {Animal plant and microbial ecology ; atmosphere ; Biological and medical sciences ; carbon ; carbon dioxide ; cattle ; Ecology ; economic development ; emissions ; Environmental Sciences & Ecology ; Forestry ; Fundamental and applied biological sciences. Psychology ; General aspects. Techniques ; General forest ecology ; Generalities. Production biomass. Quality of wood and forest products. General forest ecology ; greenhouse gases ; issues and policy ; Life Sciences & Biomedicine ; Methods and techniques (sampling tagging trapping modelling...) ; rain forests ; ranching ; reforestation ; Science & Technology},
}

@article{Galvao2011,
author = {Galvao Jr., Antonio F. and Montes-Rojas, Gabriel and Olmo, Jose},
title = {Threshold quantile autoregressive models},
journal = {Journal of Time Series Analysis},
volume = {32},
number = {3},
pages = {253-267},
keywords = {Nonlinear models, quantile regression, threshold models, C14, C22, C32, C50},
doi = {https://doi.org/10.1111/j.1467-9892.2010.00696.x},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9892.2010.00696.x},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467-9892.2010.00696.x},
abstract = {This article studies estimation and asymptotic properties of Threshold Quantile Autoregressive processes. In particular, we show the consistency of the threshold and slope parameter estimators for each quantile and regime, and derive the asymptotic normality of the slope parameter estimators. A Monte Carlo experiment shows that the standard ordinary least squares estimation method is not able to detect important nonlinearities produced in the quantile process. The empirical study concentrates on modelling the dynamics of the conditional distribution of unemployment growth after the second world war. The results show evidence of important heterogeneity associated with unemployment and strong asymmetric persistence of unemployment growth in the higher quantiles.},
year = {2011}
}

@article{ChavasJean-Paul2016Hsem,
issn = {0167-2681},
abstract = {Economists modeling climate policy face an array of choices when modeling climate change, including the role of uncertainty/ambiguity, irreversibility, and tipping points. After filtering out estimated cycles due to orbital climate forcing, we use a threshold quantile autoregressive model to characterize anomalies in atmospheric CO2 concentrations. We then test for local instability and tipping points, and we characterize the stationary distribution of anomalies. We find evidence of nonlinear dynamics, tipping points and a non-normal stationary distribution.},
journal = {Journal of economic behavior & organization},
pages = {56--65},
volume = {132},
publisher = {Elsevier B.V},
number = {B},
year = {2016},
title = {How should economists model climate? Tipping points and nonlinear dynamics of carbon dioxide concentrations},
copyright = {2016 Elsevier B.V.},
language = {eng},
address = {AMSTERDAM},
author = {Chavas, Jean-Paul and Grainger, Corbett and Hudson, Nicholas},
keywords = {Business & Economics ; Climate change ; Economics ; Nonlinear dynamics ; Social Sciences ; Threshold quantile autoregression ; Tipping points},
}
@INPROCEEDINGS{Unscented,
  author={Wan, E.A. and Van Der Merwe, R.},
  booktitle={Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373)},
  title={The unscented Kalman filter for nonlinear estimation},
  year={2000},
  volume={},
  number={},
  pages={153-158},
  keywords={Nonlinear systems;Random variables;Nonlinear dynamical systems;Filters;Sampling methods;Taylor series;Computational complexity;Performance gain;Machine learning;Neural networks},
  doi={10.1109/ASSPCC.2000.882463}}

@misc{yang2013sequential,
      title={Sequential Markov Chain Monte Carlo},
      author={Yun Yang and David B. Dunson},
      year={2013},
      eprint={1308.3861},
      archivePrefix={arXiv},
      primaryClass={math.ST}
}

@inbook{particle,
  author    = {Hedibert Freitas Lopes and Carlos M. Carvalho},
  title     = {Online Bayesian learning in dynamic models: An illustrative introduction to particle methods},
    publisher = {Oxford University Press},
    year = {2013},
  editor    = {Damien, Paul and Dellaportas, Petros and Polson, Nicholas G. and Stephens, David A.},
  chapter   = {11},
  edition   = {First edition},
    url = {https://repositorio.insper.edu.br/entities/publication/c9982d3d-62d7-4931-8b87-ed66dab68363}
}

@book{moragaSpat,
title = "Spatial Statistics for Data Science: Theory and Practice with R",
abstract = "Spatial data is crucial to improve decision-making in a wide range of fields including environment, health, ecology, urban planning, economy, and society. Spatial Statistics for Data Science: Theory and Practice with R describes statistical methods, modeling approaches, and visualization techniques to analyze spatial data using R. The book provides a comprehensive overview of the varying types of spatial data, and detailed explanations of the theoretical concepts of spatial statistics, alongside fully reproducible examples which demonstrate how to simulate, describe, and analyze spatial data in various applications. Combining theory and practice, the book includes real-world data science examples such as disease risk mapping, air pollution prediction, species distribution modeling, crime mapping, and real state analyses. The book utilizes publicly available data and offers clear explanations of the R code for importing, manipulating, analyzing, and visualizing data, as well as the interpretation of the results. This ensures contents are easily accessible and fully reproducible for students, researchers, and practitioners. Key Features: Describes R packages for retrieval, manipulation, and visualization of spatial data. Offers a comprehensive overview of spatial statistical methods including spatial autocorrelation, clustering, spatial interpolation, model-based geostatistics, and spatial point processes. Provides detailed explanations on how to fit and interpret Bayesian spatial models using the integrated nested Laplace approximation (INLA) and stochastic partial differential equation (SPDE) approaches.",
author = "Paula Moraga",
note = "Publisher Copyright: {\textcopyright} Paula Moraga.",
year = "2023",
month = jan,
day = "1",
doi = "10.1201/9781032641522",
language = "English (US)",
isbn = "9781032633510",
publisher = "CRC Press",
}

@article{infinite_log_normal,
author = {Olof Thorin},
title = {On the infinite divisibility of the lognormal distribution},
journal = {Scandinavian Actuarial Journal},
volume = {1977},
number = {3},
pages = {121--148},
year = {1977},
publisher = {Taylor \& Francis},
doi = {10.1080/03461238.1977.10405635},
URL = { https://doi.org/10.1080/03461238.1977.10405635
},
eprint = { https://doi.org/10.1080/03461238.1977.10405635
}
}

@book{box2015time,
  title={Time Series Analysis: Forecasting and Control},
  author={Box, G.E.P. and Jenkins, G.M. and Reinsel, G.C. and Ljung, G.M.},
  isbn={9781118674925},
  lccn={2015016616},
  series={Wiley Series in Probability and Statistics},
  url={https://books.google.com.br/books?id=rNt5CgAAQBAJ},
  year={2015},
  publisher={Wiley}
}

@article{HarrisonVeerapen1994,
author = {Harrison, P. J. and Veerapen, P. P.},
title = {A bayesian decision approach to model monitoring and cusums},
journal = {Journal of Forecasting},
volume = {13},
number = {1},
pages = {29-36},
keywords = {Bayes, Cusums, Decisions, Dynamic models, Exponential family, Forecasting, Monitoring, Quality control, Sequential tests},
doi = {https://doi.org/10.1002/for.3980130105},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/for.3980130105},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/for.3980130105},
abstract = {Abstract Cumulative Sum techniques are widely used in quality control and model monitoring. A single-sided cusum may be regarded essentially as a sequence of sequential tests which, in many cases, such as those for the Exponential Family, is equivalent to a Sequence of Sequential Probability Ratio Tests. The relationship between cusums and Bayesian decisions is difficult to establish using conventional methods. An alternative approach is proposed which not only reveals a relation but also offers a very simple formulation of the decision process involved in model monitoring. This is first illustrated for a Normal mean and then extended to other important practical cases including Dynamic Models. For V-mask cusum graphs a particular feature is the interpretation of the distance of the V vertex from the latest plotted point in terms of the prior precision as measured in ‘equivalent’ observations.},
year = {1994}
}

@article{Harrison1999,
author = {P. J. Harrison},
title = {Statistical process control and model monitoring},
journal = {Journal of Applied Statistics},
volume = {26},
number = {2},
pages = {273--292},
year = {1999},
publisher = {Taylor \& Francis},
doi = {10.1080/02664769922601},
URL = {
        https://doi.org/10.1080/02664769922601
},
eprint = {
        https://doi.org/10.1080/02664769922601
}
}





@InProceedings{Naesseth2018,
  title = 	 {Variational Sequential Monte Carlo},
  author = 	 {Naesseth, Christian and Linderman, Scott and Ranganath, Rajesh and Blei, David},
  booktitle = 	 {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics},
  pages = 	 {968--977},
  year = 	 {2018},
  editor = 	 {Storkey, Amos and Perez-Cruz, Fernando},
  volume = 	 {84},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {09--11 Apr},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v84/naesseth18a/naesseth18a.pdf},
  url = 	 {https://proceedings.mlr.press/v84/naesseth18a.html},
  abstract = 	 {Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to find the member of this family that most closely approximates the exact posterior. In this paper we present a new approximating family of distributions, the variational sequential Monte Carlo (VSMC) family, and show how to optimize it in variational inference. VSMC melds variational inference (VI) and sequential Monte Carlo (SMC), providing practitioners with flexible, accurate, and powerful Bayesian inference. The VSMC family is a variational family that can approximate the posterior arbitrarily well, while still allowing for efficient optimization of its parameters. We demonstrate its utility on state space models, stochastic volatility models for financial data, and deep Markov models of brain neural circuits.}
}

@inproceedings{JohnsonWillsky2014,
author = {Johnson, Matthew James and Willsky, Alan S.},
title = {Stochastic variational inference for Bayesian time series models},
year = {2014},
publisher = {JMLR.org},
abstract = {Bayesian models provide powerful tools for analyzing complex time series data, but performing inference with large datasets is a challenge. Stochastic variational inference (SVI) provides a new framework for approximating model posteriors with only a small number of passes through the data, enabling such models to be fit at scale. However, its application to time series models has not been studied.In this paper we develop SVI algorithms for several common Bayesian time series models, namely the hidden Markov model (HMM), hidden semi-Markov model (HSMM), and the non-parametric HDP-HMM and HDP-HSMM. In addition, because HSMM inference can be expensive even in the minibatch setting of SVI, we develop fast approximate updates for HSMMs with durations distributions that are negative binomials or mixtures of negative binomials.},
booktitle = {Proceedings of the 31st International Conference on International Conference on Machine Learning - Volume 32},
pages = {II–1854–II–1862},
location = {Beijing, China},
series = {ICML'14}
}

@ARTICLE{ZhangBütepageKjellströmMandt2019,
  author={Zhang, Cheng and Bütepage, Judith and Kjellström, Hedvig and Mandt, Stephan},
  journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
  title={Advances in Variational Inference},
  year={2019},
  volume={41},
  number={8},
  pages={2008-2026},
  keywords={Bayes methods;Hidden Markov models;Computational modeling;Optimization;Probabilistic logic;Stochastic processes;Market research;Variational inference;approximate Bayesian inference;reparameterization gradients;structured variational approximations;scalable inference;inference networks},
  doi={10.1109/TPAMI.2018.2889774}}

@article{LingHuiFox2016Tfbv,
issn = {1469-7688},
abstract = {Methods developed for making time-varying forecasts in economic and financial analysis include (a) equal-weighted moving-window (or rolling) regression, (b) time-weighted (e.g. exponentially weighted) regression, (c) the Kalman filter (KF) and (d) adaptive Kalman filters. This paper developed a new method based on variational approximation of sequential Bayesian inference (VASB). Concepts and notions of the sequential Bayesian analysis and the variational approximation of an intractable posterior are simple and straightforward. Our VASB algorithm is not complicated and is easy to code. For a regression on multiple time-series, the regression coefficients, standard errors, prediction and residual error are time-varying and are estimated jointly at every time step. For a single time-series (e.g. price returns of an asset), its mean and variance are time-varying and are predicted jointly at every time step. The VASB algorithm performs better than the rolling and time-weighted statistics or regressions and the KF in terms of higher predictive power and stronger robustness. Derivations of the VASB algorithm are presented in the appendices.},
journal = {Quantitative finance},
pages = {43--67},
volume = {16},
publisher = {Routledge},
number = {1},
year = {2016},
title = {Time-varying forecasts by variational approximation of sequential Bayesian inference},
copyright = {2015 Taylor & Francis 2015},
language = {eng},
address = {Bristol},
author = {Ling, Hui 'Fox' and Stone, Douglas B.},
keywords = {Algorithms ; Approximation ; Bayesian analysis ; Bayesian filtering ; Economic forecasts ; Financial analysis ; Kalman filter ; Kalman filters ; Sequential Bayesian inference ; State space modelling of time-series ; Studies ; Time-varying forecasts ; Time-varying regression ; Time-varying variance ; Variational Bayes},
}

@article{TomasettiNathaniel2022UVBf,
issn = {0960-3174},
abstract = {Variational Bayesian (VB) methods produce posterior inference in a time frame considerably smaller than traditional Markov Chain Monte Carlo approaches. Although the VB posterior is an approximation, it has been shown to produce good parameter estimates and predicted values when a rich classes of approximating distributions are considered. In this paper, we propose the use of recursive algorithms to update a sequence of VB posterior approximations in an online, time series setting, with the computation of each posterior update requiring only the data observed since the previous update. We show how importance sampling can be incorporated into online variational inference allowing the user to trade accuracy for a substantial increase in computational speed. The proposed methods and their properties are detailed in two separate simulation studies. Additionally, two empirical illustrations are provided, including one where a Dirichlet Process Mixture model with a novel posterior dependence structure is repeatedly updated in the context of predicting the future behaviour of vehicles on a stretch of the US Highway 101.},
journal = {Statistics and computing},
volume = {32},
publisher = {Springer US},
number = {1},
year = {2022},
title = {Updating Variational Bayes: fast sequential posterior inference},
copyright = {The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021},
language = {eng},
address = {New York},
author = {Tomasetti, Nathaniel and Forbes, Catherine and Panagiotelis, Anastasios},
keywords = {Algorithms ; Approximation ; Artificial Intelligence ; Computer Science ; Dirichlet problem ; Importance sampling ; Inference ; Markov chains ; Parameter estimation ; Probability and Statistics in Computer Science ; Production methods ; Statistical Theory and Methods ; Statistics and Computing/Statistics Programs},
}

