Bayesian Inference of State Space Models
Bayesian Inference of State Space Models

Author: Kostas Triantafyllopoulos

Publisher: Springer Nature

Published: 2021-11-12

Total Pages: 503

ISBN-13: 303076124X

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Bayesian Inference of State Space Models: Kalman Filtering and Beyond offers a comprehensive introduction to Bayesian estimation and forecasting for state space models. The celebrated Kalman filter, with its numerous extensions, takes centre stage in the book. Univariate and multivariate models, linear Gaussian, non-linear and non-Gaussian models are discussed with applications to signal processing, environmetrics, economics and systems engineering. Over the past years there has been a growing literature on Bayesian inference of state space models, focusing on multivariate models as well as on non-linear and non-Gaussian models. The availability of time series data in many fields of science and industry on the one hand, and the development of low-cost computational capabilities on the other, have resulted in a wealth of statistical methods aimed at parameter estimation and forecasting. This book brings together many of these methods, presenting an accessible and comprehensive introduction to state space models. A number of data sets from different disciplines are used to illustrate the methods and show how they are applied in practice. The R package BTSA, created for the book, includes many of the algorithms and examples presented. The book is essentially self-contained and includes a chapter summarising the prerequisites in undergraduate linear algebra, probability and statistics. An up-to-date and complete account of state space methods, illustrated by real-life data sets and R code, this textbook will appeal to a wide range of students and scientists, notably in the disciplines of statistics, systems engineering, signal processing, data science, finance and econometrics. With numerous exercises in each chapter, and prerequisite knowledge conveniently recalled, it is suitable for upper undergraduate and graduate courses.

Beyesian Semiparametric Models for Discrete Longitudinal Data
Beyesian Semiparametric Models for Discrete Longitudinal Data

Author: Sylvie Tchumtchoua

Publisher:

Published: 2010

Total Pages:

ISBN-13:

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Discrete longitudinal data are common in various disciplines and are often used to assess the change over time of one or several outcomes, and/or what covariates might be associated with the outcomes. Existing parametric and nonparametric/semiparametric models typically attribute the heterogeneity across subjects and/or through time to the effects of included explanatory variables or the effect of omitted variables that do not vary across subjects and over time. This dissertation focuses on developing new flexible semiparametric models for discrete longitudinal data using Dirichlet processes. It consists of three parts. In chapter 2 we propose a semiparametric Bayesian framework for the analysis of associations among multivariate longitudinal categorical variables in high-dimensional data settings. This type of data is frequent, especially in the social and behavioral sciences. A semiparametric hierarchical factor analysis model is developed in which the distributions of the factors are modeled nonparametrically through a dynamic Dirichlet process. A Markov chain Monte Carlo algorithm is developed for fitting the model, and the methodology is applied to study the dynamics of public attitudes toward science and technology in the United States over the period 1992-2001. In chapter 3 we consider the estimation of nonparametric regression for binary longitudinal data. Instead of assuming a parametric link function, we specify the joint distribution of the covariates and the latent variable underlying the binary outcome as a multivariate normal with subject and time-specific mean vector and covariance matrix. We then modeled the distribution of these parameters nonparametrically using a dynamic Dirichlet process. The resulting binary regression model is a finite mixture of probit regressions and a nonlinear regression. The proposed model is more flexible than the existing models in that it models the relationship between the binary response and the covariates nonparametrically while at the same time allowing the shape of the relationship to change over time. The methodology is illustrated using simulated data and a real dataset, the data on labor force participation of married women in the US over the period 1979 to 1992. Finally, chapter 4 proposes two functional generalized linear models where the response variables are discrete functional data and one of the covariates is also functional. Functional regression is combined with penalized B-splines in a semiparametric Bayesian framework to jointly estimate the response model and the predictor curves, clustering curves with similar shapes. The methodology is applied to study the price and bids arrivals dynamics in online auctions using data for the palm M515 Personal Digital Assistant (PDA) units from eBay.com.

Missing Data in Longitudinal Studies
Missing Data in Longitudinal Studies

Author: Michael J. Daniels

Publisher: CRC Press

Published: 2008-03-11

Total Pages: 324

ISBN-13: 1420011189

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Drawing from the authors' own work and from the most recent developments in the field, Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis describes a comprehensive Bayesian approach for drawing inference from incomplete data in longitudinal studies. To illustrate these methods, the authors employ

Bayesian Hierarchical Models
Bayesian Hierarchical Models

Author: Peter D. Congdon

Publisher: CRC Press

Published: 2019-09-16

Total Pages: 506

ISBN-13: 0429532903

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An intermediate-level treatment of Bayesian hierarchical models and their applications, this book demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables, and in methods where parameters can be treated as random collections. Through illustrative data analysis and attention to statistical computing, this book facilitates practical implementation of Bayesian hierarchical methods. The new edition is a revision of the book Applied Bayesian Hierarchical Methods. It maintains a focus on applied modelling and data analysis, but now using entirely R-based Bayesian computing options. It has been updated with a new chapter on regression for causal effects, and one on computing options and strategies. This latter chapter is particularly important, due to recent advances in Bayesian computing and estimation, including the development of rjags and rstan. It also features updates throughout with new examples. The examples exploit and illustrate the broader advantages of the R computing environment, while allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. Features: Provides a comprehensive and accessible overview of applied Bayesian hierarchical modelling Includes many real data examples to illustrate different modelling topics R code (based on rjags, jagsUI, R2OpenBUGS, and rstan) is integrated into the book, emphasizing implementation Software options and coding principles are introduced in new chapter on computing Programs and data sets available on the book’s website

Longitudinal Data Analysis
Longitudinal Data Analysis

Author: Ikuko Funatogawa

Publisher: Springer

Published: 2019-02-04

Total Pages: 141

ISBN-13: 9811000778

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This book provides a new analytical approach for dynamic data repeatedly measured from multiple subjects over time. Random effects account for differences across subjects. Auto-regression in response itself is often used in time series analysis. In longitudinal data analysis, a static mixed effects model is changed into a dynamic one by the introduction of the auto-regression term. Response levels in this model gradually move toward an asymptote or equilibrium which depends on covariates and random effects. The book provides relationships of the autoregressive linear mixed effects models with linear mixed effects models, marginal models, transition models, nonlinear mixed effects models, growth curves, differential equations, and state space representation. State space representation with a modified Kalman filter provides log likelihoods for maximum likelihood estimation, and this representation is suitable for unequally spaced longitudinal data. The extension to multivariate longitudinal data analysis is also provided. Topics in medical fields, such as response-dependent dose modifications, response-dependent dropouts, and randomized controlled trials are discussed. The text is written in plain terms understandable for researchers in other disciplines such as econometrics, sociology, and ecology for the progress of interdisciplinary research.

Basic and Advanced Bayesian Structural Equation Modeling
Basic and Advanced Bayesian Structural Equation Modeling

Author: Sik-Yum Lee

Publisher: John Wiley & Sons

Published: 2012-07-05

Total Pages: 396

ISBN-13: 1118358872

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This book provides clear instructions to researchers on how to apply Structural Equation Models (SEMs) for analyzing the inter relationships between observed and latent variables. Basic and Advanced Bayesian Structural Equation Modeling introduces basic and advanced SEMs for analyzing various kinds of complex data, such as ordered and unordered categorical data, multilevel data, mixture data, longitudinal data, highly non-normal data, as well as some of their combinations. In addition, Bayesian semiparametric SEMs to capture the true distribution of explanatory latent variables are introduced, whilst SEM with a nonparametric structural equation to assess unspecified functional relationships among latent variables are also explored. Statistical methodologies are developed using the Bayesian approach giving reliable results for small samples and allowing the use of prior information leading to better statistical results. Estimates of the parameters and model comparison statistics are obtained via powerful Markov Chain Monte Carlo methods in statistical computing. Introduces the Bayesian approach to SEMs, including discussion on the selection of prior distributions, and data augmentation. Demonstrates how to utilize the recent powerful tools in statistical computing including, but not limited to, the Gibbs sampler, the Metropolis-Hasting algorithm, and path sampling for producing various statistical results such as Bayesian estimates and Bayesian model comparison statistics in the analysis of basic and advanced SEMs. Discusses the Bayes factor, Deviance Information Criterion (DIC), and $L_\nu$-measure for Bayesian model comparison. Introduces a number of important generalizations of SEMs, including multilevel and mixture SEMs, latent curve models and longitudinal SEMs, semiparametric SEMs and those with various types of discrete data, and nonparametric structural equations. Illustrates how to use the freely available software WinBUGS to produce the results. Provides numerous real examples for illustrating the theoretical concepts and computational procedures that are presented throughout the book. Researchers and advanced level students in statistics, biostatistics, public health, business, education, psychology and social science will benefit from this book.