Bayesian Statistical Modeling with Stan, R, and Python

 
Kiadás sorszáma: 1st ed. 2022
Kiadó: Springer
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A termék adatai:

ISBN13:9789811947544
ISBN10:9811947546
Kötéstípus:Keménykötés
Terjedelem:385 oldal
Méret:235x155 mm
Súly:850 g
Nyelv:angol
Illusztrációk: 251 Illustrations, black & white; 10 Illustrations, color
698
Témakör:
Rövid leírás:

This book provides a highly practical introduction to Bayesian statistical modeling with Stan, which has become the most popular probabilistic programming language.

The book is divided into four parts. The first part reviews the theoretical background of modeling and Bayesian inference and presents a modeling workflow that makes modeling more engineering than art. The second part discusses the use of Stan, CmdStanR, and CmdStanPy from the very beginning to basic regression analyses. The third part then introduces a number of probability distributions, nonlinear models, and hierarchical (multilevel) models, which are essential to mastering statistical modeling. It also describes a wide range of frequently used modeling techniques, such as censoring, outliers, missing data, speed-up, and parameter constraints, and discusses how to lead convergence of MCMC. Lastly, the fourth part examines advanced topics for real-world data: longitudinal data analysis, state space models, spatial data analysis, Gaussian processes, Bayesian optimization, dimensionality reduction, model selection, and information criteria, demonstrating that Stan can solve any one of these problems in as little as 30 lines.

Using numerous easy-to-understand examples, the book explains key concepts, which continue to be useful when using future versions of Stan and when using other statistical modeling tools. The examples do not require domain knowledge and can be generalized to many fields. The book presents full explanations of code and math formulas, enabling readers to extend models for their own problems. All the code and data are on GitHub.


Hosszú leírás:

This book provides a highly practical introduction to Bayesian statistical modeling with Stan, which has become the most popular probabilistic programming language.

The book is divided into four parts. The first part reviews the theoretical background of modeling and Bayesian inference and presents a modeling workflow that makes modeling more engineering than art. The second part discusses the use of Stan, CmdStanR, and CmdStanPy from the very beginning to basic regression analyses. The third part then introduces a number of probability distributions, nonlinear models, and hierarchical (multilevel) models, which are essential to mastering statistical modeling. It also describes a wide range of frequently used modeling techniques, such as censoring, outliers, missing data, speed-up, and parameter constraints, and discusses how to lead convergence of MCMC. Lastly, the fourth part examines advanced topics for real-world data: longitudinal data analysis, state space models, spatial data analysis, Gaussian processes, Bayesian optimization, dimensionality reduction, model selection, and information criteria, demonstrating that Stan can solve any one of these problems in as little as 30 lines.

Using numerous easy-to-understand examples, the book explains key concepts, which continue to be useful when using future versions of Stan and when using other statistical modeling tools. The examples do not require domain knowledge and can be generalized to many fields. The book presents full explanations of code and math formulas, enabling readers to extend models for their own problems. All the code and data are on GitHub.


Tartalomjegyzék:
Preface

Part I: Introduction 
Chapter 1: Overview of Statistical Modeling and Stan
Chapter 2: Review of Bayesian Inference
Chapter 3: Before Starting Statistical Modeling

Part II: Introduction of Stan
Chapter 4: Start with Stan, RStan and PyStan
Chapter 5: Elementary Regression and Model Check

Part III: Essential Components and Techniques for Experts
Chapter 6: Introduction of Distributions from Modeling Viewpoints
Chapter 7: Issues of Regression
Chapter 8: Nonlinear Model
Chapter 9: Hierarchical Model
Chapter 10: Advanced Grammars
Chapter 11: How to Lead Convergence
Chapter 12: Discrete Parameters
Chapter 13: Usage of MCMC Samples

Part IV: Advanced  Topics for Real
-world Data
Chapter 14: Longitudinal Data Analysis with State Space Model 
Chapter 15: Spatial Data Analysis with Markov Field Model
Chapter 16: Survival Analysis
Chapter 17: Causal Inference
Chapter 18: Model selection

Appendix: Differences between Stan and BUGS
Reference
Index