Shemyakin A., Kniazev A. Introduction to Bayesian Estimation and Copula Models of Dependence

John Wiley & Sons, Inc., USA, 2017. — 336 p. — ISBN: 1118959019.Presents an introduction to Bayesian statistics, presents an emphasis on Bayesian methods (prior and posterior), Bayes estimation, prediction, MCMC, Bayesian regression, and Bayesian analysis of statistical models of dependence, and features a focus on copulas for risk management.
Introduction to Bayesian Estimation and Copula Models of Dependence emphasizes the applications of Bayesian analysis to copula modeling and equips readers with the tools needed to implement the procedures of Bayesian estimation in copula models of dependence. This book is structured in two parts: the first four chapters serve as a general introduction to Bayesian statistics with a clear emphasis on parametric estimation and the following four chapters stress statistical models of dependence with a focus of copulas.
A review of the main concepts is discussed along with the basics of Bayesian statistics including prior information and experimental data, prior and posterior distributions, with an emphasis on Bayesian parametric estimation. The basic mathematical background of both Markov chains and Monte Carlo integration and simulation is also provided. The authors discuss statistical models of dependence with a focus on copulas and present a brief survey of pre-copula dependence models. The main definitions and notations of copula models are summarized followed by discussions of real-world cases that address particular risk management problems.Bayesian Estimation
Random Variables and Distributions
Foundations of Bayesian Analysis
Background for Markov Chain Monte Carlo
Markov Chain Monte Carlo Methods
Modeling Dependence
Statistical Dependence Structures
Copula Models of Dependence
Statistics of Copulas
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