Introduction to Bayesian estimation and copula models of dependence

Introduction to Bayesian estimation and copula models of dependence / Arkady Shemyakin, Alexander Kniazev.

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 modelsof dependence, and features a focus on copulas for risk management Introduction to Baye...

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Bibliographic Details
Main Author: Shemyakin, Arkady
Other Authors: Kniazev, Alexander (Mathematician)
Format: eBook
Language:English
Published: Hoboken, New Jersey : John Wiley & Sons, Inc., [2017]
Subjects:
Bayesian statistical decision theory.
Copulas (Mathematical statistics)
MATHEMATICS > Applied.
MATHEMATICS > Probability & Statistics > General.
Bayesian statistical decision theory
Online Access:Click for online access
Table of Contents:
  • Introduction to Bayesian Estimation and Copula Models of Dependence; Contents; List of Figures; List of Tables; Acknowledgments; Acronyms; Glossary; About the Companion Website; Introduction; Part I Bayesian Estimation; 1 Random Variables and Distributions; 1.1 Conditional Probability; 1.2 Discrete Random Variables; 1.3 Continuous Distributions on the Real Line; 1.4 Continuous Distributions with Nonnegative Values; 1.5 Continuous Distributions on a Bounded Interval; 1.6 Joint Distributions; 1.7 Time-Dependent Random Variables; References; 2 Foundations of Bayesian Analysis.
  • 2.1 Education and Wages2.2 Two Envelopes; 2.3 Hypothesis Testing; 2.3.1 The Likelihood Principle; 2.3.2 Review of Classical Procedures; 2.3.3 Bayesian Hypotheses Testing; 2.4 Parametric Estimation; 2.4.1 Review of Classical Procedures; 2.4.2 Maximum Likelihood Estimation; 2.4.3 Bayesian Approach to Parametric Estimation; 2.5 Bayesian and Classical Approaches to Statistics; 2.5.1 Classical (Frequentist) Approach; 2.5.2 Lady Tasting Tea; 2.5.3 Bayes Theorem; 2.5.4 Main Principles of the Bayesian Approach; 2.6 The Choice of the Prior; 2.6.1 Subjective Priors; 2.6.2 Objective Priors.
  • 2.6.3 Empirical Bayes2.7 Conjugate Distributions; 2.7.1 Exponential Family; 2.7.2 Poisson Likelihood; 2.7.3 Table of Conjugate Distributions; References; 3 Background for Markov Chain Monte Carlo; 3.1 Randomization; 3.1.1 Rolling Dice; 3.1.2 Two Envelopes Revisited; 3.2 Random Number Generation; 3.2.1 Pseudo-random Numbers; 3.2.2 Inverse Transform Method; 3.2.3 General Transformation Methods; 3.2.4 Accept-Reject Methods; 3.3 Monte Carlo Integration; 3.3.1 Numerical Integration; 3.3.2 Estimating Moments; 3.3.3 Estimating Probabilities; 3.3.4 Simulating Multiple Futures.
  • 3.4 Precision of Monte Carlo Method3.4.1 Monitoring Mean and Variance; 3.4.2 Importance Sampling; 3.4.3 Correlated Samples; 3.4.4 Variance Reduction Methods; 3.5 Markov Chains; 3.5.1 Markov Processes; 3.5.2 Discrete Time, Discrete State Space; 3.5.3 Transition Probability; 3.5.4 "Sun City"; 3.5.5 Utility Bills; 3.5.6 Classification of States; 3.5.7 Stationary Distribution; 3.5.8 Reversibility Condition; 3.5.9 Markov Chains with Continuous State Spaces; 3.6 Simulation of a Markov Chain; 3.7 Applications; 3.7.1 Bank Sizes; 3.7.2 Related Failures of Car Parts; References.
  • 4 Markov Chain Monte Carlo Methods4.1 Markov Chain Simulations for Sun City and Ten Coins; 4.2 Metropolis-Hastings Algorithm; 4.3 Random Walk MHA; 4.4 Gibbs Sampling; 4.5 Diagnostics of MCMC; 4.5.1 Monitoring Bias and Variance of MCMC; 4.5.2 Burn-in and Skip Intervals; 4.5.3 Diagnostics of MCMC; 4.6 Suppressing Bias and Variance; 4.6.1 Perfect Sampling; 4.6.2 Adaptive MHA; 4.6.3 ABC and Other Methods; 4.7 Time-to-Default Analysis of Mortgage Portfolios; 4.7.1 Mortgage Defaults; 4.7.2 Customer Retention and Infinite Mixture Models; 4.7.3 Latent Classes and Finite Mixture Models.

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