| Description |
1 online resource |
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data file |
| 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. |
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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. |
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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. |
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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. |
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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. |
| Bibliography |
Includes bibliographical references and index. |
| Summary |
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 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. In addition, this book includes: - Practical examples of copulas in use including within the Basel Accord II documents that regulate the world banking system as well as examples of Bayesian methods within current FDA recommendations - Step-by-step procedures of multivariate data analysis and copula modeling, allowing readers to gain insight for their own applied research and studies - Separate reference lists within each chapter and end-of-the-chapter exercises within Chapters 2 through 8 - A companion website containing appendices: data files and demo files in Microsoft Office Excel, basic code in R, and selected exercise solutions Introduction to Bayesian Estimation and Copula Models of Dependence is a reference and resource for statisticians who need to learn formal Bayesian analysis as well as professionals within analytical and risk management departments of banks and insurance companies who are involved in quantitative analysis and forecasting. This book can also be used as a textbook for upper-undergraduate and graduate-level courses in Bayesian statistics and analysis. ARKADY SHEMYAKIN, PhD, is Professor in the Department of Mathematics and Director of the Statistics Program at the University of St. Thomas. A member of the American Statistical Association and the International Society for Bayesian Analysis, Dr. Shemyakin's research interests include informationtheory, Bayesian methods of parametric estimation, and copula models in actuarial mathematics, finance, and engineering. ALEXANDER KNIAZEV, PhD, is Associate Professor and Head of the Department of Mathematics at Astrakhan State University in Russia. Dr. Kniazev's research interests include representation theory of Lie algebras and finite groups, mathematical statistics, econometrics, and financial mathematics. |
| Subject |
Bayesian statistical decision theory.
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Copulas (Mathematical statistics)
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Théorie de la décision bayésienne. |
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Copules (Statistique mathématique) |
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Bayesian statistical decision theory |
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Copulas (Mathematical statistics) |
| Added Author |
Kniazev, Alexander (Mathematician)
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| Other Form: |
Print version: Shemyakin, Arkady. Introduction to Bayesian estimation and copula models of dependence. Hoboken, New Jersey : John Wiley & Sons, Inc., [2017] 9781118959015 (DLC) 2016042826 (OCoLC)956623737 |
| ISBN |
9781118959039 (electronic bk.) |
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1118959035 (electronic bk.) |
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9781118959046 (electronic bk.) |
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1118959043 (electronic bk.) |
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1118959027 |
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9781118959022 |
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(epub) |
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