Introduction to Bayesian estimation and copula models of dependence

Introduction to Bayesian estimation and copula models of dependence

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 Bayes...

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Detalles Bibliográficos
Otros Autores: Shemyakin, Arkady, author (author), Kniazev, Alexander (Mathematician), author
Formato: Libro electrónico
Idioma:Inglés
Publicado: Hoboken, New Jersey : John Wiley & Sons, Incorporated 2017.
Edición:1st edition
Colección:THEi Wiley ebooks.
Materias:
Bayesian statistical decision theory.
Copulas (Mathematical statistics)
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009631589106719
Tabla de Contenidos:
  • Intro
  • 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 Wages
  • 2.2 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 Bayes
  • 2.7 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 Method
  • 3.4.1 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 Methods
  • 4.1 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
  • 4.7.4 Maximum Likelihood Estimation
  • 4.7.5 A Bayesian Model
  • References
  • PART II Modeling Dependence
  • 5 Statistical Dependence Structures
  • 5.1 Introduction
  • 5.2 Correlation
  • 5.2.1 Pearson's Linear Correlation
  • 5.2.2 Spearman's Rank Correlation
  • 5.2.3 Kendall's Concordance
  • 5.3 Regression Models
  • 5.3.1 Heteroskedasticity
  • 5.3.2 Nonlinear Regression
  • 5.3.3 Prediction
  • 5.4 Bayesian Regression
  • 5.5 Survival Analysis
  • 5.5.1 Proportional Hazards
  • 5.5.2 Shared Frailty
  • 5.5.3 Multistage Models of Dependence
  • 5.6 Modeling Joint Distributions
  • 5.6.1 Bivariate Survival Functions
  • 5.6.2 Bivariate Normal.
  • 5.6.3 Simulation of Bivariate Normal
  • 5.7 Statistical Dependence and Financial Risks
  • 5.7.1 A Story of Three Loans
  • 5.7.2 Independent Defaults
  • 5.7.3 Correlated Defaults
  • References
  • 6 Copula Models of Dependence
  • 6.1 Introduction
  • 6.2 Definitions
  • 6.2.1 Quasi-Monotonicity
  • 6.2.2 Definition of Copula
  • 6.2.3 Sklar's Theorem
  • 6.2.4 Survival Copulas
  • 6.3 Simplest Pair Copulas
  • 6.3.1 Maximum Copula
  • 6.3.2 Minimum Copula
  • 6.3.3 FGM Copulas
  • 6.4 Elliptical Copulas
  • 6.4.1 Elliptical Distributions
  • 6.4.2 Method of Inverses
  • 6.4.3 Gaussian Copula
  • 6.4.4 The t-copula
  • 6.5 Archimedean Copulas
  • 6.5.1 Definitions
  • 6.5.2 One-Parameter Copulas
  • 6.5.3 Clayton Copula
  • 6.5.4 Frank Copula
  • 6.5.5 Gumbel-Hougaard Copula
  • 6.5.6 Two-Parameter Copulas
  • 6.6 Simulation of Joint Distributions
  • 6.6.1 Bivariate Elliptical Distributions
  • 6.6.2 Bivariate Archimedean Copulas
  • 6.7 Multidimensional Copulas
  • References
  • 7 Statistics of Copulas
  • 7.1 The Formula that Killed Wall Street
  • 7.2 Criteria of Model Comparison
  • 7.2.1 Goodness-of-Fit Tests
  • 7.2.2 Posterior Predictive p-values
  • 7.2.3 Information Criteria
  • 7.2.4 Concordance Measures
  • 7.2.5 Tail Dependence
  • 7.3 Parametric Estimation
  • 7.3.1 Parametric, Semiparametric, or Nonparametric?
  • 7.3.2 Method of Moments
  • 7.3.3 Minimum Distance
  • 7.3.4 MLE and MPLE
  • 7.3.5 Bayesian Estimation
  • 7.4 Model Selection
  • 7.4.1 Hybrid Approach
  • 7.4.2 Information Criteria
  • 7.4.3 Bayesian Model Selection
  • 7.5 Copula Models of Joint Survival
  • 7.6 Related Failures of Vehicle Components
  • 7.6.1 Estimation of Association Parameters
  • 7.6.2 Comparison of Copula Classes
  • 7.6.3 Bayesian Model Selection
  • 7.6.4 Conclusions
  • References
  • 8 International Markets
  • 8.1 Introduction
  • 8.2 Selection of Univariate Distribution Models.
  • 8.3 Prior Elicitation for Pair Copula Parameter
  • 8.4 Bayesian Estimation of Pair Copula Parameters
  • 8.5 Selection of Pair Copula Model
  • 8.6 Goodness-of-Fit Testing
  • 8.7 Simulation and Forecasting
  • References
  • Index
  • EULA.

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