Efficient and accurate approximate Bayesian inference with an application to insurance data

Efficient and accurate Bayesian Markov chain Monte Carlo methodology is proposed for the estimation of event rates under an overdispersed Poisson distribution. An approximate Gibbs sampling method and an exact independence-type Metropolis–Hastings algorithm are derived, based on a log-normal/gamma m...

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Bibliographic Details
Published in:Computational statistics & data analysis Vol. 52; no. 5; pp. 2604 - 2622
Main Authors: Streftaris, George, Worton, Bruce J.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 20.01.2008
Elsevier Science
Elsevier
Series:Computational Statistics & Data Analysis
Subjects:
Bayes risk
Distribution theory
Effective sample size
Entropy distance
Exact sciences and technology
General topics
Hierarchical Bayesian analysis
Insurance claims
Markov chain Monte Carlo
Mathematics
Mixture distribution
Monte Carlo error
Multivariate analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Probability and statistics
Sciences and techniques of general use
Statistics
Bayes risk
Hierarchical Bayesian analysis
Monte Carlo error
Effective sample size
Insurance claims
Markov chain Monte Carlo
Mixture distribution
Entropy distance
Density estimation
Conditional distribution
Mixing
Divergence
Statistical distribution
Estimator robustness
Gaussian distribution
Entropy
Stochastic method
Statistical simulation
Markov chain
Loss function
Distribution function
Approximation theory
Conditional moment
Bayes estimation
Mixed distribution
Metropolis algorithm
Monte Carlo method
Data analysis
Approximate method
Statistical moment
Finance
Metropolis Hastings algorithm
Independence
Statistical estimation
Moment matching
Gibbs sampling
Poisson distribution
Gamma distribution
Statistical method
Estimating function
Numerical analysis
Statistical computation
Insurance
ISSN:0167-9473, 1872-7352
Online Access:Get full text
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Description
Summary:Efficient and accurate Bayesian Markov chain Monte Carlo methodology is proposed for the estimation of event rates under an overdispersed Poisson distribution. An approximate Gibbs sampling method and an exact independence-type Metropolis–Hastings algorithm are derived, based on a log-normal/gamma mixture density that closely approximates the conditional distribution of the Poisson parameters. This involves a moment matching process, with the exact conditional moments obtained employing an entropy distance minimisation (Kullback–Liebler divergence) criterion. A simulation study is conducted and demonstrates good Bayes risk properties and robust performance for the proposed estimators, as compared with other estimating approaches under various loss functions. Actuarial data on insurance claims are used to illustrate the methodology. The approximate analysis displays superior Markov chain Monte Carlo mixing efficiency, whilst providing almost identical inferences to those obtained with exact methods.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2007.09.006