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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Vydáno v:	Computational statistics & data analysis Ročník 52; číslo 5; s. 2604 - 2622
Hlavní autoři:	Streftaris, George, Worton, Bruce J.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 20.01.2008 Elsevier Science Elsevier
Edice:	Computational Statistics & Data Analysis
Témata:	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
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Popis
Shrnutí:	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