Ventura , Laura and Ruli, Erlis and Racugno, Walter (2013) A note on approximate Bayesian credible sets based on modified loglikelihood ratios. [Working Paper] WORKING PAPER SERIES, 2/2013 . , PADOVA
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Asymptotic arguments are widely used in Bayesian inference, and in recent years there has been considerable developments of the so-called higher-order asymptotics. This theory provides very accurate approximations to posterior distributions, and to related quantities, in a variety of parametric statistical problems, even for small sample sizes.
The aim of this contribution is to discuss recent advances in approximate Bayesian computations based on the asymptotic theory of modified loglikelihood ratios, both from theoretical and practical point of views. Results on third-order approximations for univariate posterior distributions, also in the presence of nuisance parameters, are reviewed and a new formula for a vector parameter of interest is presented.
All these approximations may routinely be applied in practice for Bayesian inference, since they require little more than standard likelihood quantities for their implementation, and hence they may be available at little additional computational cost over simple first-order approximations. Moreover, these approximations give rise to a simple simulation scheme, alternative to MCMC, for Bayesian computation of marginal posterior distributions for a scalar parameter of interest. In addition, they can be used for testing precise null hypothesis and to define accurate Bayesian credible sets. Some illustrative examples are discussed, with particular attention to the use of matching priors.
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|EPrint type:||Working Paper|
|Anno di Pubblicazione:||January 2013|
|More information:||Pubblicato anche in: Statistics and Probability Letters, (2013) 83, 2467-2472, DOI: 10.1214/13-BA851|
|Key Words:||Asymptotic expansion, Bayesian simulation, Credible set, Laplace approximation, Marginal posterior distribution, Matching priors, Modified likelihood root, Nuisance parameter, Pereira-Stern measure of evidence, Precise null hypothesis, Tail area probability.|
|Settori scientifico-disciplinari MIUR:||Area 13 - Scienze economiche e statistiche > SECS-S/01 Statistica|
|Struttura di riferimento:||Dipartimenti > Dipartimento di Scienze Statistiche|
|Depositato il:||12 May 2015 16:02|
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