Bayesian Analysis

Marginal Posterior Simulation via Higher-order Tail Area Approximations

Erlis Ruli, Nicola Sartori, and Laura Ventura

Full-text: Open access

Abstract

A new method for posterior simulation is proposed, based on the combination of higher-order asymptotic results with the inverse transform sampler. This method can be used to approximate marginal posterior distributions, and related quantities, for a scalar parameter of interest, even in the presence of nuisance parameters. Compared to standard Markov chain Monte Carlo methods, its main advantages are that it gives independent samples at a negligible computational cost, and it allows prior sensitivity analyses under the same Monte Carlo variation. The method is illustrated by a genetic linkage model, a normal regression with censored data and a logistic regression model.

Article information

Source
Bayesian Anal., Volume 9, Number 1 (2014), 129-146.

Dates
First available in Project Euclid: 24 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.ba/1393251773

Digital Object Identifier
doi:10.1214/13-BA851

Mathematical Reviews number (MathSciNet)
MR3188302

Zentralblatt MATH identifier
1327.62159

Keywords
Asymptotic expansion Bayesian computation Inverse transform sampling Marginal posterior distribution MCMC Modified likelihood root Nuisance parameter Sensitivity analysis

Citation

Ruli, Erlis; Sartori, Nicola; Ventura, Laura. Marginal Posterior Simulation via Higher-order Tail Area Approximations. Bayesian Anal. 9 (2014), no. 1, 129--146. doi:10.1214/13-BA851. https://projecteuclid.org/euclid.ba/1393251773


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