The Annals of Statistics

A Quasirandom Approach to Integration in Bayesian Statistics

J. E. H. Shaw

Abstract

Practical Bayesian statistics with realistic models usually gives posterior distributions that are analytically intractable, and inferences must be made via numerical integration. In many cases, the integrands can be transformed into periodic functions on the unit $d$-dimensional cube, for which quasirandom sequences are known to give efficient numerical integration rules. This paper reviews some relevant theory, defines new criteria for identifying suitable quasirandom sequences and suggests some extensions to the basic integration rules. Various quasirandom methods are then compared on the sort of integrals that arise in Bayesian inference and are shown to be much more efficient than Monte Carlo methods.

Article information

Source
Ann. Statist., Volume 16, Number 2 (1988), 895-914.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350842

Digital Object Identifier
doi:10.1214/aos/1176350842

Mathematical Reviews number (MathSciNet)
MR947584

Zentralblatt MATH identifier
0645.62043

JSTOR