A Quasirandom Approach to Integration in Bayesian Statistics

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 quasi...

Full description

Saved in:
Bibliographic Details
Published in:The Annals of statistics 1988-06, Vol.16 (2), p.895-914
Main Author: Shaw, J. E. H.
Format: Article
Language:English
Subjects:
10K05
62F15
65D30
Bayesian inference
Bayesian statistics
Bayesian theories
Coordinate systems
Cubes
Exact sciences and technology
Integrands
Integration tables
Mathematics
Numerical integration
Parametric inference
Periodic functions
Probability and statistics
quasirandom sequences
Sampling distributions
Sciences and techniques of general use
Statistics
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1176350842