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June, 1988 A Quasirandom Approach to Integration in Bayesian Statistics
J. E. H. Shaw
Ann. Statist. 16(2): 895-914 (June, 1988). DOI: 10.1214/aos/1176350842


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.


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J. E. H. Shaw. "A Quasirandom Approach to Integration in Bayesian Statistics." Ann. Statist. 16 (2) 895 - 914, June, 1988.


Published: June, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0645.62043
MathSciNet: MR947584
Digital Object Identifier: 10.1214/aos/1176350842

Primary: 62F15
Secondary: 10K05, 65D30

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 2 • June, 1988
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