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Biometrika 2005 92(2):451-464; doi:10.1093/biomet/92.2.451
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© 2005 Biometrika Trust

Monte Carlo conditioning on a sufficient statistic

Bo Henry Lindqvist1 and Gunnar Taraldsen2

1 Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway bo{at}math.ntnu.no, 2 SINTEF Information and Communication Technology, N-7465 Trondheim, Norway gunnar.taraldsen{at}sintef.no

In this paper we derive general formulae suitable for Monte Carlo computation of conditional expectations of functions of a random vector given a sufficient statistic. The problem of direct sampling from the conditional distribution is considered in particular. It is shown that this can be done by a simple parameter adjustment of the original statistical model, provided the model has a certain pivotal structure. A connection with a classical problem regarding fiducial and posterior distributions is pointed out.

Key Words: Conditional distribution; Fiducial distribution; Monte Carlo simulation; Pivotal statistic; Sufficiency

Received March 2004. Revised September 2004.


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