JSM 2004 - Toronto

Abstract #301295

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Activity Number: 414
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract - #301295
Title: A Fundamental Lemma of Specifying Conditional Densities for the Existence of a Joint Density
Author(s): Lung-An Li*+
Companies: Academia Sinica
Address: Institute of Statistical Science, Taipei, 11529, Taiwan
Keywords: conditional density ; compatibility ; joint density
Abstract:

Specifying conditional densities is a crucial step in Markov chain Monte Carlo methodology, which is an important tool in applied stochastically modeling and Bayesian inference, when the joint density has no closed analytical form or is hard to be implemented. However, some compatible requirements among these conditional densities are needed to guarantee the existence of a joint density of a random vector to have these specified conditional densities as its conditional densities. The lemma shown in this paper gives necessary and sufficient conditions for such compatibility requirement, and provides a solution to the uniqueness problem that the joint density is the only one for those given conditional densities. The conditions in this lemma also provide a closed form of the "u" and "v" functions in a necessary and sufficient condition of the existence problem given in an Arnold and Press (1989) paper.

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