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Independence Structure of Natural Conjugate Densities to Exponential Families and the Gibbs' Sampler
Author(s) -
Piccioni Mauro
Publication year - 2000
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00182
Subject(s) - mathematics , exponential family , gibbs sampling , bernoulli's principle , conjugate prior , gaussian , independence (probability theory) , block (permutation group theory) , exponential function , statistics , combinatorics , mathematical analysis , prior probability , bayesian probability , thermodynamics , physics , quantum mechanics
In this paper the independence between a block of natural parameters and the complementary block of mean value parameters holding for densities which are natural conjugate to some regular exponential families is used to design in a convenient way a Gibbs' sampler with block updates. Even when the densities of interest are obtained by conditioning to zero a block of natural parameters in a density conjugate to a larger “saturated” model, the updates require only the computation of marginal distributions under the “unconditional” density. For exponential families which are closed under marginalization, including both the zero mean Gaussian family and the cross‐classified Bernoulli family such an implementation of the Gibbs' sampler can be seen as an Iterative Proportional Fitting algorithm with random inputs.