Non-central Cochran's theorem for elliptically contoured distributions

1986 ◽  
Vol 2 (3) ◽  
pp. 185-198 ◽  
Author(s):  
Fan Jianqing
Keyword(s):  
Elliptically Contoured Distributions ◽  
Elliptically Contoured

scholarly journals Exact likelihood-free Markov chain Monte Carlo for elliptically contoured distributions

2015 ◽  
Vol 14 (4) ◽  
Author(s):  
Patrick Muchmore ◽  
Paul Marjoram
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Stationary Distribution ◽  
Large Family ◽  
Multivariate Normal ◽  
Elliptically Contoured Distributions ◽  
Simulation Based ◽  
A Chain ◽  
Elliptically Contoured

AbstractRecent results in Markov chain Monte Carlo (MCMC) show that a chain based on an unbiased estimator of the likelihood can have a stationary distribution identical to that of a chain based on exact likelihood calculations. In this paper we develop such an estimator for elliptically contoured distributions, a large family of distributions that includes and generalizes the multivariate normal. We then show how this estimator, combined with pseudorandom realizations of an elliptically contoured distribution, can be used to run MCMC in a way that replicates the stationary distribution of a likelihood based chain, but does not require explicit likelihood calculations. Because many elliptically contoured distributions do not have closed form densities, our simulation based approach enables exact MCMC based inference in a range of cases where previously it was impossible.

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