If you can specify priors for the parameters (based on your ML fitting),
and accurately describe the model using the BUGS language, then you can use
BUGS to generate samples from the posterior. You simply write a model which
contains the priors and the model structure, but has no data (you already
used the data for the ML fit, and so the information contained within the
data is now contained within the priors derived from the data). This is
likely more straightforward than doing analytical stuff, or writing custom
code for rejection sampling.
I'm not sure what appropriate literature might be. I think this is a
reasonable application of BUGS, and wouldn't require supporting citations.
If you're looking for help with the BUGS language, I suggest starting with
the examples included with BUGS, and then perhaps asking more specific
questions of folks on this list.
Tim Handley
Fire Effects Monitor
Santa Monica Mountains NRA
805-370-2300 x2412
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1. Obtaining posterior distributions from a sample from the distribution
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stochastic likelihood
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Date: Wed, 14 Sep 2011 14:57:17 +0200
From: Tom Smith <[log in to unmask]>
Subject: Obtaining posterior distributions from a sample from the
distribution of a stochastic likelihood
Dear list members,
I am trying to obtain samples from the multidimensional posterior
distribution of the parameters of a complex stochastic model.
For computational reasons, the model has been fitted to data by maximum
likelihood (using a genetic algorithm) rather than Bayesian MCMC.
However, because it is stochastic, a single maximum likelihood solution
is not available, but rather a sample from the multidimensional
likelihood surface (which can be plotted against iteration number, and
which seems to have converged).
We would like to obtain further samples from the posterior distribution
of the parameter vector. We can specify priors for the parameters, so
we could multiplying likelihoods and priors and approximate the
posterior by using some kind of some kind of multidimensional
smoothing. Once we have a numerical approximation to the posterior, I
suppose we can sample from it by rejection sampling. Or would it be
better to fit a parametric model to the likelihood surface (with
WinBUGs)? Then it would be trivial to obtain further samples from the
posterior.
Does anyone have any experience of anything like this, and can point me
to the appropriate literature?
Regards,
Tom Smith
--
Tom Smith
Swiss Tropical& Public Health Institute
Department of Epidemiology& Public Health
Socinstrasse 57
P.O . Box
CH-4002 Basel
Switzerland
Tel 61-284 8273 Fax 61-284 8101
email: [log in to unmask]
http://www.swisstph.ch/en/research/epidemiology-and-public-health-eph/biostatistics-and-computational-sciences.html
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