Adaptive Polar Sampling
with an application to a Bayes measure of Value-at-Risk
Charles S. BOS1,
Luc Bauwens and Herman K. van Dijk
Econometric and Tinbergen Institutes, Erasmus University
Rotterdam,
CORE, Université catholique de Louvain and
Econometric Institute, Erasmus University
Rotterdam
October 21, 1999
Abstract
Adaptive Polar Sampling (APS) is proposed as a Markov chain Monte Carlo method
for Bayesian analysis of models with ill-behaved posterior distributions. In
order to sample efficiently from such a distribution, a location-scale
transformation and a transformation to polar coordinates are used. After the
transformation to polar coordinates, a Metropolis-Hastings algorithm is applied
to sample directions and, conditionally on these, distances are generated
by inverting the CDF. A sequential procedure is applied to update the
location and scale.
Tested on a set of canonical models that feature near
non-identifiability, strong correlation, and bimodality, APS compares
favourably with the standard Metropolis-Hastings sampler in terms of
parsimony and robustness. APS is applied within a Bayesian analysis of a
GARCH-mixture model which is used for the evaluation of the
Value-at-Risk of the return of the Dow Jones stock index.
|
JEL classification: | C11, C15, C63 |
| Keywords: |
Markov chain Monte Carlo, simulation, polar coordinates, GARCH,
ill-behaved posterior, Value-at-Risk
|
Footnotes:
1
Correspondence to Charles S. Bos,
Tinbergen Institute, Erasmus University Rotterdam,
Burg. Oudlaan 50, NL-3062 PA Rotterdam, The Netherlands.
Email: cbos@feweb.vu.nl,
URL:
http://www.tinbergen.nl/~cbos/.
Support from HCM grant ERBCHRXCT 940514 is gratefully
acknowledged. We thank Michel Lubrano and participants at ESEM'99
for helpful comments on earlier versions of this paper.
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