Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk

Luc Bauwens, Charles Bos and Herman van Dijk

No 99-082/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: Adaptive Polar Sampling (APS) is proposed as a Markov chain Monte Carlomethod for Bayesian analysis of models with ill-behaved posteriordistributions. In order to sample efficiently from such a distribution,a location-scale transformation and a transformation to polarcoordinates are used. After the transformation to polar coordinates, aMetropolis-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 nearnon-identifiability, strong correlation, and bimodality, APS comparesfavourably with the standard Metropolis-Hastings sampler in terms ofparsimony and robustness. APS is applied within a Bayesian analysisof a GARCH-mixture model which is used for the evaluation of theValue-at-Risk of the return of the Dow Jones stock index.

Keywords: Markov chain Monte Carlo; simulation; polar coordinates; GARCH; ill-behaved posterior; Value-at-Risk (search for similar items in EconPapers)
JEL-codes: C11 C15 C63 (search for similar items in EconPapers)
Date: 1999-11-02
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

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Related works:
Working Paper: ADAPTIVE POLAR SAMPLING WITH AN APPLICATION TO A BAYES MEASURE OF VALUE-AT-RISK (2000)
Working Paper: Adaptive polar sampling with an application to a Bayes measure of value-at-risk (1999)
Working Paper: Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk (1999)
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