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

Luc Bauwens, Charles Bos and Herman van Dijk

No TI 99-082/4, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

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.

Keywords: GARCH; Markov Chain Monte Carlo; ill-behaved posterior; polar coordinates; simulation; value-at-risk (search for similar items in EconPapers)
JEL-codes: C11 C15 C63 (search for similar items in EconPapers)
Date: 1999-10-21
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Citations: View citations in EconPapers (16)

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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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