Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk - Luc Bauwens; Charles S. Bos; Herman K. van Dijk (Tinbergen Institute, 1999)
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: C11; C15; C63; 330; Markov chain Monte Carlo; simulation; polar coordinates; GARCH; ill-behaved posterior; Value-at-Risk; Stichprobenverfahren; Theorie