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.

GARCH, Markov Chain Monte Carlo, ill-behaved posterior, polar coordinates, simulation, value-at-risk
Bayesian Analysis (jel C11), Simulation Methods; Monte Carlo Methods; Bootstrap Methods (jel C15), Computational Techniques; Simulation Modelling (jel C63)
Tinbergen Institute Discussion Paper Series , Econometric Institute Research Papers
Discussion paper / Tinbergen Institute
Erasmus School of Economics

Bauwens, L, Bos, C.S, & van Dijk, H.K. (1999). Adaptive Polar Sampling with an Application to a Bayes Measure of Value-at-Risk (No. TI 99-082/4). Discussion paper / Tinbergen Institute. Retrieved from