New Importance Sampling Densities.
Preprint Series / Department of Applied Statistics and Data Processing, 56.
Department of Statistics and Mathematics, Abt. f. Angewandte Statistik u. Datenverarbeitung, WU Vienna University of Economics and Business, Vienna.
To compute the expectation of a function with respect to a multivariate distribution naive Monte Carlo is often not feasible. In such cases importance sampling leads to better estimates than the rejection method. A new importance sampling distribution, the product of one-dimensional table mountain distributions with exponential tails, turns out to be flexible and useful for Bayesian integration problems. To obtain a heavy-tailed importance sampling distribution a new radius transform for the above distribution is suggested. Together with a linear transform the new importance sampling distributions lead to simple and fast integration algorithms with reliable error bounds. (author's abstract)