In a distribution ray tracer, the crucial part of the direct lighting calculation is the sampling strategy for shadow ray testing. Monte Carlo integration with importance sampling is used to carry out this calculation. Importance sampling involves the design of integrand-specic probability density functions which are used to generate sample points for the numerical quadrature. Probability densi...

In a distribution ray tracer, the crucial part of the direct lighting calculation is the sampling strategy for shadow ray testing. Monte Carlo integration with importance sampling is used to carry out this calculation. Importance sampling involves the design of integrand-speci c probability density functions which are used to generate sample points for the numerical quadrature. Probability dens...

Much modern work in phylogenetics depends on statistical sampling approaches to phylogeny construction to estimate probability distributions of possible trees for any given input data set. Our theoretical understanding of sampling approaches to phylogenetics remains far less developed than that for optimization approaches, however, particularly with regard to the number of sampling steps needed...

In this paper we develop a methodology that we call split sampling methods to estimate high dimensional expectations and rare event probabilities. Split sampling uses an auxiliary variable MCMC simulation and expresses the expectation of interest as an integrated set of rare event probabilities. We derive our estimator from a Rao-Blackwellised estimate of a marginal auxiliary variable distribut...

Case-control sampling is an extremely common design used to generate data to estimate effects of exposures or treatments on a binary outcome of interest when the proportion of cases (i.e., binary outcome equal to 1) in the population of interest is low. Case-control sampling represents a biased sample of a target population of interest by sampling a disproportional number of cases. Case-control...

A new method, termed probability perturbation, is developed for solving nonlinear inverse problem under a prior model constraint. The method proposed takes a different route from the traditional Bayesian inverse models that rely on prior and likelihood distribution for stating, then sampling, from a posterior distribution. Instead, the probability perturbation method relies on so-called pre-pos...