We propose a new Monte Carlo algorithm for complex discrete distributions. The algorithm is motivated by the N-Fold Way, which is an ingenious event-driven MCMC sampler that avoids rejection moves at any specific state. The N-Fold Way can however get “trapped” in cycles. We surmount this problem by modifying the sampling process. This correction does introduce bias, but the bias is subsequently...

Importance sampling is a fundamental Monte Carlo technique. It involves generating a sample from a proposal distribution in order to estimate some property of a target distribution. Importance sampling can be highly sensitive to the choice of proposal distribution, and fails if the proposal distribution does not sufficiently well approximate the target. Procedures which involve truncation of la...

Importance sampling has become an indispensable strategy to speed up optimization algorithms for large-scale applications. Improved adaptive variants—using importance values defined by the complete gradient information which changes during optimization—enjoy favorable theoretical properties, but are typically computationally infeasible. In this paper we propose an efficient approximation of gra...

In this paper we introduce Refractor Importance Sampling (RIS), an improvement to reduce error variance in Bayesian network importance sampling propagation under evidential reasoning. We prove the existence of a collection of importance functions that are close to the optimal importance function under evidential reasoning. Based on this theoretic result we derive the RIS algorithm. RIS approach...

The Adaptive Multiple Importance Sampling (AMIS) algorithm is aimed at an optimal recycling of past simulations in an iterated importance sampling scheme. The difference with earlier adaptive importance sampling implementations like Population Monte Carlo is that the importance weights of all simulated values, past as well as present, are recomputed at each iteration, following the technique of...

Importance sampling involves approximation of functionals (such as expectations) of a target distribution by sampling from a design distribution. In many applications, it is natural or convenient to use a design distribution which is a mixture of given distributions. One typically has wide latitude in selecting the mixing probabilities of the design distribution. Furthermore, one can reduce var...

There arise two problems when the expectation of some function with respect to a nonuniform multivariate distribution has to be computed by (quasi-) Monte Carlo integration: the integrand can have singularities when the domain of the distribution is unbounded and it can be very expensive or even impossible to sample points from a general multivariate distribution. We show that importance sampli...

We consider inference about the history of a sample of DNA sequences, conditional upon the haplotype counts and the number of segregating sites observed at the present time. After deriving some theoretical results in the coalescent setting, we implement rejection sampling and importance sampling schemes to perform the inference. The importance sampling scheme addresses an extension of the Ewens...

SUMMARY Multivariate normal or Student importance sampling is a commonly used technique for integration problems in statistical inference. This integration approach is easy to implement, has straightforward error estimates and is eeective in a number of problems. A variety of variance reduction techniques can be considered with importance sampling. Stratiied sampling is one of these and in fact...