Probabilistic inference is an attractive approach to uncertain reasoning and empirical learning in artificial intelligence. Computational difculties arise, however, because probabilistic models with the necessary realism and flexibility lead to complex distributions over high-dimensional spaces. Related problems in other fields have been tackled using Monte Carlo methods based on sampling using Markov chains, providing a rich array of techniques that can be applied to problems in artificial intelligence. The "Metropolis algorithm" has been used to solve difficult problems in statistical physics for over forty years, and, in the last few years, the related method of "Gibbs sampling" has been applied to problems of statistical inference. Concurrently, an alternative method for solving problems in statistical physics by means of dynamical simulation has been developed as well, and has recently been unified with the Metropolis algorithm to produce the "hybrid Monte Carlo" method. In computer science, Markov chain sampling is the basis of the heuristic optimization technique of "simulated annealing", and has recently been used in randomized algorithms for approximate counting of large sets. In this review, I outline the role of probabilistic inference in artificial intelligence, and present the theory of Markov chains, and describe various Markov chain Monte Carlo algorithms, along with a number of supporting techniques. I try to present a comprehensive picture of the range of methods that have been developed, including techniques from the varied literature that have not yet seen wide application in artificial intelligence, but which appear relevant. As illustrative examples, I use the problems of probabilitic inference in expert systems, discovery of latent classes from data, and Bayesian learning for neural networks.

In this paper we present some variants of transformed density rejection (TDR) that provide more exibility (including the possibility to halve the expected number of uniform random numbers) at the expense of slightly higher memory requirements. Using a synchronized rst stream of uniform variates and a second auxiliary stream (as suggested by Schmeiser and Kachitvichyanukul (1990)) TDR is well suited for correlation induction. Thus high positive and negative correlation between two streams of random variates with same or dierent distributions can be induced.

This paper presents an overview of the most powerful universal methods. These are based on acceptance/rejection techniques where hat and squeezes are constructed automatically. Although originally motivated to sample from non-standard distributions these methods have advantages that make them attractive even for sampling from standard distributions and thus are an alternative to special generators tailored for particular distributions. Most important are: the marginal generation time is fast and does not depend on the distribution. They can be used for variance reduction techniques, and they produce random numbers of predictable quality. These algorithms are implemented in a library, called UNURAN, which is available by anonymous ftp.

Abstract. We use inequalities to design short universal algorithms that can be used to generate random variates from large classes of univariate continuous or discrete distributions (including all log-concave distributions). The expected time is uniformly bounded over all these distributions for a particular generator. The algorithms can be implemented in a few lines of high level language code. 1.

There exists a vast literature on nonuniform random variate generators. Most of these generators are especially designed for a particular distribution. However in pratice only a few of these are available to practioners. Moreover for problems as (e.g.) sampling from the truncated normal distribution or sampling from fairly uncommon distributions there are often no algorithms available. In the last decade so called universal methods have been developed for these cases. The resulting algorithms are fast and have properties that make them attractive even for standard distributions.

Road safety has recently become a major concern in most modern societies. The identification of sites that are more dangerous than others (black spots) can help in better scheduling road safety policies. This paper proposes a methodology for ranking sites according to their level of hazard. The model is innovative in at least two respects. Firstly, it makes use of all relevant information per accident location, including the total number of accidents and the number of fatalities, as well as the number of slight and serious injuries. Secondly, the model includes the use of a cost function to rank the sites with respect to their total expected cost to society. Bayesian estimation for the model via a Markov Chain Monte Carlo (MCMC) approach is proposed. Accident data from 519 intersections in Leuven (Belgium) are used to illustrate the proposed methodology. Furthermore, different cost functions are used in the paper in order to show the impact of the proposed method on the use of different costs per injury type.

Abstract. In the convolution model Zi = Xi + εi, we give a model selection procedure to estimate the density of the unobserved variables (Xi)1≤i≤n, when the sequence (Xi)i≥1 is strictly stationary but not necessarily independent. This procedure depends on wether the density of εi is super smooth or ordinary smooth. The rates of convergence of the penalized contrast estimators are the same as in the independent framework, and are minimax over most classes of regularity on R. Our results apply to mixing sequences, but also to many other dependent sequences. When the errors are super smooth, the condition on the dependence coefficients is the minimal condition of that type ensuring that the sequence (Xi)i≥1 is not a long-memory process.