Particle filters (PFs) are powerful sampling-based inference/learning algorithms for dynamic Bayesian networks (DBNs). They allow us to treat, in a principled way, any type of probability distribution, nonlinearity and non-stationarity. They have appeared in several fields under such names as “condensation”, “sequential Monte Carlo” and “survival of the fittest”. In this paper, we show how we can exploit the structure of the DBN to increase the efficiency of particle filtering, using a technique known as Rao-Blackwellisation. Essentially, this samples some of the variables, and marginalizes out the rest exactly, using the Kalman filter, HMM filter, junction tree algorithm, or any other finite dimensional optimal filter. We show that Rao-Blackwellised particle filters (RBPFs) lead to more accurate estimates than standard PFs. We demonstrate RBPFs on two problems, namely non-stationary online regression with radial basis function networks and robot localization and map building. We also discuss other potential application areas and provide references to some Þnite dimensional optimal filters.

This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.

In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters to obtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available information and, secondly, it can have heavy tails. As a result, we find that the algorithm outperforms standard particle filtering and other nonlinear filtering methods very substantially. This experimental finding is in agreement with the theoretical convergence proof for the algorithm. The algorithm also includes resampling and (possibly) Markov chain Monte Carlo (MCMC) steps.

In this paper, we address the complex problem of sequential Bayesian estimation and model selection/averaging. This problem does not usually admit any type of closed-form analytical solutions and, as a result, one has to resort to numerical methods. We propose here an original and powerful sequential simulation-based strategy to perform the necessary computations. This strategy is based on Monte Carlo particle methods and model selection/averaging using predictive distributions. It combines sequential importance sampling, Rao-Blackwellisation, a selection procedure and reversible jump MCMC moves. We demonstrate the eectiveness of the method by performing inference and learning on a hybrid model consisting of a dynamic linear model and a dynamic mixture of kernel basis functions. 1 Authorship based on alphabetical order 2 Corresponding author 1 Introduction Model selection is a fundamental data analysis task that arises in many elds of science and engineering. Research in this a...

In this paper, we apply particle filters to the problem of on-line classification with possibly overlapping classes. This allows us to compute the probabilities of class membership as the classes evolve. Although we adopt neural network classifiers, the work can be extended to any other parametric classification scheme. We demonstrate our methodology on a simple example and on the problem of fault detection of dynamical operated marine diesel engines.