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Optimal estimation problems for non-linear non-Gaussian state-space models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. recursively as observations become available, and are now… (More)

- Adam M. Johansen
- 2008

Sequential Monte Carlo methods are a very general class of Monte Carlo methods for sampling from sequences of distributions. Simple examples of these algorithms are used very widely in the tracking and signal processing literature. Recent developments illustrate that these techniques have much more general applicability, and can be applied very effectively… (More)

The Auxiliary Particle Filter (APF) introduced by Pitt and Shephard (1999) is a very popular alternative to Sequential Importance Sampling and Resampling (SISR) algorithms to perform inference in state-space models. We propose a novel interpretation of the APF as an SISR algorithm. This interpretation allows us to present simple guidelines to ensure good… (More)

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of " likelihood-free " methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in… (More)

- Arnaud Doucet, Adam M. Johansen, Vladislav B. Tadic
- Applied Mathematics and Computation
- 2010

In this paper, we propose an original approach to the solution of Fredholm equations of the second kind. We interpret the standard von Neumann expansion of the solution as an expectation with respect to a probability distribution defined on a union of subspaces of variable dimension. Based on this representation, it is possible to use trans-dimensional… (More)

This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any finite collection of time points. Within this framework we extend existing exact algorithms and introduce novel adaptive… (More)

We develop strategies for Bayesian modelling as well as model comparison, averaging and selection for compartmental models with particular emphasis on those which occur in the analysis of Positron Emission Tomography (PET) data. Both modelling and computational issues are considered. It is shown that an additive normal error structure does not describe… (More)

- Adam M. Johansen, Arnaud Doucet, Manuel Davy
- Statistics and Computing
- 2008

Standard methods for maximum likelihood parameter estimation in latent variable models rely on the Expectation-Maximization algorithm and its Monte Carlo variants. Our approach is different and motivated by similar considerations to simulated annealing; that is we build a sequence of artificial distributions whose support concentrates itself on the set of… (More)

We present novel sequential Monte Carlo (SMC) algorithms for the simulation of two broad classes of rare events which are suitable for the estimation of tail probabilities and probability density functions in the regions of rare events, as well as the simulation of rare system trajectories. These methods have some connection with previously proposed… (More)

i Abstract The probability hypothesis density (PHD) filter is a first moment approximation to the evolution of a dynamic point process which can be used to approximate the optimal filtering equations of the multiple-object tracking problem. We show that, under reasonable assumptions, a sequential Monte Carlo (SMC) approximation of the PHD filter converges… (More)