There is currently great interest in understanding the way in which recombination rates vary, over short scales, across the human genome. Aside from inherent interest, an understanding of this local variation is essential for the sensible design and analysis of many studies aimed at elucidating...

We propose an on-line algorithm for exact filtering of multiple changepoint problems. This algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models. The computational cost of this exact algorithm is...

The forward-backward algorithm is an exact filtering algorithm which can efficiently calculate likelihoods, and which can be used to simulate from posterior distributions. Using a simple result which relates gamma random variables with different rates, we show how the forward-backward algorithm...

We consider the on-line Bayesian analysis of data by using a hidden Markov model, where inference is tractable conditional on the history of the state of the hidden component. A new particle filter algorithm is introduced and shown to produce promising results when analysing data of this type....

The objective of the paper is to present a novel methodology for likelihood-based inference for discretely observed diffusions. We propose Monte Carlo methods, which build on recent advances on the exact simulation of diffusions, for performing maximum likelihood and Bayesian estimation....

We introduce a novel particle filter scheme for a class of partially observed multivariate diffusions. We consider a variety of observation schemes, including diffusion observed with error, observation of a subset of the components of the multivariate diffusion and arrival times of a Poisson...

It is possible to implement importance sampling, and particle filter algorithms, where the importance sampling weight is random. Such random-weight algorithms have been shown to be efficient for inference for a class of diffusion models, as they enable inference without any (time discretization)...