# Statistical Inference Methods for Signal Processing

Faculty

Postdocs

Research Students

## Background

Underpinning much of the above applications work is the Bayesian paradigm and associated algorithms for inference about the parameters and structure of complex systems. In the Bayesian approach data is combined with any prior information available in an optimal fashion using probability distributions. We are particularly concerned with the development of new methods appropriate to the applications above. These applications are often sequential in nature (the data arrive one-by-one and a decision/estimate is required with small or no delay), hence we focus considerable attention on sequential learning methods such as Sequential Monte Carlo (particle filtering). Other problems are batch in nature (the data arrive all at once, or we can wait until all of the data have arrived before processing) - in those cases batch algorithms can be used, and we focus attention on stochastic simulation methods such as Markov chain Monte Carlo (MCMC), including those for model uncertainty problems (reversible jump MCMC, etc.). Novel techniques are developed to help tailor these methods to the applications at hand.

## Projects

Some of the current projects in the group:

- Approximate Bayesian Computation (ABC): using the ABC likelihood for static parameter estimation in Hidden Markov Models
- Multi-target tracking: new models for interaction, model calibration, applications to Single Molecule Fluorescence Microscopy
- Particle Markov Chain Monte Carlo (PMCMC)
- Performance analysis of Sequential Monte Carlo algorithms
- Parameter learning in Hidden Markov Models: recursive maximum likelihood, online Expectation-Maximization, PMCMC

You can find more details by clicking on the individual web-pages of the group's members.