MCMC (Markov Chain Monte Carlo) and MC Statistical Methods are very powerful statistical techniques for parameter estimation and related problems. They are particularly useful for the difficult nonlinear or non-Gaussian case. Using a large data set, these techniques can also be used to make inference on parameters, to integrate nuisance parameters, to evaluate functions numerically or to solve optimization problems.
We have applied these methods to several interesting problems:

1. Joint model order detection and DOA estimation in coloured noise (J-R. Larocque)
   Model order detection has always been a difficult problem in array signal processing when the noise is coloured. A novel reversible jump MCMC approach has been proposed to solve this problem [1].
2. Tracking of multiple targets using arrays of sensors (J-R. Larocque)
   In this project, arrays of sensors are used to detect the number of targets and to jointly track their directions of arrival using particle filters or sequential Monte Carlo approaches. These methods approach real-time efficiency and show considerable advantages over previous techniques [2].
3. Wideband Array Processing (William Ng)

MCMC and sequential MC methods were used to develop an array processing algorithm for extraction of a signal of interest in the presence of multiple interfering sources for the more difficult wideband case [3].

References

1. Larocque JR, Reilly JP. Reversible jump MCMC for joint detection and estimation of sources in colored noise. IEEE Transactions on Signal Processing. 2002 Aug 7;50(2):231-40.
2. Larocque JR, Reilly JP, Ng W. Particle filters for tracking an unknown number of sources. IEEE Transactions on Signal Processing. 2002 Dec 16;50(12):2926-37.
3. Ng W, Reilly JP, Kirubarajan T, Larocque JR. Wideband array signal processing using MCMC methods. IEEE Transactions on Signal Processing. 2005 Dec 5;53(2):411-26.