Sequential Monte Carlo Methods. 1.1 Definitions

Sampling from a sequence of distributions that change over time is difficult task in MCMC methology. This is, however, an important problem that arises in a range of applications. For instance, the observations may be arriving sequentially in time and one could be interested in performing Bayesian inference in real time. To take full advantage of data, one should update the posterior distribution as data become available. Some real-life applications include tracking of aircrafts using radar measurements, estimating the trends and volatility of financial measurements, etc. An additional benefit of sequential methods is their computational simplicity since the data are dealt in a sequential manner. More details can be found in the monograph Doucet et al. (2001). Also, there is a page devoted to Sequential Monte Carlo Methods/ Particle Filtering at Cambridge, http://www-sigproc.eng.cam.ac.uk/smc/