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Parts 4 and 5 of this lecture are presented in [[mlss07_davy_smcmc|//Manuel Davy's// "%title"]]

We will first review the Monte Carlo principle and standard Monte Carlo methods including rejection sampling, importance sampling and standard Markov chain Monte Carlo (MCMC) methods. We will then discuss more advanced MCMC methods such as adaptive MCMC methods and auxiliary variable methods such as ...

Over the last fifteen years, sequential Monte Carlo (SMC) methods gained popularity as powerful tools for solving intractable inference problems arising in the modelling of sequential data. Much effort was devoted to the development of SMC methods, known as particle filters (PFs), for estimating the ...