Description: Monte Carlo methods are stochastic simulation based algorithms designed to compute answers to problems where exact solutions are intractable and take exponential time to compute. While these techniques provide an exact answer only asymptotically, they perform remarkably well in practice and are now used extensively in science and engineering, including statistics, machine learning, aerospace, computer vision, network analysis, speech recognition, robotics, physics and bioinformatics.

The scope of this course is to review the following fundamental aspects in Monte Carlo computations:

* Model construction
* Design of strategies for inference
* Theoretical aspects (convergence proofs, performance analysis)

Our exposure will be primarily slanted towards inference strategies.

In particular, we will study Markov Chain Monte Carlo methods and Sequential Monte Carlo. Our ultimate aim is to provide a basic understanding of computational techniques based on Monte Carlo simulations and associated concepts such that the students can orient themselves in the relevant literature and understand the current state of the art.