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University of Cambridge > Talks.cam > Signal Processing and Communications Lab Seminars > Multilevel sequential Monte Carlo Samplers.

## Multilevel sequential Monte Carlo Samplers.Add to your list(s) Download to your calendar using vCal - Dr Ajay Jasra, National University of Singapore
- Thursday 28 May 2015, 15:00-16:00
- LR5, Department of Engineering.
If you have a question about this talk, please contact Prof. Ramji Venkataramanan. In this talk we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a discretisation bias, with the step-size level h_L. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence of probability distributions. A sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. It is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context. This is a joint work with Alex Beskos (UCL), Kody Law (KAUST), Raul Tempone (KAUST) and Yan Zhou (NUS).
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