Ajay Jasra (National University of Singapore)

On the convergence of Adaptive sequential Monte Carlo Methods

In several implementations of Sequential Monte Carlo (SMC) methods, it is natural and important in terms of algorithmic efficiency, to exploit the information on the history of the particles to optimally tune their subsequent propagations. In the following talk we provide an asymptotic theory for a class of such adaptive SMC methods. Our theoretical framework developed here will cover for instance, under assumptions, the algorithms in Chopin (2002), Jasra et al (2011), Schafer & Chopin (2013). There are limited results about the theoretical underpinning of such adaptive methods: we will bridge this gap by providing a weak law of large numbers (WLLN) and a central limit theorem (CLT) for some of the algorithms. The latter seems to be the first result of its kind in the literature and provides a formal justification of algorithms that are used in many practical scenarios. This is a joint work with Alex Beskos (NUS/UCL).