データ同化セミナー / Data Assimilation Seminar by Dr. Leah Price

Complex models can help us to gain a more complete understanding of the process believed to generate the observed data. However, working with these complex models often requires the ability to sample from complex models and to perform inference when the likelihood function is intractable. In this talk, I will describe our recent work on reducing these computational issues.

Sequential Monte Carlo (SMC) represents a powerful alternative to Markov chain Monte Carlo (MCMC) methods for sampling from the posterior distribution of static Bayesian models. SMC involves specifying a sequence of distributions connecting one that is easy to sample from with the posterior distribution. A population of particles is traversed through this sequence of distributions using a sequence of reweighting, resampling and move steps. The move step is often performed using MCMC kernels and is generally the most computationally expensive step. I will demonstrate the use of efficient independent proposals and the resulting ability to reuse all information for posterior inference and obtain accurate estimates of the model evidence.

When evaluation of the likelihood function is infeasible, the benefits of working with likelihood-free methods become apparent. One of these methods is called the synthetic likelihood (SL), which uses a multivariate normal approximation of the distribution of a set of summary statistics. In this talk, I will explore the accuracy and computational efficiency of the Bayesian version of the synthetic likelihood (BSL) approach in comparison to a competitor known as approximate Bayesian computation (ABC) and its sensitivity to its tuning parameters and assumptions. We also accelerate BSL by using a sparse estimation of the precision matrix.

This is joint work with Christopher C. Drovandi, Tony. N. Pettitt, Anthony Lee, David J. Nott and Ziwen An.