Speaker
Description
In various application domains, one wishes to determine which parameter values should be used for a model to match its simulation output with measurement data. In practice however, measurement error on the data means that, at best, one can produce a so-called posterior probability distribution of these parameter values, given an assumed noise model. The Markov chain Monte Carlo method is a popular approach that constructs a Markov chain with this posterior distribution as its invariant distribution. The parameter samples in the chain are selected through an accept-reject strategy, that accepts proposal samples, based on their likelihood, relative to that of the previous accepted sample.
Evaluating this likelihood requires the solution of the given model. Therefore, any errors in the discrete solver will result in errors in the likelihood evaluation. In this presentation, we discuss the case where the Markov chain Monte Carlo method is run on top of a stochastic solver, such as a Monte Carlo particle solver. In this case, the likelihood—and thus the acceptance probability—becomes a random variable whose variance scales with the number of random trajectories simulated by the solver. We discuss the mismatch between theory and practice in this setting. To this end, we combine classical error analysis and simulation results to understand the behavior of the pseudomarginal Markov chains. We then present practical approaches for efficient estimation in such settings.
