This talk is an exploration of the possible role for branching processes and related models in Monte Carlo simulation from a complex distribution, such as a Bayesian posterior. The motivation is that branching processes can support antithetic behaviour in a natural way by making offspring negatively correlated, and also that branching paths may assist in navigating past slowly-mixing parts of the state space. The basic theory of branching processes as used for sampling is established, including the appropriate analogue of global balance with respect to the target distribution, evaluation of moments, in particular asymptotic variances, and a start on the spectral theory. Although our model is a kind of 'population Monte Carlo', it should be noted that it has virtually nothing to do with particle filters, etc. Our target is not sequentially evolving, and we rely on ergodicity for convergence of functionals of the target distribution, rather than using importance sampling.
This is joint work with Antonietta Mira (University of Insubria, Varese, Italy).