We investigate Bayesian alternatives to classical Monte Carlo methods for evaluating integrals. Bayesian Monte Carlo (BMC) allows the incorporation ofprior knowledge, such as smoothness of the integrand, into the estimation. In a simple problem we show that this outperforms any classical importance sampling method. We also attempt more challenging multidimensionalintegrals involved in computing marginal likelihoods ofstatistical models (a.k.a.
Localization is a fundamental challenge for autonomous robotics. Although accurate and efficient techniques now exist for solving this problem, they require explicit probabilistic models of the robot's motion and sensors. These models are usually obtained from time-consuming and error-prone measurement or tedious manual tuning. In this paper we examine automatic calibration of sensor and motion models from a Bayesian perspective. We introduce an efficient MCMC procedure for sampling from the posterior distribution of the model parameters. We also present a novel extension of particle filters to make use of our posterior parameter samples. Finally, we demonstrate our approach both in simulation and on a physical robot. Our results demonstrate effective inference of model parameters as well as a paradoxical result that using posterior parameter samples can produce more accurate position estimates than the true parameters.
Adaptive Monte Carlo schemes developed over the last years usually seek to ensure ergodicity of the sampling process in line with MCMC tradition. This poses constraints on what is possible in terms of adaptation. In the general case ergodicity can only be guaranteed if adaptation is diminished at a certain rate. Importance Sampling approaches offer a way to circumvent this limitation and design sampling algorithms that keep adapting. Here I present a gradient informed variant of SMC (and its special case Population Monte Carlo) for static problems.