Consistent and efficient sampler for geometric computation

This paper shows how the random sampling, M-estimators, random walk can be combined to create a consistent sampler for generic models in problems that are difficult due to outliers and multimodality of the solution. Our method contains three major steps: (1) finding the local peaks of the selected robust cost function (M-estimator) using seeds from random sampling of minimal configurations, (2) constructing an approximation of the posterior density by using the local Hessian approximations of the cost function, and (3) sampling by the Metropolis-Hastings selection rule with a mixture proposal distribution containing both draws from the approximated posterior density and random walk to achieve consistence of the samples. The experiments verify that the sampler has much better mixing properties than a conventional random walk sampler. Thus, the approach is promising MCMC method for Bayesian inference that need to numerically evaluate integrals over the posterior density.