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Exact MAP States and Expectations from Perfect Sampling: Greig, Porteous and Seheult revisited

By Seheult Revisited, C. Fox and G. K. Nicholls


this paper we seek to clarify the issues, for this audience, by treating a simple image recovery problem and comparing the MAP estimator to other estimates based on sampling the posterior, and to the mean which provides information about the bulk of posterior probability mass. We have chosen the problem of recovering a binary image from a pixel-wise degraded image and using an Ising Markov random eld (MRF) prior model for the image. For that problem, Greig Porteous and Seheult[3] demonstrated that the MAP state can be exactly calculated via an equivalent minimum cut problem in a certain capacitated network, thereby removing any question of convergence when using iterative algorithms such as simulated annealing. We im1 plement that calculation along with a MCMC algorithm that perfectly samples the posterior, i.e. that actually draws i.i.d. samples from the posterior distribution and hence for which there is no question of burn in as occurs for standard algorithms. Thus we are able to compare the MAP state with exact samples and actual estimates over the posterior distribution, there being no issues of algorithmic convergence in our results

Year: 2000
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