Adaptive Bayesian sampling with application to 'bubbles'.
MSc(R) thesis, University of Glasgow.
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The project consists in applying the Markov Random Fields (MRF) theory in order to make inference in spatial graphical models. We are interested in solving the problem of the use of information in certain categorization problems where facial image information is revealed by a certain number of trials and the observer facing an image tries to classify the sampled information. MRFs have the purpose to render information sampling less exhaustive: they allow to identify significantly informative image regions which are used
for further sampling and to exclude from sampling those image regions which contribute at least to solving our categorization problem.
Denoting the observed lattice of data values y and
the underlying latent/hidden field x, the problem ofinterest can be formulated in the following way: conditioned on y, we aim to make inference about all unknown parameters, that is, we aim to evaluate the posterior distribution pi(x|y) which is proportional to the product of the likelihood L(y|x) and the prior distribution pi(x).
Generating samples from the posterior by running the Markov Chain Monte Carlo (MCMC), we compute the posterior expectation/posterior probability map of lattice x given the observed data y. Calculated posterior probability map
values comprise the information on importance of certain sampling regions. Based on this information, we can adopt the sampling strategy sequentially, thereby minimizing the number of sampling trials. The project contains certain simulated experiments to compare the exhaustive and the adaptive sampling approaches. Thereby, images with incorporated spatial dependence are used. We
conclude that the adaptive sampling algorithm which uses MRFs performs better than the exhaustive sampling algorithm.
This results in a lower number of trials and a smaller
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