Mathematical Sciences: Bayesian Computations

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Analytic methods for Bayesian analysis hinge upon the "posterior distribution" as the representation for the accumulated information upon observation of the data. For many observational studies as well as many or most experimental situations, an adequate analysis depends on representing complicated information in a satisfactory way. Advances in computational techniques, notably adaptive Monte-Carlo integration, have begun to make the reconstruction of suitable posterior distributions possible. This research will extend the range of existing methods both by incorporating quantile integration to increase efficiency and by formulating the distribution approximation problem in terms of mixture distributions and then imposing a clustering approach to gain efficiency.