Bayesian Centroid Estimation Carvalho, Luis E. X. creator 2008 xv, 87 p. born digital Thesis (Ph.D.) -- Brown University (2009) Lawrence, Charles director Geman, Stuart reader Raphael, Ben reader Brodsky, Alexander reader Brown University. Applied Mathematics sponsor theses Maximum likelihood estimators have traditionally dominated discrete inference for a long time. In this work we apply statistical decision theory to derive a new contender that minimizes posterior Hamming loss: the centroid estimator. We show that the centroid estimator is also the minimum Bayes risk estimator for a family of loss functions, including the important case when the data being compared is not only categorical, but also ordinal and interval. The centroid estimator is formally characterized as a solution to a discrete optimization problem having posterior marginal distributions as inputs. We discuss both specific constraints of interest and broad conditions under which this optimization problem becomes tractable, present efficient algorithms for its solution, and offer further generalizations to centroid estimation. We apply centroid estimation to many applications of general, well-known models---partition set pertinence models, hidden Markov models, change point models, and graphical models---and to classical problems in computational biology---sequence alignment, RNA secondary structure prediction, and reconstruction of ancestral states. centroid estimator high-dimensional discrete space statistical inference Mathematical statistics RPB 20091218 engEnglish10.7301/Z00G3HHZIn CopyrightCollection is open for research.dissertations