Paganin, Sally (2018) Prior-driven cluster allocation in bayesian mixture models. [Ph.D. thesis]
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Abstract (italian or english)
There is a very rich literature proposing Bayesian approaches for clustering starting with a prior probability distribution on partitions. Most approaches assume exchangeability, leading to simple representations of such prior in terms of an Exchangeable Partition Probability Function (EPPF). Gibbs-type priors encompass a broad class of such cases, including Dirichlet and Pitman-Yor processes. Even though there have been some proposals to relax the exchangeability assumption, allowing covariate-dependence and partial exchangeability, limited consideration has been given on how to include concrete prior knowledge on the partition. Our motivation is drawn from an epidemiological application, in which we wish to cluster birth defects into groups and we have a prior knowledge of an initial clustering provided by experts. The underlying assumption is that birth defects in the same group may have similar coefficients in logistic regression analysis relating different exposures to risk of developing the defect. As a general approach for including such prior knowledge, we propose a Centered Partition (CP) process that modifies a base EPPF to favor partitions in a convenient distance neighborhood of the initial clustering. This thesis focus on providing characterization of such new class, along with properties and general algorithms for posterior computation. We illustrate the methodology through simulation examples and an application to the motivating epidemiology study of birth defects.
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