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- W2912095295 abstract "We introduce a Bayesian nonparametric regression model for data with multiway (tensor) structure, motivated by an application to periodontal disease (PD) data. Our outcome is the number of diseased sites measured over four different tooth types for each subject, with subject-specific covariates available as predictors. The outcomes are not well-characterized by simple parametric models, so we use a nonparametric approach with a binomial likelihood wherein the latent probabilities are drawn from a mixture with an arbitrary number of components, analogous to a Dirichlet Process (DP). We use a flexible probit stick-breaking formulation for the component weights that allows for covariate dependence and clustering structure in the outcomes. The parameter space for this model is large and multiway: patients $times$ tooth types $times$ covariates $times$ components. We reduce its effective dimensionality, and account for the multiway structure, via low-rank assumptions. We illustrate how this can improve performance, and simplify interpretation, while still providing sufficient flexibility. We describe a general and efficient Gibbs sampling algorithm for posterior computation. The resulting fit to the PD data outperforms competitors, and is interpretable and well-calibrated. An interactive visual of the predictive model is available at this http URL , and the code is available at this https URL ." @default.
- W2912095295 created "2019-02-21" @default.
- W2912095295 creator A5037811012 @default.
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- W2912095295 date "2019-01-31" @default.
- W2912095295 modified "2023-09-27" @default.
- W2912095295 title "Bayesian nonparametric multiway regression for clustered binomial data" @default.
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