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Abstract:
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We present a flexible Bayesian semiparametric approach to covariate informed multivariate density deconvolution. The problem, to our knowledge, has never been considered before, not even in the univariate setting. Building on recent advances in conditional tensor factorization techniques, our proposed method not only allows the joint and the marginal densities to vary flexibly with the associated predictors but also allows automatic selection of the most influential predictors. We design Markov chain Monte Carlo algorithms that enable efficient posterior inference, appropriately accommodating uncertainty in all aspects of our analysis. The efficacy of the proposed method is illustrated through simulation experiments and a real-world nutritional epidemiology application in estimating the long term average intakes of different dietary components adjusted by demographic covariates of the consumers such as sex, ethnicity, age etc.
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