Bayesian Semiparametric Covariate Informed Multivariate Density Deconvolution

by   Abhra Sarkar, et al.

Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hour recalls of the intakes. The problem of estimating the density of the latent long-term average intakes from their observed but error contaminated recalls then becomes a problem of multivariate deconvolution of densities. The underlying densities could potentially vary with the subjects' demographic characteristics such as sex, ethnicity, age, etc. The problem of density deconvolution in the presence of associated precisely measured covariates has, however, never been considered before, not even in the univariate setting. We present a flexible Bayesian semiparametric approach to covariate informed multivariate deconvolution. Building on recent advances in copula deconvolution and 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. Importantly, the method also allows the density of interest and the density of the measurement errors to vary with potentially different sets of predictors. We design Markov chain Monte Carlo algorithms that enable efficient posterior inference, appropriately accommodating uncertainty in all aspects of our analysis. The empirical efficacy of the proposed method is illustrated through simulation experiments. Its practical utility is demonstrated in the afore-described nutritional epidemiology applications in estimating covariate-adjusted long term intakes of different dietary components. Supplementary materials include substantive additional details and R codes are also available online.


page 4

page 17

page 18

page 25

page 37

page 38

page 39

page 41


Bayesian Copula Density Deconvolution for Zero-Inflated Data in Nutritional Epidemiology

Estimating the marginal and joint densities of the long-term average int...

Bayesian Semiparametric Multivariate Density Deconvolution via Stochastic Rotation of Replicates

We consider the problem of multivariate density deconvolution where the ...

Colombian Women's Life Patterns: A Multivariate Density Regression Approach

Women in Latin America and the Caribbean face difficulties related to th...

Visualizing and comparing distributions with half-disk density strips

We propose a user-friendly graphical tool, the half-disk density strip (...

A Bayesian Model of Cash Bail Decisions

The use of cash bail as a mechanism for detaining defendants pre-trial i...

Spatially dependent mixture models via the Logistic Multivariate CAR prior

We consider the problem of spatially dependent areal data, where for eac...

Bayesian Nonparametric Modelling of Conditional Multidimensional Dependence Structures

In recent years, conditional copulas, that allow dependence between vari...