Bayesian Semiparametric Multivariate Density Deconvolution via Stochastic Rotation of Replicates

TL;DR

This paper introduces a robust Bayesian method for multivariate density deconvolution that uses stochastic rotation of replicates to accurately estimate true distributions from contaminated data, even with heteroscedastic errors.

Contribution

It presents a novel stochastic rotation approach combined with Bayesian inference to handle complex heteroscedastic measurement errors in multivariate density estimation.

Findings

Method demonstrates strong empirical performance in simulations.

Effective in estimating dietary intake distributions from error-prone data.

Provides asymptotic convergence guarantees.

Abstract

We consider the problem of multivariate density deconvolution where the distribution of a random vector needs to be estimated from replicates contaminated with conditionally heteroscedastic measurement errors. We propose a conceptually straightforward yet fundamentally novel and highly robust approach to multivariate density deconvolution by stochastically rotating the replicates toward the corresponding true latent values. We also address the additionally significantly challenging problem of accommodating conditionally heteroscedastic measurement errors in this newly introduced framework. We take a Bayesian route to estimation and inference, implemented via an efficient Markov chain Monte Carlo algorithm, appropriately accommodating uncertainty in all aspects of our analysis. Asymptotic convergence guarantees for the method are also established. We illustrate the method's empirical efficacy through simulation experiments and its practical utility in estimating the long-term joint average intakes of different dietary components from their measurement error contaminated 24-hour dietary recalls.