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Bayesian Semiparametric Univariate and Multivariate Density Deconvolution for Continuous and Zero-Inflated Data with the R Package BayesDecon
Blake Moya   Mainak Manna   Abhra Sarkar  

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https://doi.org/10.6339/26-JDS1244
Pub. online: 21 September 2026      Type: Computing In Data Science      Open accessOpen Access

Received
9 January 2026
Accepted
28 August 2026
Published
21 September 2026

Abstract

Density deconvolution is a fundamental problem in measurement error settings, arising when the goal is to recover the distribution of unobserved latent variables based on their error-contaminated proxies. An important application arises in nutritional epidemiology, where the objective is to estimate the long-term average intake of nutritional components using 24-hour dietary recall data. This task involves complex multivariate models that account for conditionally heteroscedastic measurement errors, zero-inflated proxies for episodically consumed dietary components, diverse marginal distribution shapes across components, etc. While flexible Bayesian hierarchical methods, coupled with Markov chain Monte Carlo techniques, have been increasingly successful in recent years to enable deconvolution under such intricate but realistic scenarios, the development of rapid and user-friendly software implementations has lagged behind. The $\mathsf{R}$ package BayesDecon has been developed to address this challenge, providing a fast and accessible implementation of flexible Bayesian deconvolution methods for practitioners working with measurement errors. In the process, we have introduced substantial improvements to several aspects of the original models and algorithms, and have also added options to fit simpler parametric models. Although illustrated on challenges in nutritional epidemiology, the package addresses general deconvolution problems and hence is broadly applicable to other domains as well.

Supplementary material

 Supplementary Material
Supplementary materials present results from additional simulation experiments and further analyses of the NHANES data set, providing additional validation of the efficiency and reliability of the BayesDecon package. A separate zip file includes data and codes to replicate the results therein.

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Copyright
2026 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.
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Open access article under the CC BY license.

Keywords
Measurement error NHANES data

Funding
We gratefully acknowledge support for this research provided by the National Science Foundation (NSF) Grant DMS-2515902.

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