Bayesian predictive modeling of multi-source multi-way data

Research output: Contribution to journalArticlepeer-review


A Bayesian approach to predict a continuous or binary outcome from data that are collected from multiple sources with a multi-way (i.e., multidimensional tensor) structure is described. As a motivating example, molecular data from multiple 'omics sources, each measured over multiple developmental time points, as predictors of early-life iron deficiency (ID) in a rhesus monkey model are considered. The method uses a linear model with a low-rank structure on the coefficients to capture multi-way dependence and model the variance of the coefficients separately across each source to infer their relative contributions. Conjugate priors facilitate an efficient Gibbs sampling algorithm for posterior inference, assuming a continuous outcome with normal errors or a binary outcome with a probit link. Simulations demonstrate that the model performs as expected in terms of misclassification rates and correlation of estimated coefficients with true coefficients, with large gains in performance by incorporating multi-way structure and modest gains when accounting for differing signal sizes across the different sources. Moreover, it provides robust classification of ID monkeys for the motivating application.

Original languageEnglish (US)
Article number107783
JournalComputational Statistics and Data Analysis
StatePublished - Oct 2023

Bibliographical note

Funding Information:
This work was supported by the National Institute of General Medical Sciences (NIGMS) grant R01-GM130622 . Funding for the data application in Section 3.3 was also provided by grants from the National Institute of Health/Eunice Kennedy Shriver National Institute of Child Health and Development [ HD089989 , HD080201 , HD057064 and HD39386 ].

Publisher Copyright:
© 2023 Elsevier B.V.


  • Bayesian modeling
  • Iron deficiency
  • Multi-omics integration
  • Multi-way data
  • Reduced rank regression
  • Tensors

PubMed: MeSH publication types

  • Journal Article


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