December 2022 Parsimonious Bayesian factor analysis for modelling latent structures in spectroscopy data
Alessandro Casa, Tom F. O’Callaghan, Thomas Brendan Murphy
Author Affiliations +
Ann. Appl. Stat. 16(4): 2417-2436 (December 2022). DOI: 10.1214/21-AOAS1597


In recent years, within the dairy sector, animal diet and management practices have been receiving increased attention, in particular, examining the impact of pasture-based feeding strategies on the composition and quality of milk and dairy products in line with the prevalence of premium grass-fed dairy products appearing on market shelves. To date, methods to thoroughly investigate the more relevant differences induced by the diet on milk chemical features are limited; enhanced statistical tools exploring these differences are required.

Infrared spectroscopy techniques are widely used to collect data on milk samples and to predict milk related traits and characteristics. While these data are routinely used to predict the composition of the macro components of milk, each spectrum also provides a reservoir of unharnessed information about the sample. The accumulation and subsequent interpretation of these data present some challenges due to their high-dimensionality and the relationships amongst the spectral variables.

In this work, directly motivated by a dairy application, we propose a modification of the standard factor analysis to induce a parsimonious summary of spectroscopic data. Our proposal maps the observations into a low-dimensional latent space while simultaneously clustering the observed variables. The method indicates possible redundancies in the data, and it helps disentangle the complex relationships among the wavelengths. A flexible Bayesian estimation procedure is proposed for model fitting, providing reasonable values for the number of latent factors and clusters. The method is applied on milk mid-infrared (MIR) spectroscopy data from dairy cows on distinctly different pasture and nonpasture based diets, providing accurate modelling of the correlation, clustering of variables, and information on differences among milk samples from cows on different diets.

Funding Statement

This publication has emanated from research conducted with the financial support of Science Foundation Ireland (SFI) and the Department of Agriculture, Food and Marine on behalf of the Government of Ireland under grant number (16/RC/3835) and the SFI Insight Research Centre under grant number (SFI/12/RC/2289_P2).


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Alessandro Casa. Tom F. O’Callaghan. Thomas Brendan Murphy. "Parsimonious Bayesian factor analysis for modelling latent structures in spectroscopy data." Ann. Appl. Stat. 16 (4) 2417 - 2436, December 2022.


Received: 1 September 2021; Revised: 1 December 2021; Published: December 2022
First available in Project Euclid: 26 September 2022

Digital Object Identifier: 10.1214/21-AOAS1597

Keywords: chemometrics , clustering , Dairy science , factor analysis , Gibbs sampling , redundant variables , spectroscopy

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.16 • No. 4 • December 2022
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