Toward Bayesian chemometrics—A tutorial on some recent advances

Chemometrics is increasingly being perceived as a maturing science. While this perception seems to be true with regards to the traditional methods and applications of chemometrics, this article argues that advances in instrumentation, computation, and statistical theory may combine to drive a resurgence in chemometrics research. Previous surges in chemometrics research activity were driven by the development of new ways of making better use of available information. Bayesian statistics can further enhance the ability to use domain specific information to obtain more accurate and useful models, and presents many research opportunities as well as challenges.Although Bayesian statistics is not new, recent advances via sampling-based Monte Carlo methods make these methods practical for large scale applications without making the common assumptions of Gaussian noise and uniform prior distributions, made by most chemometric methods. This article provides an overview of traditional chemometric methods from a Bayesian view and a tutorial of some recently developed techniques in Bayesian chemometrics, such as Bayesian PCA and Bayesian latent variable regression. New challenges and opportunities for future work are also identified.