Bayesian Methods for Factor Analysis in Chemometrics

Abstract

Factor analysis is widely used in various scientific disciplines including chemometrics. Factor analysis models and fundamental issues are introduced from the perspective of chemometrics. Bayesian methods offer great potential in that they provide alternative ways to resolve main problems in factor analysis such as the unknown number of factors and model non-identifiability which leads to factor indeterminacy or rotational ambiguity in estimation. Standard Bayesian nonnegative factor analysis models and principles of Bayesian estimation along with modern Bayesian computational methods are introduced. Key advantages of Bayesian factor analysis are simultaneous estimation of model parameters (factor loadings and scores) and their uncertainties and the capability to deal with the unknown number of factors, factor indeterminacy/rotational ambiguity, and parameter uncertainty in a coherent manner as well as the flexibility in modeling and incorporating prior knowledge into estimation. Other developments of extended Bayesian factor analysis models in chemometrics are also presented. Future directions of Bayesian factor analysis in chemometrics, including public release of user-friendly software facilitating its implementation, are discussed.