Bayesian Latent Factor Model for Multi-target Inference

Providing safe drinking water is essential for human health. To achieve this, analyzing multidimensional spectroscopic measurements of water, such as absorbance and fluorescence spectra, is crucial. However, measuring such parameters entails significant time and instrumental efforts. Therefore, it is essential to develop statistical tools to minimize the required lab analyses. We propose a bivariate functional data model, where each sampling unit comprises the bivariate target: absorbance and fluorescence. We employed a Bayesian bivariate functional latent factor model extending [4]. In our water analyses application, interpretable posterior distributions of the latent factors are crucial, thus we addressed their identifiability question, using Varimax-RSP method. Hamiltonian Monte Carlo sampler was applied to sample the posterior distribution. We developed a Python package, available on GitHub, implementing our model and we tested it on simulated univariate and bivariate data, anticipating its application with real data from the European Project SafeCREW [1].