Bayesian Non-Parametric Factor Analysis for Longitudinal Spatial Surfaces

TL;DR

This paper presents a Bayesian non-parametric spatial factor analysis model that captures spatial dependencies and temporal clustering in longitudinal spatial data, demonstrated on health monitoring datasets.

Contribution

The paper introduces a novel Bayesian non-parametric model incorporating spatial dependency and adaptive factor selection for longitudinal spatial data analysis.

Findings

Effective in simulated data

Successfully applied to glaucoma monitoring

Useful for malaria surveillance

Abstract

We introduce a Bayesian non-parametric spatial factor analysis model with spatial dependency induced through a prior on factor loadings. For each column of the loadings matrix, spatial dependency is encoded using a probit stick-breaking process (PSBP) and a multiplicative gamma process shrinkage prior is used across columns to adaptively determine the number of latent factors. By encoding spatial information into the loadings matrix, meaningful factors are learned that respect the observed neighborhood dependencies, making them useful for assessing rates over space. Furthermore, the spatial PSBP prior can be used for clustering temporal trends, allowing users to identify regions within the spatial domain with similar temporal trajectories, an important task in many applied settings. In the manuscript, we illustrate the model's performance in simulated data, but also in two real-world examples: longitudinal monitoring of glaucoma and malaria surveillance across the Peruvian Amazon. The R package spBFA, available on CRAN, implements the method.