Sequential Bayesian Inference for Factor Analysis

TL;DR

This paper introduces a versatile Bayesian sequential inference framework for factor analysis models applicable to various data types, enhancing computational efficiency and enabling sequential hypothesis testing.

Contribution

It adapts IBIS and MCMC techniques for continuous, binary, and ordinal data, providing a unified, efficient inference method with applications in sequential testing and model evaluation.

Findings

Effective handling of different data types in factor analysis

Improved computational efficiency over traditional MCMC

Supports sequential hypothesis testing and model evaluation

Abstract

We develop an efficient Bayesian sequential inference framework for factor analysis models observed via various data types, such as continuous, binary and ordinal data. In the continuous data case, where it is possible to marginalise over the latent factors, the proposed methodology tailors the Iterated Batch Importance Sampling (IBIS) of Chopin (2002) to handle such models and we incorporate Hamiltonian Markov Chain Monte Carlo. For binary and ordinal data, we develop an efficient IBIS scheme to handle the parameter and latent factors, combining with Laplace or Variational Bayes approximations. The methodology can be used in the context of sequential hypothesis testing via Bayes factors, which are known to have advantages over traditional null hypothesis testing. Moreover, the developed sequential framework offers multiple benefits even in non-sequential cases, by providing posterior distribution, model evidence and scoring rules (under the prequential framework) in one go, and by offering a more robust alternative computational scheme to Markov Chain Monte Carlo that can be useful in problematic target distributions.