Automated extraction of mutual independence patterns using Bayesian comparison of partition models
This work addresses the limited applicability of existing mutual independence methods for statisticians and data analysts, offering a more flexible automated approach, though it appears incremental as it builds on Bayesian model comparison.
The authors tackled the problem of investigating mutual independence between variables, which traditionally required restrictive hypothesis-driven methods, by proposing an automated Bayesian approach that searches for patterns of mutual independence. They demonstrated the method's relevance on synthetic and real datasets, showing unique insights without specifying concrete numerical results.
Mutual independence is a key concept in statistics that characterizes the structural relationships between variables. Existing methods to investigate mutual independence rely on the definition of two competing models, one being nested into the other and used to generate a null distribution for a statistic of interest, usually under the asymptotic assumption of large sample size. As such, these methods have a very restricted scope of application. In the present manuscript, we propose to change the investigation of mutual independence from a hypothesis-driven task that can only be applied in very specific cases to a blind and automated search within patterns of mutual independence. To this end, we treat the issue as one of model comparison that we solve in a Bayesian framework. We show the relationship between such an approach and existing methods in the case of multivariate normal distributions as well as cross-classified multinomial distributions. We propose a general Markov chain Monte Carlo (MCMC) algorithm to numerically approximate the posterior distribution on the space of all patterns of mutual independence. The relevance of the method is demonstrated on synthetic data as well as two real datasets, showing the unique insight provided by this approach.