Bayesian Conditional Independence Testing Using Pivotal Quantities

Music City Center 

We introduce a Bayesian approach to assessing conditional independence
assumptions when assessing the accuracy of diagnostic tests. The
approach is based on the sampling distributions of pivotal quantities,
which are distributionally invariant under the posterior predictive distribution
Johnson (2004). Specifically, we use posterior samples of chi-square
deviates derived from latent variables and obtained from an MCMC framework
to assess conditional independence.

Our method provides a Bayesian alternative to traditional marginal
likelihood-based approaches that maintains coherence with Bayesian inference
principles. We demonstrate the method's ability to detect subtle
dependence structures in complex datasets through simulations and
real-world applications, offering a computationally scalable solution for
conditional independence testing.

Conditional independence

Bayesian

Pivotal quantities

Latent variables

Chi-Squared Test 

Biometrics Section