Birgit Claus Henn | Searcharxiv

arXiv2025

The Traceplot Thickens: Developing All-Purpose Convergence Diagnostics for any Markov Chain Monte Carlo Algorithm

Markov Chain Monte Carlo (MCMC) algorithms are frequently used to perform inference under a Bayesian modeling framework. Convergence diagnostics, such as traceplots, the Gelman-Rubin potential scale reduction factor, and effective sample size, are used to visualize and monitor how well the sampler has explored the parameter space and the mixing of multiple chains. However, these classic diagnostics can be undefined or ineffective when the sample space of the algorithm varies in dimension or has a large number of discrete parameters. In this article, we develop a novel approach to produce convergence diagnostics in these difficult scenarios by mapping the original sample space to the real-line and then evaluating the convergence diagnostics on the mapped values. The effectiveness of our method is demonstrated on a MCMC algorithm sampling from a Dirichlet process mixture model. The proposed diagnostics are also used to evaluate the performance of a Bayesian kernel machine regression model for estimating the health effect of multi-pollutant mixtures in the Study of Environment, Lifestyle, and Fibroids. Based on diagnostics for the latter dataset, we then explain how we modify the MCMC sampler to improve convergence.

stat.CO↗

arXiv2021

Bayesian kernel machine regression-causal mediation analysis

Greater understanding of the pathways through which an environmental mixture operates is important to design effective interventions. We present new methodology to estimate natural direct and indirect effects and controlled direct effects of a complex mixture exposure on an outcome through a mediator variable. We implement Bayesian Kernel Machine Regression (BKMR) to allow for all possible interactions and nonlinear effects of (1) the co-exposures on the mediator, (2) the co-exposures and mediator on the outcome, and (3) selected covariates on the mediator and/or outcome. From the posterior predictive distributions of the mediator and outcome, we simulate counterfactuals to obtain posterior samples, estimates, and credible intervals of the mediation effects. Our simulation study demonstrates that when the exposure-mediator and exposure-mediator-outcome relationships are complex, BKMR--Causal Mediation Analysis performs better than current mediation methods. We applied our methodology to quantify the contribution of birth length as a mediator between in utero co-exposure to arsenic, manganese and lead, and children's neurodevelopmental scores, in a prospective birth cohort in Bangladesh. Among younger children, we found a negative (adverse) association between the metal mixture and neurodevelopment. We also found evidence that birth length mediates the effect of exposure to the metal mixture on neurodevelopment for younger children. If birth length were fixed to its $75^{th}$ percentile value, the harmful effect of the metal mixture on neurodevelopment is attenuated, suggesting nutritional interventions to help increase fetal growth, and thus birth length, could potentially block the harmful effect of the metal mixture on neurodevelopment.

stat.ME↗