Posteriorrelating

Posteriorrelating is a term used in some statistical and machine learning writings to describe techniques that focus on relating, comparing, or transferring information between Bayesian posterior distributions. It is not a widely standardized term, but appears in discussions of cross-dataset inference, multi-task learning, and hierarchical Bayesian modeling where posteriors from one analysis inform another.

Core ideas include measuring similarity between posteriors, mapping one posterior to another through linking functions or hierarchical priors, and combining posteriors to produce joint or pooled inferences. Methods can be categorized into transforming posteriors, jointly modeling posteriors, and aligning posterior distributions for predictive or decision tasks.

Applications span meta-analysis with Bayesian posteriors, cross-domain transfer learning, multi-study epidemiology, and adaptive experimental design where prior posteriors guide future data collection and analysis. In each case, the goal is to leverage information contained in posterior distributions beyond a single model or study.

Relation to related concepts is evident, as posteriorrelating overlaps with Bayesian updating, hierarchical modeling, and transfer learning. It also intersects with model averaging, posterior predictive checks, and probabilistic model comparison, offering a framework for leveraging posterior information across contexts rather than focusing on isolated analyses.

Challenges include sensitivity to prior choices and model misspecification, potential non-identifiability between posteriors, and computational demands of fitting and comparing multiple Bayesian models. As a developing area, formal definitions, standard metrics for posterior similarity, and best-practice guidelines are still evolving.