Density-Ratio Compression Cleans Up Bayesian Model Averaging

Bayesian model averaging in support-indexed regression often produces a posterior that spreads mass across many nearly interchangeable predictor support sets when predictors are redundant. This makes exact-support summaries unstable and hard to interpret, even if predictions remain stable. Li, Lu, and Chen tackle this by introducing a density-ratio posterior compression framework that reports fitted posteriors through regions of support space—hard regions, metric-ball regions, posterior-cluster regions, and pooled-pruned region dictionaries. The compressed reporting law is compared against the reference posterior using an explicit density ratio, yielding computable total-variation and Kullback–Leibler distortion metrics, as well as bounds for bounded predictive summaries, retained-mass diagnostics, and fallback-weight diagnostics.

The paper proves exact error formulas and validation bounds for these region reports, giving theoretical guarantees that a few regions can replace a long list of individual supports under specific conditions. Simulations demonstrate that region reports often deliver shorter, clearer summaries while preserving the main posterior information, and the density-ratio diagnostics indicate when too much information has been lost. The work spans 48 pages, 6 figures, and includes source code and reproducibility materials. For practitioners dealing with high-dimensional or redundant predictor sets, this method offers a principled way to compress Bayesian model averaging outputs without altering the underlying Bayesian inference—making it easier to communicate which predictors are truly active.