Efficient Bootstrap Calibration of Generalized Posteriors with Importance Reweighting
Abstract
The learning rate of a generalized posterior governs posterior uncertainty but typically has no canonical value. Generalized posterior calibration (GPC) selects this rate by matching bootstrap-estimated credible-interval coverage to its nominal level, often requiring repeated posterior simulation. We propose GPC via importance reweighting (GPC-IRW), which reuses draws from a reference posterior fitted to the original data across bootstrap resamples and candidate learning rates. For quantile-based intervals of a scalar functional, we express the coverage criterion in terms of bootstrap posterior cumulative distribution functions, avoiding computation of individual bootstrap credible intervals. Safeguards based on importance-weight effective sample size and proximity to coverage-decision boundaries invoke reweighting from cached bootstrap-specific draws or direct posterior simulation when necessary. Under the stated regularity conditions, with numerical error tending to zero, we show that median-centered calibration preserves the first-order learning-rate target and achieves asymptotically nominal coverage. The approach extends to independent clusters through cluster-level resampling. Simulations yield coverage and interval lengths comparable to those of existing GPC algorithms at substantially lower computational cost. In an exoplanet mass-radius analysis, GPC-IRW achieves 6.7- and 9.6-fold speedups over MCMC-based calibration in the single-planet and full-sample analyses, respectively, while illustrating the effects of within-host dependence.
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BibTeX
@misc{tanaka2026efficient,
title = {{Efficient Bootstrap Calibration of Generalized Posteriors with Importance Reweighting}},
author = {Masahiro Tanaka},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37232},
eprint = {2610.37232},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37232},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Efficient Bootstrap Calibration of Generalized Posteriors with Importance Reweighting
AU - Masahiro Tanaka
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37232
UR - https://arxiv.org/abs/2610.37232
AB - The learning rate of a generalized posterior governs posterior uncertainty but typically has no canonical value. Generalized posterior calibration (GPC) selects this rate by matching bootstrap-estimated credible-interval coverage to its nominal level, often requiring repeated posterior simulation. We propose GPC via importance reweighting (GPC-IRW), which reuses draws from a reference posterior fitted to the original data across bootstrap resamples and candidate learning rates. For quantile-based intervals of a scalar functional, we express the coverage criterion in terms of bootstrap posterior cumulative distribution functions, avoiding computation of individual bootstrap credible intervals. Safeguards based on importance-weight effective sample size and proximity to coverage-decision boundaries invoke reweighting from cached bootstrap-specific draws or direct posterior simulation when necessary. Under the stated regularity conditions, with numerical error tending to zero, we show that median-centered calibration preserves the first-order learning-rate target and achieves asymptotically nominal coverage. The approach extends to independent clusters through cluster-level resampling. Simulations yield coverage and interval lengths comparable to those of existing GPC algorithms at substantially lower computational cost. In an exoplanet mass-radius analysis, GPC-IRW achieves 6.7- and 9.6-fold speedups over MCMC-based calibration in the single-planet and full-sample analyses, respectively, while illustrating the effects of within-host dependence.
ER -