Optimality of the Half-Order Exponent in the Turing-Good Identities for Bayes Factors
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917288651784192 |
|---|---|
| author | Okada, Kensuke |
| author_facet | Okada, Kensuke |
| contents | Bayes factors are widely computed by Monte Carlo, yet heavy-tailed sampling distributions can make numerical validation unreliable. The Turing--Good identities provide exact moment equalities for powers of a Bayes factor (a density ratio). When these identities are used as Good-check diagnostics, the power choice becomes a statistical design parameter. We develop a nonasymptotic variance theory for Monte Carlo evaluation of the identities and show that the half-order (square-root) power is uniquely minimax-stable: it equalizes variability across the two model orientations and is the only choice that guarantees finite second moments in a distribution-free worst-case sense over all mutually absolutely continuous model pairs. This yields a balanced two-sample half-order diagnostic that is symmetric in model labeling and has a uniform variance bound at fixed computational budget; in small-overlap regimes it is guaranteed to be no less efficient than the standard one-sided Turing check. Simulations for binomial Bayes factor workflows illustrate stable finite-sample behavior and sensitivity to simulator--evaluator mismatches. We further connect the half-order overlap viewpoint to stable primitives for normalizing-constant ratios and importance-sampling degeneracy summaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19838 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimality of the Half-Order Exponent in the Turing-Good Identities for Bayes Factors Okada, Kensuke Methodology Statistics Theory Bayes factors are widely computed by Monte Carlo, yet heavy-tailed sampling distributions can make numerical validation unreliable. The Turing--Good identities provide exact moment equalities for powers of a Bayes factor (a density ratio). When these identities are used as Good-check diagnostics, the power choice becomes a statistical design parameter. We develop a nonasymptotic variance theory for Monte Carlo evaluation of the identities and show that the half-order (square-root) power is uniquely minimax-stable: it equalizes variability across the two model orientations and is the only choice that guarantees finite second moments in a distribution-free worst-case sense over all mutually absolutely continuous model pairs. This yields a balanced two-sample half-order diagnostic that is symmetric in model labeling and has a uniform variance bound at fixed computational budget; in small-overlap regimes it is guaranteed to be no less efficient than the standard one-sided Turing check. Simulations for binomial Bayes factor workflows illustrate stable finite-sample behavior and sensitivity to simulator--evaluator mismatches. We further connect the half-order overlap viewpoint to stable primitives for normalizing-constant ratios and importance-sampling degeneracy summaries. |
| title | Optimality of the Half-Order Exponent in the Turing-Good Identities for Bayes Factors |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2602.19838 |