# Combining Bayesian and Frequentist Inference for Laboratory-Specific Performance Guarantees in Copy Number Variation Detection

arXiv: https://arxiv.org/abs/2604.14305 · HTML: https://mlsanity.com/paper/2604.14305/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [Bayesian Model Selection, the Marginal Likelihood, and Generalization](https://mlsanity.com/paper/2202.11678/) (2022)
- [Assigning a value to a power likelihood in a general Bayesian model](https://mlsanity.com/paper/1701.08515/) (2017)
- [Robust Bayesian inference via coarsening](https://mlsanity.com/paper/1506.06101/) (2015)
- [Detecting Batch Heterogeneity via Likelihood Clustering](https://mlsanity.com/paper/2601.09758/) (2026)

## Abstract (arXiv)

Targeted amplicon panels are widely used in oncology diagnostics, but providing per-gene performance guarantees for copy number variant (CNV) detection remains challenging due to amplification artifacts, process-mismatch heterogeneity, and limited validation sample sizes. While Bayesian CNV callers naturally quantify per-sample uncertainty, translating this into the frequentist population-level guarantees required for clinical validation, coverage rates, false-positive bounds, and minimum detectable copy-number changes, is a fundamentally different inferential problem. We show empirically that even robust Bayesian credible intervals, including coarsened posteriors and sandwich-adjusted intervals, are severely miscalibrated on panels with small amplicon counts per gene. To address this, we propose a hybrid framework that evaluates Bayesian posterior functionals on validation samples and models the resulting squared losses with a Gamma distribution, yielding tolerance intervals with valid frequentist coverage. Three components make the method practical under real-world constraints: (1) imputation that removes the influence of true CNV-positive samples without requiring known ground truth, (2) regularization to address small sample variability, and (3) evidence-based stratification on the log model evidence to accommodate non-exchangeable noise profiles arising from process mismatch. Evaluated on two targeted amplicon panels using leave-one-out cross-validation, the proposed method achieves single-digit mean absolute coverage error across all genes under both process-matched and unmatched conditions, whereas Bayesian comparators exhibit mean absolute errors exceeding 60% on clinically relevant genes such as ERBB2.