The Bayes factor (BF) is a central tool in Bayesian hypothesis testing and model selection, yet its practical use is often challenged. Classical BFs depend heavily on prior specification, cannot be applied with improper priors, and are typically interpreted through arbitrary evidence scales. Moreover, they fail to capture uncertainty inherent in the data, leading to an analogy with frequentist p-values, and primarily reflect prior-predictive rather than posterior-predictive performance. We introduce the stochastic Bayes factor (SBF), a new framework that extends the BF by explicitly incorporating uncertainty via replicated data. Formally, the SBF is defined as a push-forward measure transferring the BF from the observed data space to that of replications. This approach generalizes previous calibration proposals, while emphasizing posterior-predictive replication as a robust alternative. We establish key theoretical properties, including model consistency, compatibility and dominance, ensuring that SBFs preserve desirable Bayesian guarantees. An algorithmic routine is then proposed to operationalize the SBF, guiding model discrimination in a principled way while naturally providing model calibration. Simulation studies and real applications confirm that the SBF offers improved robustness and predictive reliability compared to the classical BF, by providing a valuable tool for model comparison.
The interplay between somatic mutations and copy number alterations influences tumor evolution and prognosis. These alterations are often treated independently, overlooking gene mutant dosage (GMD)—a key property of their interaction. Here we develop a computational framework that infers mutation copy number and multiplicity from targeted sequencing panels without requiring matched normal samples. We derive GMD for over 500,000 mutations across 60,000 pan-cancer samples. By stratifying more than 20,000 patients according to GMD across multiple genes, we identify 46 tumor-type-specific biomarkers predictive of survival, 13 of which were undetectable using binary mutant/wild-type models, 26 were associated with metastatic spread and 20 predicted metastatic tropism. Our method reveals GMD patterns as independent predictors of disease prognosis, metastatic potential and site-specific dissemination across diverse tumor types. This augmented insight into genomic drivers enhances our understanding of cancer progression and metastasis and holds the potential to substantially enhance biomarker discovery. The authors present INCOMMON, an open-source Bayesian inference tool that determines the multiplicity and copy number of driver mutations from tumor sequencing datasets.
N. Calonaci, E. Krasniqi, D. Čolić et al.· Nature Genetics· 0 citations
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