Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2410.20169

Bayes-assisted Confidence Regions: Focal Point Estimator and Bounded-influence Priors

Stefano Cortinovis·François Caron
View original source ↗Read source document ↗Export metadata ↓

Abstract

The Frequentist, Assisted by Bayes (FAB) framework constructs confidence regions that leverage prior information about parameter values. FAB confidence regions (FAB-CRs) have smaller volume for values of the parameter that are likely under the prior while maintaining exact frequentist coverage. This work introduces several methodological and theoretical contributions to the FAB framework. For Gaussian likelihoods, we show that the posterior mean of the mean parameter is contained in the FAB-CR. More generally, this result extends to the posterior mean of the natural parameter for likelihoods in the natural exponential family. These results provide a natural Bayes-assisted estimator to be reported alongside the FAB-CR. Furthermore, for Gaussian likelihoods, we show that power-law tail conditions on the marginal likelihood induce robust FAB-CRs that are uniformly bounded and revert to standard frequentist confidence intervals for extreme observations. We translate this result into practice by proposing a class of shrinkage priors for the FAB framework that satisfy this condition without sacrificing analytic tractability. The resulting FAB estimators equal prominent Bayesian shrinkage estimators, including the horseshoe estimator, thereby establishing insightful connections between robust FAB-CRs and Bayesian shrinkage methods.

Explore related subjects

stat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Stefano Cortinovis, François Caron. 2026-06-08. Bayes-assisted Confidence Regions: Focal Point Estimator and Bounded-influence Priors. https://arxiv.org/abs/2410.20169

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Generalised Covariances and Correlations

The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or thresholds. Deviations from these functionals are defined via generalised errors, typically induced through identification or moment functions. As a normalised measure of dependence, a generalised correlation is constructed. Replacing the common Cauchy--Schwarz normalisation by a novel Fréchet--Hoeffding normalisation, we obtain attainability of the entire interval $[-1, 1]$ for any given marginal distributions. We uncover favourable properties of these new dependence measures and establish consistent estimators. The families of quantile and threshold correlations make it possible to measure local dependence and give rise to function-valued distributional correlations, exhibiting the entire dependence structure. Quantile correlations also lead to tail correlations, new measures of tail dependence, closely related to and refining classical coefficients of tail dependence. Finally, we construct summary covariances (correlations), a class of regional or global dependence measures, which arise as (normalised) weighted averages of distributional covariances. We retrieve covariance, Pearson and Spearman correlation as special cases. The usefulness of our new dependence measures is illustrated on demographic data from the Panel Study of Income Dynamics.

stat.ME↗
arXiv2026

Compressive Bayesian non-negative matrix factorization for mutational signatures analysis

Non-negative matrix factorization (NMF) is a popular tool for dimensionality reduction, especially for count matrices. However, inferring an appropriate number of factors is challenging. Existing approaches based on information criteria or nonparametric sparsity-inducing priors tend to be computationally burdensome or highly sensitive to prior choices. Moreover, theoretical properties of the posterior distribution of Poisson NMF parameters endowed with shrinkage priors remain under-explored. This paper introduces a novel Bayesian NMF method that automatically infers the number of factors while also incorporating information on the latent factors from previous studies. This is achieved using compressive hyperpriors, which are hierarchical priors that make the sample-specific weights of unneeded factors concentrate near zero in the posterior. We provide novel distribution theory for posterior inference to elucidate this shrinkage mechanism, both in finite samples and asymptotically. We apply our method to mutational signatures analysis in cancer genomics, in simulations and on real data from breast cancer. Compared to state-of-the-art alternatives, our method is more robust to mild overdispersion and improves detection and estimation of signatures aligned with prior information.

stat.ME↗
arXiv2026

On Relative Cumulative Residual Information Measure and Its Applications

We develop a relative cumulative residual information measure (RCRI) that aims to quantify the divergence between two survival functions. The dynamic relative cumulative residual information (DRCRI) measure is also introduced. We establish some characterization results under the assumption of the proportional hazards model. Additionally, we obtained the non-parametric estimators of RCRI and DRCRI measures based on the kernel density type estimator for the survival function. The effectiveness of the estimators are assessed through an extensive Monte Carlo simulation study. We consider data from the third Gaia data release (Gaia DR3) to demonstrate the use of the proposed measure. For this study, we have collected epoch photometry data for the objects Gaia DR3 4111834567779557376 and Gaia DR3 5090605830056251776. RCRI-based image analysis is conducted using Chest X-ray data from the publicly available dataset.

stat.ME↗