For many years, the pairwise comparison method has been widely used for decision-making involving experts. The best-known example of this method is the Analytic Hierarchy Process (AHP). In this now classic approach, the weights of alternatives are calculated using the principal eigenvector of the comparison matrix. In this paper, we present a statistical view of the pairwise comparison method, using reference values and the geometric mean to calculate alternative priorities. Thanks to this approach, we can simultaneously capture both the phenomenon of inconsistency in pairwise comparisons and the preference distance between alternatives. In this paper, we define indicators that measure the quality of the obtained weight vector, which, thanks to the statistical approach, have a clear and intuitive interpretation.
We show that the Benjamini--Hochberg procedure can fail to control the false discovery rate (FDR) at its nominal level for correlated two-sided Gaussian $p$-values. We construct a factor model for which, at level $α=0.01$, a rigorous interval-arithmetic certificate proves $FDR>0.…
Integrating information across related tasks can improve estimation and prediction in transfer, multi-task, and federated learning, but contamination and heterogeneity make robust borrowing challenging. We study a contaminated multi-task empirical risk minimization (ERM) framewor…
Empirical Bayes methods are among the most widely used statistical methods for large-scale inference. A central paradigm is the NPMLE, whose theoretical guarantees are by now well understood for the independent Gaussian sequence model. In this paper, we study empirical Bayes esti…
Language models produce probabilities over words, but professional decisions require uncertainty over meaningful states such as diagnoses, hypotheses or operational conditions. A model's printed numerical confidence does not establish reliability. We introduce a semantic map: a p…
The rise of human-AI collaborative writing has created a growing need for fine-grained detection methods that support localizing likely LLM-generated content in mixed-authorship documents. Existing methods for detecting LLM-generated text mainly focus on document-level classifica…
Neyman--Pearson classification prioritizes one class by constraining its accuracy above a prespecified level, and then takes the accuracy of the other class as the utility objective. This paradigm is well suited for disease screening and diagnosis, among other applications. Stati…