Optimal methods for combining discrete p-values.

Abstract:

Combining the significance of multiple experiments regarding the same scientific hypothesis is a crucial method for global hypothesis testing, with applications in meta-analysis, signal detection, and other data-integrative studies.  Such procedures consider a group of p-values, $P_1, \cdots, P_n$, to form a summary statistic to determine the overall evidence against a global null hypothesis. Mathematical studies often assume that the underlying statistics are continuous and independent, due to their homogeneous and straightforward mathematical structure. In reality, however, data and its corresponding statistics are often discrete. Discrete tests present an array of extra challenges that make the continuous framework unsuitable, and calculating the exact distribution of the summary statistic is often computationally challenging. Using tools from optimal transport, we propose an omnibus modification of a discrete statistic towards a continuous probability integral transform and show that, under mild hypothesis, the sum of discrete modifications produces an asymptotically correct test for any type I error control $\alpha \in (0,1)$. Furthermore, by expressing this transformation as a likelihood ratio, we delve into the optimal choice of combination statistic for some common discrete tests.

Date: Apr 03, 2024 at 16:15:00 h
Venue: Sala Multimedia CMM, Piso 6, Beaucheff 851 Edificio Norte.
Speaker: Gonzalo Contador
Affiliation: UTFSM
Coordinator: Avelio Sepúlveda
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Posted on Apr 3, 2024 in Seminario de Probabilidades de Chile, Seminars