Anytime-Valid Inference for Multinomial Count Data

TL;DR

This paper develops a comprehensive framework for anytime-valid inference in experiments involving count data, enabling continuous monitoring and hypothesis testing in non-stationary environments with practical industry applications.

Contribution

It introduces sequential tests and confidence sequences for multinomial, Bernoulli, and Poisson processes, addressing non-stationarity and enabling real-time inference.

Findings

Provides practical sequential testing methods for count data

Develops confidence sequences for various count-based models

Demonstrates industry applications of the proposed methods

Abstract

Many experiments are concerned with the comparison of counts between treatment groups. Examples include the number of successful signups in conversion rate experiments, or the number of errors produced by software versions in canary experiments. Observations typically arrive in data streams and practitioners wish to continuously monitor their experiments, sequentially testing hypotheses while maintaining Type I error probabilities under optional stopping and continuation. These goals are frequently complicated in practice by non-stationary time dynamics. We provide practical solutions through sequential tests of multinomial hypotheses, hypotheses about many inhomogeneous Bernoulli processes and hypotheses about many time-inhomogeneous Poisson counting processes. For estimation, we further provide confidence sequences for multinomial probability vectors, all contrasts among probabilities of inhomogeneous Bernoulli processes and all contrasts among intensities of time-inhomogeneous Poisson counting processes. Together, these provide an "anytime-valid" inference framework for a wide variety of experiments dealing with count outcomes, which we illustrate with a number of industry applications.