# Continuous testing for Poisson process intensities: A new perspective on scanning statistics

## TL;DR

This paper introduces a continuous testing framework for Poisson process intensities, enabling rigorous, non-asymptotic control of error rates and extending traditional scanning window methods with new test statistics and Monte Carlo estimation.

## Contribution

It presents a novel continuous testing approach for Poisson processes that controls error rates non-asymptotically and introduces kernel-based test statistics.

## Key findings

- Framework effectively controls family-wise error rate and false discovery rate.
- Method successfully applied to Neurosciences and Genomics data.
- Provides a Monte Carlo-based estimation for p-value processes.

## Abstract

We propose a novel continuous testing framework to test the intensities of Poisson Processes. This framework allows a rigorous definition of the complete testing procedure, from an infinite number of hypothesis to joint error rates. Our work extends traditional procedures based on scanning windows, by controlling the family-wise error rate and the false discovery rate in a non-asymptotic manner and in a continuous way. The decision rule is based on a \pvalue process that can be estimated by a Monte-Carlo procedure. We also propose new test statistics based on kernels. Our method is applied in Neurosciences and Genomics through the standard test of homogeneity, and the two-sample test.