Conjunction probability of smooth centered Gaussian processes

TL;DR

This paper establishes an accurate upper bound for the conjunction probability of independent Gaussian smooth processes, confirming heuristic approximations and deriving the exact generalized Pickands constant in a specific case.

Contribution

It introduces a precise upper bound for conjunction probability and demonstrates its accuracy, extending understanding of Gaussian process intersections and confirming heuristic methods.

Findings

Upper bound for conjunction probability of Gaussian processes

Approximation with exponentially smaller error

Exact generalized Pickands constant in a special case

Abstract

In this paper we provide an upper bound for the conjunction probability of independent Gaussian smooth processes and then we prove that this bound is a good approximation with exponentially smaller error. Our result confirms the heuristic approximation by Euler characteristic method of Worsley and Friston and also implies the exact value of generalized Pickands constant in a special case. Some results for conjunction probability of correlated processes are also discussed.