PHYSTAT Informal Review: Marginalizing versus Profiling of Nuisance Parameters

Understand

This is a writeup, with some elaboration, of the talks by the two authors (a physicist and a statistician) at the first PHYSTAT Informal review on January 24, 2024.

• We discuss Bayesian and frequentist approaches to dealing with nuisance parameters, in particular, integrated versus profiled likelihood methods.
• In regular models, with finitely many parameters and large sample sizes, the two approaches are asymptotically equivalent.
• But, outside this setting, the two methods can lead to different tests and confidence intervals.