DeepAI AI Chat
Log In Sign Up

Are profile likelihoods likelihoods? No, but sometimes they can be

03/01/2019
by   Alan Huang, et al.
The University of Queensland
0

We contribute our two cents to the ongoing discussion on whether profile likelihoods are "true" likelihood functions, by showing that the profile likelihood function can in fact be identical to a marginal likelihood in the special case of normal models. Thus, profile likelihoods can be "true" likelihoods insofar as marginal likelihoods are "true" likelihoods. The prior distribution that achieves this equivalence turns out to be the Jeffreys prior. We suspect, however, that normal models are the only class of models for which such an equivalence between maximization and marginalization is exact.

READ FULL TEXT

page 1

page 2

page 3

page 4

01/13/2018

Is profile likelihood a true likelihood? An argument in favor

Profile likelihood is the key tool for dealing with nuisance parameters ...
01/30/2013

On the Semi-Markov Equivalence of Causal Models

The variability of structure in a finite Markov equivalence class of cau...
03/24/2022

Learning Optimal Test Statistics in the Presence of Nuisance Parameters

The design of optimal test statistics is a key task in frequentist stati...
02/18/2020

Observational nonidentifiability, generalized likelihood and free energy

We study the parameter estimation problem in mixture models with observa...
01/08/2018

Monte Carlo modified profile likelihood for panel data models

The main focus of the analysts who deal with panel data is usually not o...
01/08/2018

Monte Carlo modified profile likelihood in models for clustered data

The main focus of the analysts who deal with clustered data is usually n...
03/27/2018

MLE-induced Likelihood for Markov Random Fields

Due to the intractable partition function, the exact likelihood function...