A new likelihood inequality for models with latent variables

Niels Aske Lundtorp Olsen

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Abstract

Likelihood-based approaches are central in statistics and its applications, yet often challenging since likelihoods can be intractable. Many methods such as the EM algorithm have been developed to alleviate this. We present a new likelihood inequality involving posterior distributions of a latent variable that holds under conditions similar to the EM algorithm. Potential scopes of the inequality includes maximum-likelihood estimation, likelihood ratios tests and model selection. We demonstrate the latter by performing selection in a non-linear mixed-model using MCMC.

Original languageEnglish
Article number109998
JournalStatistics and Probability Letters
Volume206
Number of pages6
ISSN0167-7152
DOIs
Publication statusPublished - Mar 2024

Keywords

  • Latent variables
  • Likelihood theory
  • Model selection
  • Statistical Inference

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