A new likelihood inequality for models with latent variables

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 inequal-ity 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.