Let's Practice What We Preach: Likelihood Methods for Monte Carlo Data

• Activity Number: 481
• Type: Invited
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Xiao-Li Meng*+
• Companies: Harvard University
• Keywords: Bridge Sampling ; Empirical Likelihood ; MCMC ; Monte Carlo Integration ; Normalizing Constant ; Semi-parametric models

Abstract

A central challenge in statistical inferences with real data is that all models are wrong. Ironically, when we apply likelihood methods to Monte Carlo data, we face the opposite problem of knowing too much because they are simulated from a completely known model. Simply treating our direct computational ``estimand", such as a Bayes factor, as our ``unknown" model parameter turns out to be inadequate. This talk outlines recent progresses on a semi-parametric likelihood approach proposed by Kong, McCullagh, Meng, Nicolae, and Tan (2003, JRSSB), which formulated this inference problem by treating the underlying baseline measure as the model parameter and by modeling how much known information about the measure is ignored by the Monte Carlo simulation. All Monte Carlo integrals are then estimated as linear functionals of the MLE of the baseline measure. This approach not only shows that standard methods such as importance sampling and more generally bridge sampling are MLEs and thus they are the best possible ones for the amount information we typically ignore, but more importantly it leads to new estimators, if we allow ourselves to ignore less, that are more efficient.