Possibilistic Inferential Models for Gaussian Mixture Models: Inference and Prediction

Thomas M. Menino Convention & Exhibition Center 

The Gaussian mixture model has long been a staple of nonparametric density estimation, but while these models are highly flexible, inference often poses a number of non-trivial challenges. The possibilistic inferential model (IM) overcomes these challenges by offering inference with exact frequentist coverage in all sample sizes while enjoying probability-like interpretation in the style of Bayesian methodologies. Recent computational advances allow us to efficiently evaluate this IM's output. We compare existing methods with a new, more flexible approach and highlight its superior performance in challenging models like the Gaussian mixture. This paper goes on to demonstrate that this exact coverage can be leveraged into desirable behavior in ``downstream'' tasks, such as prediction and model selection, through the use of Choquet integrals. A real-data application is offered in support of the methods using the Galaxy data, a common benchmark for work in Gaussian mixture models.

Model Selection

Valid

Exact Coverage

Finite Sample

Density Estimation 

Section on Nonparametric Statistics