A Novel Bayesian Parameter Mapping Method for Estimating the Parameters of an Underlying Scientific Model

Abstract

Population-parameter mapping (PPM) is a method for estimating the parameters of latent scientific models that describe the statistical likelihood function. The PPM method involves a Bayesian inference in terms of the statistical parameters and the mapping from the statistical parameter space to the parameter space of the latent scientific parameters, and obtains a model coherence estimate, P(coh). The P(coh) statistic can be valuable for designing experiments, comparing competing models, and can be helpful in redesigning flawed models. Examples are provided where greater estimation precision was found for small sample sizes for the PPM point estimates relative to the maximum likelihood estimator (MLE).

Keywords:

• Model coherence
• Multinomial modeling
• Population-parameter mapping

Mathematics Subject Classification:

• 62C10
• 62P15
• 62F10
• 62F15