The Hard Truth

Bayesian methodology provides the means to combine prior knowledge about competing models of reality and available data to draw inferences about the validity of those models. The posterior quantifies the degree of certainty one has about those models. We propose a method to determine the uncertainty in a specific feature of a Bayesian solution. Our approach is based on an analogy between the negative logarithm of the posterior and a physical potential. This analogy leads to the interpretation of gradient of this potential as a force that acts on the model. As model parameters are perturbed from their maximum a posteriori (MAP) values, the strength of the restoring force that drives them back to the MAP solution is directly related to the uncertainty in those parameter estimates. The correlations between the uncertainties of parameter estimates can be elucidated.