Exploring the reliability of Bayesian reconstructions

The Bayesian approach allows one to combine measurement data with prior knowledge about models of reality to draw inferences about the validity of those models. The posterior probability quantifies the degree of certainty one has about those models. We propose a method to explore the reliability, or uncertainty, of specific features of a Bayesian solution. If one draws an analogy between the negative logarithm of the posterior and a physical potential, the gradient of this potential can be interpreted 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.