Bayesian Parameter Estimation

Definition

A Bayesian approach to estimating parameter values by updating a prior belief about model parameters (i.e., prior distribution) with new evidence (i.e., observed data) via a likelihood function, resulting in a posterior distribution. The posterior distribution may be summarised in a number of ways including: point estimates (mean/mode/median of a posterior probability distribution), intervals of defined boundaries, and intervals of defined mass (typically referred to as a credible interval). In turn, a posterior distribution may become a prior distribution in a subsequent estimation. A posterior distribution can also be sampled using Monte-Carlo Markov Chain methods which can be used to determine complex model uncertainties (e.g. Foreman-Mackey et al., 2013).