Objective Bayesian parameter estimation: Incorporating prior information

Climate Audit

A guest article by Nic Lewis

Introduction

In a recent article I discussed Bayesian parameter inference in the context of radiocarbon dating. I compared Subjective Bayesian methodology based on a known probability distribution, from which one or more values were drawn at random, with an Objective Bayesian approach using a noninformative prior that produced results depending only on the data and the assumed statistical model. Here, I explain my proposals for incorporating, using an Objective Bayesian approach, evidence-based probabilistic prior information about of a fixed but unknown parameter taking continuous values. I am talking here about information pertaining to the particular parameter value involved, derived from observational evidence pertaining to that value. I am not concerned with the case where the parameter value has been drawn at random from a known actual probability distribution, that being an unusual case in most areas of physics. Even when evidence-based probabilistic prior information…

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