Slides that I prepared for a talk titled “Bayesian parameter esimation with weak data and when combining evidence: the case of climate sensitivity” that I gave at the July 2016 CliMathNet conference are available at https://niclewis.files.wordpress.com/2016/07/bayesian-parameter-estimation-with-weak-data-ecs-slides_all.pdf. A version with explanatory notes included is available at https://niclewis.files.wordpress.com/2016/07/bayesian-parameter-estimation-with-weak-data-ecs-slidesnotes_all.pdf.
The method used to combine evidence is novel. It differs from, and is incompatible with, the standard Bayesian updating method that is accepted as valid by the vast majority of Bayesians. The new method provides much superior probability matching, and in the case considered its results agree closely with those using a non-Bayesian likelihood ratio method.
A 2013 paper of mine (arXiv: non-peer reviewed) that develops, expressed in terms of modifying Bayesian updating, the objective method that I use to combine estimates is available here.
I have written a paper that sets out in more detail the new method and its application to combining evidence regarding a parameter, exemplified by climate sensitivity, that can be regarded as the ratio of two approximately normally-distributed variables. A copy of the manuscript, titled “Combining independent Bayesian posteriors into a confidence distribution, with application to estimating climate sensitivity”, is available here. It has been accepted for publication by Journal of Statistical Planning and Inference.
Slides, with notes, for a seminar I gave at Reading University Department of Meteorology in October 2016 are available here