Last year, a paper of mine (Lewis 2014) showing that the approach used in Frame et al (2005), which argued for using a uniform prior for estimating equilibrium (strictly, effective) climate sensitivity (ECS), in fact led to a unique, objective Bayesian estimate for ECS upon undertaking a simple transformation (change) of variables. The estimate was lower, and far better constrained at the upper end, than the one resulting from use of a uniform prior in ECS, as recommended in Frame et al (2005) when estimating ECS. The only uniform priors involved were those for estimating posterior probability density functions (PDFs) for observational variables with Gaussian (normally distributed) data uncertainties, where they are totally noninformative and their use is uncontroversial. I wrote an article about Lewis (2014) at the time, and a version of the paper is available here.
I’ve now had a new paper that uses an essentially identical method to Lewis (2014), but with updated, higher quality data, published by Climate Dynamics, here. A copy of the accepted version is available on my web page, here.