William Morris writes:
A discussion of the use of Bayesian estimation in calculating climate sensitivity (to doubled CO2) occurred recently in the comments at the And Then There’s Physics (ATTP) blog.
One protagonist, ‘niclewis’, a well known climate sensitivity researcher, uses the Jeffreys prior in his estimations. His estimations are always at the low end of the range and the suggestion is that using Jeffreys prior may be part of the reason. The prior has a peak at zero – a physically implausible value for climate sensitivity. There is much too and fro in the discussion . . . which you will doubtless not want to read in full.
I know from reading your blog that you are an authority on Bayesian estimation. Would you have the patience to give your opinion on the blog (or just to me if you prefer) – is the Jeffreys prior a good choice for estimating climate sensitivity?
Despite what the Wikipedia entry says, there’s no objective prior or subjective prior, nor is there any reason to think the Jeffreys prior is a good idea in any particular example. A prior distribution, like a data distribution, is a model of the world. It encodes information and must be taken as such. Inferences can be sensitive to the prior distribution, just as they can be sensitive to the data model. That’s just life (and science): we’re always trying to learn what we can from our data.
I’m no expert on climate sensitivity so I can’t really comment on the details except to say that I think all aspects of the model need to be evaluated on their own terms. And there is no reason to privilege “the likelihood,” which itself will be based on modeling assumptions.
P.S. See here for some general discussion of objectivity and subjectivity.