I’d suggest Phil Gregory’s book Bayesian logical data analysis for the physical sciences. Probability Theory by Edwin Jaynes (who inspired Gregory) is also excellent, albeit wider ranging. Both are quite long. For a shorter introduction try Sivia’ book: Data analysis – A Bayesian tutorial. Bernardo and Smith’s 1994 book Bayesian Theory is perhaps most comprehensive, but quite mathematical.

Kass and Wasserman’s review paper The Selection of Prior Distributions by Formal Rules (J A Stat Soc, 1996) is well worth reading, albeit a bit mathematical. And Don Fraser’s papers are maybe the best at explaining the problems of Bayesian inference with curved parameter-data relationships. Eg. Default priors for Bayesian and frequentist inference (J Roy Stat Soc, 2010).

Phil Gregory’s book here:
http://www.amazon.com/Bayesian-Logical-Analysis-Physical-Sciences/dp/0521150124

http://en.wikipedia.org/wiki/Subjective_logic

Even that tends to have an eye glazing effect on me but I might be able to extract the gist. This bit’s in English fortunately:-

“Arguments in subjective logic are subjective opinions about propositions. A binomial opinion applies to a single proposition, and can be represented as a Beta distribution. A multinomial opinion applies to a collection of propositions, and can be represented as a Dirichlet distribution. Through the correspondence between opinions and Beta/Dirichlet distributions, subjective logic provides an algebra for these functions. Opinions are also related to the belief functions of Dempster-Shafer belief theory.

A fundamental aspect of the human condition is that nobody can ever determine with absolute certainty whether a proposition about the world is true or false. In addition, whenever the truth of a proposition is expressed, it is always done by an individual, and it can never be considered to represent a general and objective belief. These philosophical ideas are directly reflected in the mathematical formalism of subjective logic.”

My simple and uneducated cynicism suggests that the “subjective” philosophy is just formal acceptability for hard-wiring bias into conditionals. Maybe you can update me on that after your reading Andy?

I did follow the BH thread though just to keep up with the play. This by Dung caught my eye:-

“If climate sensitivity to increasing CO2 maxed out at around 240 ppm which ice core records suggest then current sensitivity is zero, hence no warming for 16 years.
Science needs evidence not estimates.”

I’ve no idea where he gets that (the ice core suggestion) from but it does corroborate Prof John Eggert’s graph:-

http://tallbloke.files.wordpress.com/2010/07/eggert-co2.png

And yes I did see Nic’s comment re Annan and your response. That was an enlightening aside, threadworthy in itself for those in the know I suspect.

The issue around modal vs mean and median is fairly fundamental, in my opinion.

In my line of work, we use modal and median or mean depending on the context. It appears to me that a modal average is e beat estimate of ECS

Also, see my comment on the BH thread about Subjective Bayesian priors. As someone trained in maths, this smacks of BS to me.

[Response: All the pdfs are skewed - but using the mode to compare to the mean in previous work is just a sleight of hand to make the number smaller. The WSJ might be happy to play these kinds of games, but don't do it here. - gavin]

I see Nic Lewis’ point Andy (just grasp the stats concept I think) but I find the entire ECS debate spurious given my reading of CO2 radiative transfer from outside of climate science (e.g. combustion engineering). Consequently I follow ECS developments on a purely pragmatic level but I can’t bring myself to get interested in the statistical nuances.

I’d like to be excused from this topic if I may but I think Bob accepts the ECS rationale and might pop up with a comment.

http://www.bishop-hill.net/blog/2013/1/12/lewis-on-schmidt-on-climate-sensitivity.html#comments

http://www.realclimate.org/index.php/archives/2013/01/on-sensitivity-part-i/comment-page-2/#comments

Nic Lewis pops up in comments. There is something here that really stands out to me. They are discussing whether the mean, modal or median is the best average for CS

I agree with Nic Lewis that if you have a skewed PDF with a long tail, as we see in most. CS graphs, then modal , ie the most popular, or peak of the curve, would be best estimate. gavin disagrees. However this is a really basic stats issue.

This seems to me a fairly fundamental point but maybe I am overreacting.

Wonder what his views on averaging GCM ensemble runs (spaghetti graphs) to get a “consensus” are?

They (the IPCC and analysts)) even have standard deviation ranges from the ensemble average as if the average is somehow a reference profile to be relied on.