Data analysis: Frequently Bayesian

Despite not being a US citizen and not even having ever gone to one of their meetings, I joined the AGU recently for the princely sum of $20. The main reason for this is to stop them from spamming me with invitations to join :-) No, really it's largely because the discount on the upcoming EGU meeting registration fee is more than the AGU subscription, plus I get some freebies such as a subscription to Physics Today. Actually I can claim the fee for the EGU meeting back off my employer but not the AGU sub, so it does actually cost me money, but it still seems like too good an offer to pass up.

This month they have a nice short article discussing Bayesian and frequentist probability, which is only available to subscribers, so tough luck :-)

Hypothesis tests and the method of maximum likelihood are among the most widely used tools in the analysis of experimental data. But notice that frequentists only talk about probabilities of data, not the probability of a hypothesis or a parameter. The somewhat contorted phrasing that their methods necessitate seems to avoid the questions one really wants to ask, namely, "What is the probability that the parameter is in a given range?" or "What is the probability that my theory is correct?"

(the latter questions are precisely those which Bayesian methods can address).

Of course it's precisely this problem that leads to the contorted and easily misinterpreted language in climate science in general and IPCC SPM in particular. Not that it's particular to climate science - here's a paper complaining about the same situation in high energy physics (and for those who want more, the same author has written a lot of fairly easy reading on the same subject).