The internet was kind this week to those of you who are interested in the philosophical foundations of your statistical methods (and that should be all of you!)
He’s not really saying anything he hasn’t said before, but Andrew Gelman has two new posts up here and here on modern ideas about Bayesian vs. frequentist statistics and how they’re ultimately different approaches with the same ultimate goal. There are bits of Andrew’s point of view with which I might quibble. For instance, in ecology I think we quite often do need the analysis of each study to stand on its own, since different studies consider different questions in different systems. Wanting each study to stand on its own isn’t just some old-fashioned tradition that we can just let go of. It’s also worth emphasizing (which Andrew doesn’t really do in these posts, but which he has emphasized elsewhere) that the sort of Bayesianism that Andrew and Brad are arguing for is very far from the subjective Bayesianism that has long worried folks like Deborah Mayo and Brian Dennis (and me). But these quibbles are really just differences in emphasis; I mostly like what Andrew has to say.
See also here for an accessible (and drily witty) recent perspectives-type piece from famous frequentist Brad Efron. He gives a historical sketch of Bayesian vs. frequentist ideas and ultimately arrives at a modern point of view broadly similar to Andrew’s.
In looking at these recent pieces, I stumbled on some slightly older pieces that are also well worth your time. See here for a great old (2009) post from frequentist statistician and polymath Cosma Shalizi (summarizing a paper of his, arXived here), on how a frequentist can interpret Bayesian methods as a method of “regularization”. “Regularization” is basically just jargon for not overfitting the data. Shalizi’s paper reports some very neat results on the conditions under which Bayesian methods of regularization will converge on the truth, given enough data (at least, they sound like neat results to me, but I’m not a statistical theorist, so what do I know?) Shalizi’s paper also includes some fun linkages between Bayesian updating and “replicator dynamics” in evolutionary theory. In a rather precise formal sense, Bayes’ Rule is evolution by natural selection, in the special case when fitnesses are frequency independent and there’s no mutation. I’m sure this is closely connected to Steven Frank’s work on the deep linkages between evolution by natural selection and information theory, though I haven’t yet worked out how. And as Shalizi notes, it suggests that statisticians ought to look to the general case of evolution by natural selection for inspiration for statistical methods more general than Bayesianism! (What’s the statistical equivalent of, say, random mutation, or frequency-dependent fitnesses?) Anyway, Cosma Shalizi is always good value for money, and so is Steven Frank; click through!
And see here for an arXived version of a 2011 paper in Statistical Science by Robert Kass, articulating a “pragmatic” interpretation of Bayesian and frequentist methods, with implications for how introductory undergraduate statistics is taught. Very interesting and thoughtful.
On a completely different subject: The EEB and Flow has a guest post from Sarah Hasnain on how being a Pakistani woman affects how her fellow ecologists behave towards her. Interesting reflections on how behavior intended as welcoming can come across (presumably unintentionally) to the person at whom it is aimed:
People always came to my posters at conference poster sessions, but a number of them wanted to tell me that they are very glad to have someone “like you” here. One of the determining factors for which PhD labs I wanted to be in was that during the interview, at no point did the potential supervisor asks what made someone from my cultural, ethnic and religious background decide to pursue ecological research. This actually knocked a few labs out of the running.
And it’s undeniable that these comments and questions are about people wanting to be open and accepting and welcoming to me. But I can’t help but feel that the constant questions about my background insinuate, probably unintentionally, that my ethnic, religious and cultural affiliations are more interesting than my research. As an ecologist belonging to a minority group, these questions can have the opposite effect – instead of feeling accepted by their interest, I feel like I am constantly justifying my existence in this field.
Finally, this week’s Nature has an interview with friend of Dynamic Ecology Carl Boettiger about his practice of keeping an “open lab notebook” online for anyone to read.
After coming to the conclusion that–according to existing descriptions of the two approaches–I’m essentially Bayesian in outlook, I still don’t really understand exactly what all the fuss is about. I mean just call it “conditional probability evaluation” and be done with it. Yes, you should use all relevant available data bearing on the topic under study, including “prior” distribution information, of course–why would you ever want to ignore relevant data. Yes, you should evaluate strengths of evidence for different hypotheses/theories for some observed phenomenon. Are those supposed to be some sort of intellectual breakthroughs?? Are they somehow different than concepts already inherent in the concept of maximum likelihood? Apparently to Bayesians, they are.
“His death in 1761 was almost in vain, but his friend Richard Price had Bayes rule, or theorem, published posthumously in the 1763 Transactions of the Royal Society. (Price thought the rule was a proof of the existence of God, an attitude not entirely absent from the current Bayesian literature.)”