Astrophysicist Andrew Jaffe pointed me to this and discussion of my philosophy of statistics (which is, in turn, my rational reconstruction of the statistical practice of Bayesians such as Rubin and Jaynes). Jaffe's summary is fair enough and I only disagree in a few points:

1. Jaffe writes:

Subjective probability, at least the way it is actually used by practicing scientists, is a sort of "as-if" subjectivity -- how would an agent reason if her beliefs were reflected in a certain set of probability distributions? This is why when I discuss probability I try to make the pedantic point that all probabilities are conditional, at least on some background prior information or context.

I agree, and my problem with the usual procedures used for Bayesian model comparison and Bayesian model averaging is not that these approaches are subjective but that the particular models being considered don't make sense. I'm thinking of the sorts of models that say the truth is either A or B or C. As discussed in chapter 6 of BDA, I prefer continuous model expansion to discrete model averaging.

Either way, we're doing Bayesian inference conditional on a model; I'd just rather do it on a model that I like. There is some relevant statistical analysis here, I think, about how these different sorts of models perform under different real-world situations.

2. Jaffe writes that I view my philosophy as "Popperian rather than Kuhnian." That's not quite right. In my paper with Shalizi, we speak of our philosophy as containing elements of Popper, Kuhn, and Lakatos. In particular, we can make a Kuhnian identification of Bayesian inference within a model as "normal science" and model checking and replacement as "scientific revolution." (From a Lakatosian perspective, I identify various responses to model checks as different forms of operations in a scientific research programme, ranging from exception-handling through modification of the protective belt of auxiliary hypothesis through full replacement of a model.)

3. Jaffe writes that I "make a rather strange leap: deciding amongst any discrete set of parameters falls into the category of model comparison." This reveals that I wasn't so clear in stating my position. I'm not saying that a Bayesian such as myself shouldn't or wouldn't apply Bayesian inference to a discrete-parameter model. What I was saying is that my philosophy isn't complete. Direct Bayesian inference is fine with some discrete-parameter models (for example, a dense discrete grid approximating a normal prior distribution) but not for others (for example, discrete models for variable selection, where any given coefficient is either "in" (that is, estimated by least squares with a flat prior) or "out" (set to be exactly zero)). My incoherence is that I don't really have a clear rule of when it's OK to do Bayesian model averaging and when it's not.

As noted in my recent article, I don't think this incoherence is fatal--all other statistical frameworks I know of have incoherence issues--but it's interesting.

## Recent Comments

C Ryan King:I'd say that the previous discussion had a feature which read moreK? O'Rourke:On the surface, it seems like my plots, but read moreVic:I agree with the intervention-based approach -- spending and growth read morePhil:David: Ideally I think one would model the process that read moreBill Jefferys:Amplifying on Derek's comment: http://en.wikipedia.org/wiki/Buridan%27s_ass read moreNameless:It is not uncommon in macro to have relationships that read morederek:taking in each others' laundry It's more like the farmer read moreDK:#17. All these quadrillions and other super low p-values assume read moreAndrew Gelman:Anon: No such assumption is required. If you multiply the read moreanon:Doesn't this rely on some form of assumed orthogonality in read moreAndrew Gelman:David: Yup. What makes these graphs special is: (a) Interpretation. read moreDavid Shor:This seems pretty similar to the "Correlations" feature in the read moreDavid W. Hogg:If you want probabilistic results (probabilities over outcomes, with and read moreCheryl Carpenter:Bob is my brother and he mentioned this blog entry read moreBob Carpenter:That's awesome. Thanks. Exactly the graphs I was talking about. read more