marginalize out the density field!

In studies of the baryon acoustic feature, we like to get all Bayesian about the cosmological parameters, but then we apply all that machinery to the measured two-point functions, which are created with non-Bayesian single-point estimators! I spent a chunk of today discussing that problem with Iain Murray, who is visiting NYU for the week. Murray may have a straightforward solution to this problem, in which we try to write down the probability of the data given a density field times the probability of the density field given a two-point function. Then we can marginalize out the density field and we are left with a probability of the data given the two-point function. That would be exactly the full likelihood function we all need! It might be necessary to either approximate or else use a lot of compute cycles, but even approximate likelihood functions ought to beat single-point estimators.

I pointed out to Murray that if we are spending tens of millions (or billions, maybe?) of dollars on hardware to measure the baryon acoustic feature, it might be worth spending a few bucks to improve the inference we use to exploit it.