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.