# Can double dipping be reasonable?

I found a paper where the authors used bayesian methods to estimate asymmetric effects in impulse response functions. In short the estimation procedure is:

1. Calculate a VAR and Impulse responses (no matter what identification strategy).
2. Express this IRF´s as a a set of gaussian basis function. (This reduces the number of parameter)
3. Use this estimates as the initial guess (=prior?) of a Metropolis-Hastings Algorithm.

All steps use the same data.

I'm a bit confused if it makes sense to extract the prior information from the same data where the MCMC algorithm will be used in the next step? I learned that "double dipping" is a problem in bayesian statistics. Since it is a relatively well-known paper, I assume that there is an explanation for this point, but I don't get it.

## 1 Answer

Looking at the overall pattern you describe: yes this could be reasonable (or, it's not obviously unreasonable).

Why? The starting position for MCMC can be arbitrarily chosen. So long as the chain is run to stationarity. Choosing a reasonable starting position will reduce compute time.

You do have to look out for some problems though. In the case of a multimodal distribution, starting multiple chains at the same mode could fool you into believing you've sampled the whole space when you have not (but this is a special problem).

Using the data to form a prior is a conceptually separate issue, which sometimes goes under the name of empirical Bayes. Empirical Bayes is neither wrong nor right.

In my opinion it's often safe to extract some extremely general information from a dataset using empirical Bayes. E.g. extract the range of possible values |max - min| of the data in order to calibrate, say, a prior on the variance of some parameter - is it 10^1 or 10^6? But not, e.g. what was the value of unit $$i$$ at time $$t$$?

• Thank you very much. You gave me exactly the buzzwords I needed to know :) (sorry for the late acceptance -> I did some readings first) – Martin Feb 13 at 15:43