# Using posteriors as priors in Bayesian estimation

Hi,

I am trying to figure out if it is possible to use posteriors that are coming out of Bayesian estimation as priors for another Bayesian estimation exercise.

For instance if there are 2 rolling estimations, I would like to use the posteriors that are coming out from the 1st estimation as priors for the 2nd estimation. Is that doable in dynare?

Thank you very much,
b

Hi

If I understand correctly you want to split the sample in two parts and use the first part as a prior for the estimation on the second sub-sample. In this case I don’t think you need to do anything because it’s perfectly equivalent to estimate with the whole sample. Let Y be the sample and Y_0 and Y_1 be the two subsamples. Let theta be the vector of estimated parameters. The likelihood of the
model is:

p(Y|theta)

which, by virtue of the Bayes theorem, can be rewritten as:

p(Y_1|Y_0,theta)*p(Y_0|theta)

the second term can then be interpreted as a prior for the estimation with the second sub-sample. Obviously we can add a prior density for theta, but this does not change the way we can decompose the likelihood.

If I misunderstand your problem, you can use a posterior as a prior for a model by fitting the prior density on the posterior draws from the metropolis hastings. But there is nothing in Dynare to do this an you have to code it yourself…

Best regards,
Stéphane.

Hi Stephane,

Thank you very much for the reply. I might have to code it myself then.