# Posterior probability

Hi All,

For example, the prior probability of determinacy model vs indeterminacy model is 0.6 vs 0.4 while log data density is -100 vs -105, then should the posterior probability of determinacy model is 0.4/0.6*e^(-100)/[e^(-100)+e^(-105)]? or other rules?

Huan



Dear Huan,

I do not understand what would be the indeterminacy model (in Dynare we do not provide the possibility to estimate models that do not satisfy Blanchard and Kahn conditions). The posterior distribution of the models is

p(\mathcal{I}|\mathcal Y_T) = \frac{p(\mathcal{I})p(\mathcal Y_T|\mathcal{I})} {\sum_{\mathcal{I}=\mathcal{A},\mathcal{B}}p(\mathcal{I})p(\mathcal Y_T|\mathcal{I})}

where p(\mathcal{I}) is the prior probability of model \mathcal I, and p(\mathcal Y_T|\mathcal{I}) is the likelihood of model \mathcal I, i.e. the marginal density of the sample fir model \mathcal I. You just have to replace p(\mathcal Y_T|\mathcal{I}) by the exponential of the logged marginal density returned by Dynare.

Note that Dynare provides a command model_comparison (see the doc here) which may help.

Best,
Stéphane.

Maybe Model Comparison Bayesian Estimation (again) is related

Can you please tell me where the model’s posterior probability output is located?

You mean the marginal data density? That would be oo_.MarginalDensity`