Dear Johannes,

Thank you for your guidance, I am grateful.

I am wondering that does log marginal likelihood obtained in Dynare output is the same as log posterior predictive probability?

Thank you very much and look forward to hearing from you.

Best regards,

Jesse

Terminology differs, but we are talking about the density of observing the data Y_t from the first observation to t, given your model at hand M, i.e. p(Y_{1:t}|M)

As such, it is the constant of proportionality for the posterior density, i.e the numerator in

p(\theta|Y_{1:t};M)=\frac{p(Y_{1:t}|\theta;M)p(\theta|M)}{p(Y_{1:t}|M)}

where \theta denotes the parameter vector