Question about Bayesian estimation?


#1

Dear Professor Pfeifer,

I have ecountered a problem when doing the Bayestion estimation. Would you please give some advice? Thank you very much.

Question description:
The parameter gamma is the one that I want to estimate in the model. I set its prior mean as 2 for example, and then run the code. The Dynare displays that ‘‘Initial value of the log posterior (or likelihood): -729.6099’’.
When I change its prior mean to 0.5, Dynare displays that ‘‘Initial value of the log posterior (or likelihood): -1734452.5732’’, which is a very large number.
(1) Does this mean that setting prior mean at 2 is better than 0.5?
(2) When I write the estimated_params block, I write like
‘‘rhoR,0.5,BETA_PDF,0.5,0.2;’’
But I do not quite understand what is the meaning of first ‘‘0.5’’? and in what situation should I change it ?

Any reply will be appreciated. Thank you !


#2

(1) What exactly is the parameter gamma? Not sure if the mean of 2 is necessarily ‘better’ than the mean of 0.5. Obviously the shift in the prior mean alters the posterior density quite a bit, but I am not sure that is for the ‘better’ or for the ‘worse’. Depends on what you are aiming to achieve.

(2) 0.5 is the initial value used to evaluate the posterior density. If you do not specify that, then the prior mean becomes the initial value by default.

Reuben