[Gretl-users] Bayesian approach in Gretl?

Riccardo (Jack) Lucchetti r.lucchetti at univpm.it
Sun Jun 3 04:14:25 EDT 2007


On Tue, 29 May 2007, Mariusz Doszyń wrote:

> What do you think about implentation of some (basic at first) Bayesian 
> econometric methods in Gretl (for example estimation of linear 
> regression models with natural conjugate priors, Gibbs sampling, ect.)?

This sounds intriguing. Can you be more specific on what you'd like to 
see?

For example, suppose you want to analyse a linear model with Bayesian 
methods: if everything is Gaussian (your priors and the likelihood), then 
the posteriors are Gaussian too, and the output should just show mean and 
variance. But in this case, you can use the old trick of augmenting your 
dataset with some fake observations containing your priors, and you're 
good to go.

Now, what happens if your priors are not Gaussian? Let us just assume for 
the moment that we find a sensible way to let the user say something like 
"\beta_1 is N(0,1), \beta_2 is a uniform and \beta_3 is, conditionally on 
\beta_1 and \beta_2, a gamma with parameters \beta_1^2 and 
floor(4*\beta_2+1)." (Just kidding.)

Then, in general, your posteriors are not Gaussian either, so you'll 
probably need something more than the first two moments. The mode? Most 
definitely. The median? Probably. The interquartile range? Possibly. Best 
of all, maybe, you want a nice graph of the density. Gibbs? Metropolis? 
Something else invented while I wasn't looking? :-)

I'm not trying to dismiss your idea; in fact, as I said, I find it 
tempting. I'm just trying to imgine what the exact details would be.
In general, everything is a bit fuzzy in my mind at the moment.

One thing that could be done in the short term is implement a Gibbs 
(possibly Metropolis) simulator, leaving it to the user to work out its 
connection with the model being estimated. Would that help?


Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche

r.lucchetti at univpm.it
http://www.econ.univpm.it/lucchetti


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