Bayesian updating - which distribution to use I'd like to use Bayesian updating to form price expectations to be used in another model. I'm very new to this area, so your help would be highly appreciated. 
I'm not sure which distribution to use for the prior. When I use normal distribution, I do not get much variability between prior and posterior. However it would be better if there is more variability.
Would it better to use beta or Gaussian distributions for the prior? If so, can I use java for coding? Again because of the model limitations, I cannot use winbugs. 
Many thanks! 
Erin 
 A: It depends! The prior is supposed to capture what you already know (or don't know) about the posterior distribution. If you're very confident that the price about \$1000, then a normal distribution with $\mu=\$1000$ and a small variance is a good choice, since new information should only slightly update your beliefs about the item's price. If you're less certain, a larger variance would allow the same update to affect the posterior more.
On the other hand, normal distributions are non-zero for negative values, which may be a little weird for a price. A gamma distribution might be a good choice for two reasons:


*

*It's only got support for positive values (which makes sense for pricing something)

*It's a conjugate prior for the normal distribution, so the posterior would also be normal.


As I recall, beta distributions (of the first kind) only take values between zero and one, which might not be ideal for a price, and also aren't conjugate to normal distributions (though they are to binomials). The beta prime might be a slightly better choice than beta, but I might still go with a gamma distribution. 
All that said, you can use nearly anything you want for a prior, ranging from very specific (e.g., N(1000,0.10)) to the uninformative priors (e.g., Jeffery's prior), and you should pick one based on your prior beliefs and application.
As for platform, there are lots of Bayesian libraries for Java. You may find this blog post helpful: Gibbs sampler in various languages (revisited)
