After running OLS regressions of hedge funds' excess returns with respect to its benchmark excess return, I found that t-statistics of alpha can be unreasonably high (around 60) which could be due to short track record and noise. I would like to improve estimates of alpha and t-statistic of alpha using a Bayesian linear regression. I found a paper http://limnology.wisc.edu/regime/appendix_14jul03.pdf that gives guidance on implementation of Bayesian linear regression. I'm particularly interested in linear regression with informative prior when the prior distribution of regression parameters (alpha, beta) is multi-variate Student distribution (p 10). I am comfortable with specifying values of 0 for alpha and 1 for beta as expected values of the prior distribution. The other three inputs include the parameters covariance matrix S0, model variance s02 and degrees of freedom n0. I would appreciate any advice in how I can approach defining those in a meaningful way as well as explanation of the meaning of the model variance s02 as I don't have a clear idea of what it means.

See Kitagawa and Gerch, "Smoothness Priors Analysis of Time Series". You will find the Monte Carlo "particle filter" algorithms especially helpful for what you are trying to do.