normal-gamma

A useful choice of any particular prior, normal gamma priors included, in a statistical problem involving the mean and variance parameters of a normal should reflect one's prior knowledge of the values of these parameters in the problem. Consulting the plots of normal gamma priors, an opinion about the adequacy of one's choice in representing, by the choice of parameters in the prior, one's prior knowledge about the mean and variance of the unknown normal distribution can be formed. There are sophisticated methods, but just eyeballing the plots should not be too bad. Typically the prior knowledge is imprecise so the particular family of distributions, like normal-gammas, is probably not crucial; the choice of parameters of the prior should perhaps reflect the prior opinion about means and variances of the unknown mean and variance. If the normal gamma priors do not reflect the approximate shape of the "known" prior, one can use other models that do the job. Then computations must typically be done numerically. What is the cost of misspecification of the prior? In large samples the posterior distribution of the mean, for example, will be roughly normal centered at the maximum likelihood estimator as long as the original prior meets certain specifications. The normal gamma priors meet these so the choice of any particular normal gamma prior should not have serious deleterious effects on the inference in large samples.