Computational algorithms in bayesian inferences for a normal mean with t prior distributions

Bayesian inference is considered when both the likelihood and the prior distributions are t-densities. Some efficient calculational algorithms in basic normal inference problems concerning the mean over a range of the prior parameters are compared. The algorithms discussed include an approximation via Taylor expansion, the Naylor-Smith algorithm, and the exact formulas developed earlier. Each of them has some drawbacks in terms of accuracy or speed. A combination for efficient calculation over a grid of the prior parameters is suggested.