Simple Metropolis: Normal Precision - Gamma

1. Simple Metropolis: Normal Precision Gamma. Suppose X = 2 was observed from the p0pulation distributed as N (0, g) and one wishes to estimate the parameter 9. (Here 6 is the reciprocal of the variance 02 and is called the precision parameter). Suppose the analyst believes that the prior on 6' is Qa(1/2, 1). Using Metmpolis algorithm, approximate the posterior distribution and the Bayes' esti- mator of 6'. As the proposal distribution, use gamma (Jam, ,3) with parameters a, 5 selected to ensure efcacy of the sampling (this may require some experimenting)