A Physicist's Introduction to Bayesian Statistics. II
D E Raeside · American Journal of Physics · 1972
This sequel to an earlier paper applies Bayesian estimation theory to several probability distributions of importance in physics [Poisson, Maxwell, Rayleigh, exponential, Druyvesteyn, and Gauss (zero mean) distributions]. A single tractable and physically interesting loss function (the square of the relative estimation error) is utilized. Bayes estimates are obtained by using a single conjugate prior distribution (the gamma distribution) and the vague prior limit is taken. The estimates obtained tend to the mean values of the respective posterior distributions for large sample sizes. A practical aspect of the theory is demonstrated by obtaining an optimal estimate of the most probable speed for a Maxwell distribution of speeds.