Bayes estimates as an approximation to maximum likelihood estimates

Abstract

AbstractRonald A. Fisher, who is the founder of maximum likelihood estimation (ML estimation), criticized the Bayes estimation of using a uniform prior distribution, because we can create estimates arbitrarily if we use Bayes estimation by changing the transformation used before the analysis. Thus, the Bayes estimates lack the scientific objectivity, especially when the amount of data is small. However, we can use the Bayes estimates as an approximation to the objective ML estimates if we use an appropriate transformation that makes the posterior distribution close to a normal distribution. One‐to‐one correspondence exists between a uniform prior distribution under a transformed scale and a non‐uniform prior distribution under the original scale. For this reason, the Bayes estimation of ML estimates is essentially identical to the estimation using Jeffreys prior.