# Bayes estimates as an approximation to maximum likelihood estimates

## Abstract

Ronald 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.

## Keywords

Empirical Jeffreys prior Posterior distribution Sika deer population Skewness State-space model Transformation## Notes

### Acknowledgments

I thank Dr. Yukihiko Toquenaga for providing me the opportunity for presenting my idea in a plenary symposium of the 30th Annual Meeting of the Society of Population Ecology. I thank Dr. Mark Louis Taper for giving me many suggestions including the name ‘empirical Jeffreys prior’. I sincerely thank two anonymous reviewers for their comments that helped me in greatly improving the manuscript.

## Supplementary material

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