Bayes estimates as an approximation to maximum likelihood estimates

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• 作者：Kohji Yamamura
• 关键词：Empirical Jeffreys prior ; Posterior distribution ; Sika deer population ; Skewness ; State ; space model ; Transformation
• 刊名：Population Ecology
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：58
• 期：1
• 页码：45-52
• 全文大小：624 KB
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• 作者单位：Kohji Yamamura (1)
  
  1. National Institute for Agro-Environmental Sciences, 3-1-3 Kannondai, Tsukuba, 305-8604, Japan
  
• 刊物类别：Biomedical and Life Sciences
• 刊物主题：Life Sciences
  Ecology
  Zoology
  Plant Sciences
  Evolutionary Biology
  Behavioural Sciences
  Forestry
  
• 出版者：Springer Japan
• ISSN：1438-390X

文摘

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