On Clarke and Barron's Asymptotics of Bayes Codes

• GOTOH Masayuki

  Department of Industrial and Management Systems Engineering, School of Science and Engineering, Waseda University

• MATSUSHIMA Toshiyasu

  Department of Industrial and Management Systems Engineering, School of Science and Engineering, Waseda University

• HIRASAWA Shigeichi

  Department of Industrial and Management Systems Engineering, School of Science and Engineering, Waseda University

Bibliographic Information

Other Title

• Clarke と Barron の Bayesian Asymptotics について

Abstract

The Bayes code is the Bayes optimal solution based on Bayes decision theory. This is the method which uses mixture of all models in model class for coding function. B.S.Clarke and A.R.Barron analyzed asymptotic mean codelength of the Bayes code and showed that Jaffreys' prior is the asymptotically least favorable under entropy risk for i.i.d sources. This paper consists of two parts. At first, we show the asymptotic codelengths of the Bayes codes for individual sequences for the parametric model class. The main condition required here for the parameter space is that the posterior probability of parameter has asymptotic normality. Generally speaking, the asymptotic notmality of posterior distribution distribution holds for other than i.i.d. sources. Secondly, we shall prove that Clarke and Barron's asymptotics of the Bayes code is satisfied for more general model classes than i.i.d. sources. The main conditions required here is the Central Limit Theorem for the maximum likelihood estimates. Since the target of source coding is not usually i.i.d. source, the extension is this paper is effective.

Journal

• IEICE technical report. Information theory

  IEICE technical report. Information theory 96 (494), 73-78, 1997-01-24

  The Institute of Electronics, Information and Communication Engineers

Keywords

• Bayes Code
• Minimax code
• least favorable prior
• Jaffreys' prior

Details

• CRID: 1573105977191278720
• NII Article ID: 110003197175
• NII Book ID: AN10013083
• Text Lang: ja
• Data Source:
  • CiNii Articles