Contents

• Contents
• List of Figures
• Introduction
  • Minimum Message Length principle
  • Invariance of Minimum Message Length Inference
• Derivation of the second-order MML estimator
  • Fundamental MML approximation
  • Symmetric coding region
  • Midpoint rule approximation
  • Taylor Series approximation
  • Decodability of spacing Parameter
  • Observed Fisher vs Expected Fisher
  • Multi-variate distributions
  • Optimal lattice constant
• MMLD
  • Derivation of optimal univariate coding region
  • Extension onto multi-variate distributions
  • Point estimation of the parameter
• Asymmetric Coding Region
• Fourth Order extension
  • Derivation of optimal spacing
  • Point estimation of the parameter
  • Extension onto multi-variate distributions
• Binomial Distribution
  • Second Order extension
  • Fourth Order extension
  • MMLD
• Methodology and Results
  • Kullback-Leibler Distance
  • Root-Mean-Square Distance
• Further Work and Conclusion
  • Further Work
  • Conclusion
• Acknowledgements
• Bibliography
• Poisson Distribution
  • Implementation of Poisson experiment
  • Preliminary Results
• Gaussian Distribution
• Root-Mean-Square
• Tables
  • Expected Kullback-Leibler Distance conditional upon $\theta$ (N=30)
  • Expected Kullback-Leibler Distance
  • Relative Expected Kullback-Leibler Distance
  • Expected Kullback-Leibler Distance conditional upon $\theta$ (N=30)
  • Expected Root-Mean-Square Distance
  • Relative Expected Root-Mean-Square Distance
• Source Code
  • Makefile
  • algorithm.h
  • mml.h, mml.c
  • alpha.h, alpha.c
  • beta.h, beta.c
  • delta
  • gamma.h, gamma.c