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Declaration of Originality
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
(N=30)
Expected Kullback-Leibler Distance
Relative Expected Kullback-Leibler Distance
Expected Kullback-Leibler Distance conditional upon
(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
Edmund Lam
2000-12-04