SMML - Binomial

home1 home2
 Bib
 Algorithms
 Bioinfo
 FP
 Logic
 MML
 Prog.Lang
and the
 Book

MML
 Glossary
 SMML

Bin'l MML68,87
DPA .hs
Leigh

Strict Minimum Message Length (SMML) inference partitions the data space.

Problem: Given N, devise an optimal code for a two-part message to transmit (i) a point-estimate and (ii) a sequence of N Bernoulli trials (throws of a coin). This problem has a convenient sufficient statistic - the head count. The code-book for #heads amounts to a partition of [0..N].

For this problem there is a polynomial-time algorithm (equivalent to Dijkstra's shortest-paths algorithm) to find an optimal partition of [0..N] and so construct an optimal code-book (Farr & Wallace 1997, 2002).

Assuming a uniform-prior on the parameter theta=Pr(head)...

N=

See:

  • G. E. Farr & C. S. Wallace. The Complexity of Strict Minimum Message Length Inference. The Computer Journal 45(3), pp285-292, 2002. Also, TR 97/321, Department of Computer Science, Monash University (Clayton), Victoria 3168, Australia, 11 August 1997.
    NB. Their message lengths are for transmitting Pr(head) & #head only, i.e. excluding the sequence of throws.
Coding Ockham's Razor, L. Allison, Springer

A Practical Introduction to Denotational Semantics, L. Allison, CUP

Linux
 Ubuntu
free op. sys.
OpenOffice
free office suite
The GIMP
~ free photoshop
Firefox
web browser

© L. Allison   http://www.allisons.org/ll/   (or as otherwise indicated),
Faculty of Information Technology (Clayton), Monash University, Australia 3800 (6/'05 was School of Computer Science and Software Engineering, Fac. Info. Tech., Monash University,
was Department of Computer Science, Fac. Comp. & Info. Tech., '89 was Department of Computer Science, Fac. Sci., '68-'71 was Department of Information Science, Fac. Sci.)
Created with "vi (Linux + Solaris)",  charset=iso-8859-1,  fetched Tuesday, 16-Jul-2024 13:57:00 AEST.