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Multi-state

Consider a discrete sample space of M unordered values, e.g.

and sequences of these.

This document is online at   http://www.csse.monash.edu.au/~lloyd/Archive/2005-04-Fin-state/index.shtml   and contains hyper-links to other resources.


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Distribution has M-1 parameters T1, T2, ..., TM-1.   M-1 degrees of freedom.

Also define TM = 1 - T1 - T2 ... - TM-1


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Estimators

From data, observed frequencies are n1, ..., nM, let N = SUMi=1..M ni.

Maximum likelihood: Ti,ML = ni/N   what if ni=0?

Minimum Message Length: Ti,MML = (ni + 1/2)/(N + M/2)

MinEKL estimator: Ti,MinEKL = (ni + 1)/(N + M)   minimum expected Kullback Leibler


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Some uses:


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Hidden Markov Model HMM or PFSA
Note finite number of transitions out of each state of automaton

© L. Allison, School of Computer Science and Software Engineering, Monash University, Australia 3800.
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