Papers and Books of interest:

Rabiner, L. R., A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition, Proceedings of the IEEE, vol. 77, no. 2, Feb. 1989, pgs 257 - 285. There is a lot of notation but verbose explanations accompany.

Dodge, Charles and Jerse, Thomas A. Computer Music: Synthesis, Composition, and Performance, 2nd ed., Shirmer Books: New York, 1997. pgs 361-368 are of particular interest - composing music with markov chains.

Grimmett, G.R. and Stirzaker, D.R. Probability and Random Processes, 2nd ed., Clarendon Press: Oxford, 1994. Chapter 6 is on Markov chains, intended for advanced undergrads.

Isaac, Richard. The Pleasures of Probability, Springer: New York, 1995. Chapter 16 is on Markov Chains, intended for undergrads.

Paulos, John Allen. A Mathematician Reads the Newspaper, BasicBooks: New York, 1995. pgs. 72-73, 135-137 have explanations of how conditional probability arises in the real world.

Stewart, Ian. The Magical Maze, Weidenfeld & Nicolson:London, 1997. Intended for general audience, pgs 87-98 have some interesting thoughts on conditional probability.

Bookmarks for Markov Chains (Hidden and Normal)

Markov Models


Some software packages (mainly for specific applications) involving Hidden Markov Models

Hidden Markov Model (HMM) White Paper
A pitch for GeneMatcher, a software package that uses HMM structure to recognize genes
HMMpro: a hidden Markov model (HMM) simulator
Software intended to build statistical models of proteins and gene sequences.
Myers' Hidden Markov Model software
Software intended to be used for

Explanations and Exercises

Hidden Markov Models
A sketchy adaptation of other explanations of HMMs.
Hidden Markov Models
A very good explanation of HMMs, with explanation of their use in speech recognition
Markov Model Exercise
An exercise of a markov model of the progress of diabetes, with a simulation based on this structure.
Lecture 7: hidden Markov models
A bunch of slides from a lecture on HMMs, some good pictures, but difficult to decipher without the original lecture.
Markov Chains
Lecture notes on Markov Chains, some of which are difficult to read. Look at the examples.


Hidden Markov Models for Interactive Learning of Hand Gestures
Audiovisual Sensory Integration Using Hidden Markov Models
Using Markov Models and Hidden Markov Models to Find Repetitive Extragenic Palindromic Sequences in Escherichia coli
Finding Genes in Human DNA with a Hidden Markov Model
Hidden Markov Model: Concept
Starner's work with American Sign Language and Hidden Markov Models
schro97: Pattern Recognition of International Crises using Hidden Markov Models
Hidden Markov model sequence analysis
Are the Hidden Markov Models Promising in Protein Research ?


William M. Spears: Publications about Markov Chains
Statistics of Hidden Markov Models