The Mathematical Garden

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Mathematical methods
HMMs
Introduction
The HMM
Estimate alpha
Simulate a HMM
Estimation of alpha
Extension of the model
Summary and references
Mathematical Induction
Pigeonhole principle
Random Walk
Solving Linear Systems

Hidden Markov Models

Hidden Markov Models (HMMs) are widely used in science, engineering and many other areas. In a HMM, there are two types of states: the hidden states and the observable states. Here we present a HMM via the framework of classical Markov chain model. A simple estimation method for the transition probabilities among the hidden states is also discussed.

Department of Mathematics, HKU, 2010