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

Introduction

Hidden Markov Models (HMMs) are widely used in science [1,2], engineering [3,5] and many other areas [4]. In a HMM, there are two types of states: the observable states and the hidden states. For both types of the states, the underlying process is a Markov chain process [6]. To define a HMM, one has to define the number of both types of states and also their transition probabilities. Very often, the transition probabilities of the observable states depend on the hidden states. One major problem here is to determine the transition probabilities of the hidden states because the transitions among the hidden states are supposed to be unobservable. Here we propose a simple estimation method for the transition probabilities among the hidden states.

Department of Mathematics, HKU, 2010