Topics in the Mathematical Methods Section
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 a classical Markov chain model.
A simple estimation method for the transition probabilities among the hidden states is also discussed.
Mathematical Induction is an well-known and useful method in Mathematics.
Pigeonhole Principle - "If we put n balls in m boxes, and m < n,
then at least one box must have more than n/m balls."
Random Walks, Gambler's Ruin and Queueing Systems - A losing drunk gambler queuing for loosing money ?
Solving linear systems is a problem arises in many practical applications
and it is a key issue in modern scientific computing.