Hidden Semi-Markov Models

These show that a book borrowed from library 2 and returned to library 2 often has longer holding period. Thus the mean holding times that a book is borrowed from different libraries are

$\begin{array}{l}{\overline{d}}_1=a_{1,1}{\overline{d}}_{1,1}+a_{1,2}{\overline{d}}_{1,2}\approx 3.67\hfill \\ {\overline{d}}_2=a_{2,1}{\overline{d}}_{2,1}+a_{2,2}{\overline{d}}_{2,2}=7.75.\hfill \end{array}$

These show that people hold a book borrowed from library 2 for a longer time.

1.2 Hidden Markov Models

In this chapter, we briefly review the hidden Markov model (HMM). An HMM is defined as a doubly stochastic process. The underlying stochastic process is a discrete-time finite-state homogeneous Markov chain. ...