An HMM example

We now describe a simple problem that we will analyze using the HMM tools. Consider the HMM with the following parameters:

$\displaystyle A=\left[\begin{array}{ccc}
.8 & .1 & .1 \\
.1 & .8 & .1 \\
....
...ight]
\;\;\;\;
\pi=\left[\begin{array}{c}
1 \\
0 \\
0 \end{array}\right]
$

The output of the HMM is a time series with a 16-sample step size (i.e. the state is allowed to change every 16 output samples). The output is Gaussian with mean and variance depending on the state as follows:
State Mean Var
1 0 1
2 0 4
3 2 1
For each 16-sample segment, the sample mean and standard deviation are computed. This constitutes a 2-dimensional feature vector that is the observation space of the HMM.



Baggenstoss 2017-05-19