This is an 'dishonest casino' example from Durbin, et al. 'Biological Sequence Analysis' book. A casino used two types of dice: one is a 'fair' one that has equal chance to all six numbers, and the other is a 'loaded' one that has high chance of number 6 than the others. We have a sequence of dice numbers from the casino, and want to estimate when a dealer exchanged the dice.
We assume that the Hidden Markov Model of this example as below:
As you see, both emission probability and transition probability are given.
[Emission probability] Fair: 1/6 1/6 1/6 1/6 1/6 1/6 Loaded: 0.1 0.1 0.1 0.1 0.1 0.5 [Transition probability] F -> F : 0.95 F -> L : 0.05 L -> L : 0.90 L -> F : 0.10
To be continued...