Change emission and transition frequencies to explore the behavior of the Hidden Markov Model
The Fair Bet Casino: A dealer flips a coin and the player bets on the outcome (head or tail). Every now and then, the dealer changes between a fair coin (heads and tails have the same probability) and a biased coin (heads has a higher probability than tails).
The Fair Bet Casino Problem: Given a sequence of coin tosses, determine when the dealer has used a fair/biased coin.
This Problem is often modeled with the help of a Hidden Markov Model.
A Hidden Markov Model is an abstract machine with hidden states that produces emission symbols
Each state (F/B) has an own transition probability distribution that controls how the machine switches between the states.
Each state has an own emission probability distribution that controls how the emission symbols are produced.
While being in a specific state, two decisions are made:
1. What will be the next state?
2. What symbol will be emmitted?