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When observation sequence starts you have emitted symbol for example S, but emission only happens when transition to hidden state happens, here initial state comes in play.
What does state emission probability distribution look like?
In Diagram 3 you can see how state emission probability distribution looks like visually. It is direct representation of Table 2. When you have hidden states there are two more states that are not directly related to model, but used for calculations. They are: As mentioned before these states are used for calculation.
When you have observation symbols sequence which relates to hidden states in a way that transition to hidden state emits observation symbol you have two corner cases: when observation sequence starts and ends.
How are hidden states and observable parts bind?
You have hidden states and you have observation symbols and these hidden and observable parts are bind by state emission probability distribution. This is how: every transition to hidden state emits observation symbol. Moreover, every hidden state can emit all observation symbols, only probability of emission one or the other symbol differs.
How are transitions represented in a Markov chain?
In the example above, a two state Markov Chain is displayed: We have states A and B and four transition probabilities: from A to A again, from A to B, from B to A and from B to B again. These transition probabilities are usually represented in the form of a Matrix, called the Transition Matrix, also called the Markov Matrix.
Hidden Markov Models are probabilistic models that attempt to find the value or the probability of certain hidden variables having a certain value, based on some other observed variables. These variables are commonly referred to as hidden states and observed states.
Why is the matrix of transition probabilities a Markov matrix?
Thus, the matrix of transition probabilities is a Markov matrix. Because any one transition probability can be determined once the others are known, there are a total of transition parameters.