The discussion focuses on calculating the probability P(X3=A) in a Hidden Markov Model (HMM) with two states, A and B. The initial probabilities are P(X0=A)=0.6 and P(X0=B)=0.4, with transition probabilities P(X1=A|X0=A)=0.3 and P(X1=B|X0=B)=0.8. Participants suggest using the Chapman-Kolmogorov equations and matrix multiplication to derive the probabilities over time, emphasizing the importance of understanding the Markov property for accurate calculations.
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betsyrocamora said:Can someone help me with this question.
Let us define a Markov hidden model with 2-states A and B, such that
P(X0=A)=0.6,P(X0=B)=0.4,P(X1=A/X0=A)=0.3,P(X1=B/X0=B)=0.8
what is the value of P(X3=A) ??
I like Serena said:Welcome to MHB, betsyrocamora! :)
This looks like a question that is intended to learn what a hidden Markov model actually is.
Do your notes perhaps contain a worked example?
Or perhaps an example for a Markov chain?
betsyrocamora said:No, I know what is a hidden markov model, but with this one I am a little lost, I have tried to let j denote the state A. Used p3ij:=P(X3=j|X0=i) that satisfies the Chapman Kolmogorov equations and after that I think is the total probabilities ecuation but I am lost in there hahha