![]() ![]() Our model is then described by the sets of probability distributions p ( y t ∣ θ t, ϕ )and p θ t θ t − 1 ϕ. ![]() In our applications, y twill either be an increase or decrease and the hidden process will determine the probability distribution of observing different letters. …, T, θ tthe value of the hidden process at location tand let ϕ represents parameters necessary to determine the probability distribution for y tgiven θ tand θ tgiven θ t − 1. Let y trepresents the observed value of the process at location tfor t = 1. Finally we may want the probability distribution for the hidden states at every location. And also determined the most likely sequence for the hidden process. Given such a model, we want to estimate any parameters that occur in the model. ![]() Thus a hidden Markov model is specified by the transition density of the Markov chain and the probability laws that govern what we observe given the state of the Markov chain. The fundamental idea behind a hidden Markov model is that there is a Markov process we cannot observe that determines the probability distribution for what we do observe. ![]()
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