For one of my projects I need to find posterior probability of visiting a state S and emitting a symbol. I have built a HMM in R and later I get one observation sequence. But, I am not able to interpret the output.
> # Sequence of observations > observations = c("L","L","R","R") > # Calculate posterior probablities of the states > posterior = posterior(hmm, observations) ## ---> hmm is hidden markov model > print(posterior) index states 1 2 3 4 A 0.6037344 0.56639 0.43361 0.3962656 B 0.3962656 0.43361 0.56639 0.6037344
How do I interpret this? This matrix gives output w.r.t time. But, I need posterior probability of visiting a state S and emitting a symbol say A. How can I get it?
Thanks for the response.The description says it combines forward and backward probabilities to get posterior details...But,as i have read in papers, the forward-backward algorithm gives the probability of being in a state say A and emitting a symbol say L.. which i do not see here. Here is all the details of HMM - # Initialise HMM # init HMM format: A and B are hidden states,L and R are observations,transprob: initial # transition probabilities and emissionprobs IS EMISSION probability hmm = initHMM(c("A","B"), c("L","R"), transProbs=matrix(c(.8,.2,.2,.8),2), emissionProbs=matrix(c(.6,.4,.4,.6),2)) print(hmm)
Sequence of observations
observations = c("L","L","R","R")
Calculate posterior probablities of the states
posterior = posterior(hmm,observations) print(posterior)
Description of POSTERIOR: This function computes the posterior probabilities of being in state X at time k for a given sequence of observations and a given Hidden Markov Model.
Details The posterior probability of being in a state X at time k can be computed from the forward and backward probabilities: Ws(X_k = X | E_1 = e_1, ... , E_n = e_n) = f[X,k] * b[X,k] / Prob(E_1 = e_1, ... , E_n = e_n) Where E_1...E_n = e_1...e_n is the sequence of observed emissions and X_k is a random variable that represents the state at time k.
But,in general how can we calculate posterior probability without using this algo