I read through a tutorial on MATLAB website on HMM. It is not easy to digest so I had to look for other sources and found a good explanation on Wikipedia (HMM). Everything is more understandable but there are still a couple of things I find unclear.
Please correct me if I ma wrong, in the example:
- the states are X = {1, 2} (red, green)
- probability that: system stays in red = 0.9, moves from red to green = 0.1, stays in green = 0.95, moves from green to red = 0.05. I understand rows and columns of TRANS correspond to state before and after transition
- because of two states, transition matrix T is 2x2
- Y = {1,2,3,4,5,6} - observations
- emission in the example is categorical
- probability distribution is determined in EMIS matrix
- the matrix EMIS is 2x6 due to 2 states and 6 different observations per state; probability of emission depends on a state and can be different in each state: in red, probability of each observation Y = {1,2,3, ..., 6} is equal; in green probability is weighted towards 1.
Wikipedia also explains that probability that we observe a particular output doesn't have to be categorical. In the example on MATLAB website I understand that emission is categorical. How can I chnage it to apply continuous probability distribution so that I would have similar outputs? I am thinking of Guassian distr. or Guassian Mixture distr. to increase probability of Y = 1.
Thanks