Hidden Markov Models:
We discussed an example of determining the most probable state path with the Viterbi algorithm. We also discussed in the class how to calculate the marginal probability of a sequences being generated by a given HMM model with the Forward algorithm, which is very similar to the Viterbi algorithm. In this question you are asked to calculate both, the most probable path as well as the marginal probability of observing the sequence "ILDE", for the model defined below. Please show your work of state path matrix (Cell values as well as trace-back for Viterbi)
The model and parameters are defined as following
a. The model has two possible states: transmembrane state (TM) and non-transmembrane state (NT)
b.The state transition matrix A:
S_{t+1}
TM
NT
S_{t}
0.8
0.2
c. The emission matrix E:
Amino Acids
L
I
E
D
State
0.45
0.05
Assume that transition from start state to TM or NT has equal chance 0.5.