I was interested on evaluating a catalogue that students would be using to observe how is it being used probabilistically.
The catalogue works by choosing cells in a temporal sequence, so for example:
- Student A has: ($t_1$,$Cell_3$),($t_2$,$Cell_4$)
- Student B has: $(t_1,Cell_5),(t_2,Cell_3),(t_3,Cell_7)$.
Assume that the cells of the table are states of a Hidden Markov Model, so the transition between states would map in the real world to a student going from a given cell to another.
Assuming that the catalogue is nothing more than guidance, it is expected to have a certain kind of phenomenon to occur on a given artifact. Consider this artifact to be unique, say, for example a program.
What happens to this program is a finite list of observations, thus, for a given cell we have a finite list of observations for following the suggestion mentioned on that cell. On a HMM this would be then the probability associated to a state to generate a given observation in this artifact.
Finally, consider the catalogue to be structured in a way that initially it is expected that the probability to start in a given cell is equal. The catalogue does not suggest any starting point.
Question 1: Is the mapping between the catalogue and the HMM appropriate?
Question 2: Assuming question 1 holds true. Consider now that we train the HMM using as entries $(t_1,Cell_1), (t_2,Cell_3) , ... (t_n,Cell_n)$ for the students. Would the trained HMM, once asked to generate the transition between states that it is most likely yields as result what is the most used way by the people who used the catalogue for a given experiment $\epsilon$?