1) Can Hidden Markov Model be used across both a large number of categories (districts) and cases (weeks)?
2) Is HMM appropriate for trying to model such a problem?
3) Would I need to develop a separate HMM for each district across all the weeks? This would limit me to predicting changes one district at a time.
I'm still in the planning stage of this homework assignment, but before I went too far down the HMM track I wanted to see if I'm barking up the right tree.
I want to predict the number of Ebola cases by geographical district, over time. I have a data set which tracks new confirmed Ebola cases across 20+ districts, through 100+ weeks. This data is in the form of discrete integers representing the number of confirmed new cases. I would change this into a set of ordinal categories (see x).
x - An attribute in the form of an ordinal set of states which describe the number of confirmed Ebola cases (high-medium-low-none)
y - Attributes which I have reason to believe will predict x, using mobility pattern predictions developed by FlowMinder (http://www.worldpop.org.uk/ebola/Flowminder-Mobility-Data-21.08.14.pdf)
z - The observed probability of a district going from high-low, high-medium, none-low, etc., as calculated from the data set
For the model, I was planning to use:
x as the information about my hidden state
y to calculate my emission probability
z as my transition probability, calculated by pairing up my training set data by week, then calculating probabilities for each change in state based on the frequency of those pairs
PS: I'll be doing most of this in R, most likely.