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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.

Details:

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.

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  • $\begingroup$ You'll get better answers if you describe your real problem. See here. $\endgroup$ – Kodiologist Sep 15 '16 at 21:23
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    $\begingroup$ For a Hidden Markov model, you have some variables that are not observed. For example in your case, the observed variable could be # cases reported, and the hidden variable could be # infected individuals actually present, each of these with 1 value per district per week. I would think you would want to model all the districts together, since they are coupled due to migration between them by infected individuals, and it is this spread that you want to predict. $\endgroup$ – GeoMatt22 Sep 15 '16 at 22:35

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