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Given a tree trunk with concentric circles, can we predict the weather for each year? Each concentric circle accounts for a year that the tree has been on the Earth. The innermost circle is the oldest year and the outermost circle is the current year.

I have a data set that tells how much rainfall there was for every year since rainfall could be measured. Given this information can we predict rainfall for the innermost years?

I thought maybe the size of the concentric circles were dependent upon the rainfall for that year. This assumes a direct relationship. I was asked to think of this more broadly and in particular to think about this as a Markov Model.

  1. How could I go about doing this prediction? Is a Markov model a good place to start, or are there simpler ways to approach the problem?
  2. Even if there are other ways, I want to explore the Markov model as well. Where is a good place to start learning about Markov models?

Any help and comments would be greatly appreciated!

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1 Answer 1

up vote 6 down vote accepted

1.How could I go about doing this prediction? Is a Markov Model a good place to start? Or are there more simplistic ways to approach the problem?

You need a Hidden Markov Model, the weather is the hidden state, the widths of the concentric circles are your observed variables, i.e. emissions. As a matter of fact, the problem you describe is literally a textbook example of HMM's.

2.Even if there are other ways I want to explore the Markov Model as well. Where is a good place to start learning about Markov Models?

And this is the textbook (actually paper) with the solution to your question, exactly.

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