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markov-chains-2 - Markov Chain Models(Part 2 BMI/CS 576...

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Markov Chain Models (Part 2) BMI/CS 576 www.biostat.wisc.edu/bmi576/ Mark Craven [email protected] Fall 2011 Higher order Markov chains the Markov property specifies that the probability of a state depends only on the probability of the previous state but we can build more “memory” into our states by using a higher order Markov model in an n th order Markov model P ( x i | x i " 1 , x i " 2 ,..., x 1 ) = P ( x i | x i " 1 ,..., x i " n )
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Selecting the order of a Markov chain model higher order models remember more “history” additional history can have predictive value example: – predict the next word in this sentence fragment “… the__” ( duck , end , grain , tide , wall , …?) Selecting the order of a Markov chain model but the number of parameters we need to estimate grows exponentially with the order – for modeling DNA we need parameters for an n th order model the higher the order, the less reliable we can expect our parameter estimates to be – estimating the parameters of a 2 nd
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