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Markov Models

Last update: 07 Jul 2025 12:25
First version: 16 March 2006

Markov processes are my life. Which means I don't have time to explain them. Even as a pile of pointers, this is more inadequate than usual.

Topics of particular interest: statistical inference for Markov and hidden Markov models; model selection for Markov models and HMMs; Markovian representation results, i.e., ways of representing non-Markovian processes as functions of Markov processes. Ergodic and large-deviations results. (Ergodic theory for Markov processes gets notebook.) Markov random fields. Abstractions of the usual Markov property, i.e., graphical models. Relationship between Markov properties and statistical sufficiency, i.e., if I construct a minimal predictive sufficient statistic for some process, is that statistic always Markovian? (I believe the answer is "yes"; but as Wolfgang Loehr pointed out to me, it is false without the restriction to minimal sufficient statistics.) Differential-equation approximations of Markov processes and vice versa are covered under convergence of stochastic processes.


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