Markov Models

18 Apr 2022 18:35

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.

See also: Chains with Complete Connections; Compartment Models; Convergence of Stochastic Processes; Ergodic Theory of Markov and Related Processes; Filtering and State Estimation; Hidden Markov Models; Interacting Particle Systems; Inference for Markov and Hidden Markov Models; Monte Carlo; Prediction Processes; Markovian (and Conceivably Causal) Representations of Stochastic Processes; Random Fields; Stochastic Differential Equations