Statistical Inference for Markov and Hidden Markov Models

28 Jun 2021 00:17

I am concerned here with inferring the parameters and/or the structure of the model, not with the estimation of the hidden state in a hidden Markov model with known parameters; that problem falls under filtering.

Parameter inference (what machine learning types would call "learning") given a known, fixed structure. Determining the structure ("discovery"). Order estimation as a particular case of discovery, and of model selection. (Discovery may need its own notebook soon.)

Markov models naturally form exponential families; what classes of partially-observable Markov processes also do?

See also: Inference for Stochastic Differential Equations (strictly speaking a sub-topic, but one with enough special features to get separate treatment); Markov models; Mixture Models; Prediction Processes; Markovian (and Conceivably Causal) Representations of Stochastic Processes; Statistics; Time Series; Universal Prediction Algorithms