Population states and eigenstructure: A simplifying view of Markov learning models

The structure of a Markov learning model can often be appreciably simplified by analyzing the eigenstructure (eigenvectors and eigenvalues) of its transition operator, and by focusing on population states representing distributions of individuals rather than on subject states representing individuals. This view often produces considerably simpler “reduced” models, which are equivalent to the originals in that they make identical predictions. We apply these reduced representations to determine the number of estimable parameters a model supports and to answer questions of model identifiability: when two models are mathematically equivalent and when they are likely to predict observations in practice distinguishable on the basis of limited data.