This paper provides a complete mathematical synthesis of active inference on discrete state-space models.

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• Friston, FitzGerald et al. (2017) — Active inference: A process theoryconcept0.805
  Companion paper to which readers are directed for detailed account of active inference scheme
• Discrete State-Space Modelsconcept0.805
  Mathematical formalism used in active inference for modeling hierarchical and discrete brain processes.
• "active inference separates the problems of optimizing action and perception by assuming that action fulfills predictions based on inferred states"quote0.794
• Friston, FitzGerald et al. (2016) — Active inference and learningconcept0.793
  Prior active inference paper providing detailed neurophysiological implementation of belief updates
• Active inference describes the dynamics of systems that persist at non-equilibrium steady-state and that can be statistically segregated from their environment via a Markov blanket.claim0.784
  Sets the theoretical grounding in Section 2.
• This paper may be used as a practical guide on how to implement active inference to simulate experimental behaviour.claim0.783
  Practical utility claimed in abstract and Section 1.
• The key challenge for active inference is finding the generative model that best explains observable data.claim0.777
  Identifies an outstanding problem, Section 10.
• Active inference offers an attractive natural adaptation mechanism for non-stationary environments due to its Bayesian model updating properties.claim0.777
  §3, after non-stationary results.