van Oostrum, JesseJessevan OostrumLanger, CarlottaCarlottaLangerAy, NihatNihatAy2025-06-042025-06-042025-05-16Journal of Mathematical Psychology 125: 102921 (2025)https://hdl.handle.net/11420/55734In this paper we present a concise mathematical description of active inference in discrete time. The main part of the paper serves as a basic introduction to the topic, including a detailed example of the action selection mechanism. The appendix discusses the more subtle mathematical details, targeting readers who have already studied the active inference literature but struggle to make sense of the mathematical details and derivations. Throughout, we emphasize precise and standard mathematical notation, ensuring consistency with existing texts and linking all equations to widely used references on active inference. Additionally, we provide Python code that implements the action selection and learning mechanisms described in this paper and is compatible with pymdp environments.en0022-24962025Elsevierhttps://creativecommons.org/licenses/by/4.0/Active inference | Bayesian inference | Free energy principle | Mathematical review | TutorialNatural Sciences and Mathematics::519: Applied Mathematics, ProbabilitiesComputer Science, Information and General Works::006: Special computer methods::006.3: Artificial IntelligenceReview Articlehttps://doi.org/10.15480/882.1522510.1016/j.jmp.2025.10292110.15480/882.152252406.07726Review Article