MC1 – Applications of Bayesian Inference and the Free Energy Principle

Lecturer: Christoph Mathys
Fields: Bayesian inference, free energy principle, active inference,
computational neuroscience, time series


We will start with a look at the fundamentals of Bayesian inference, model selection, and the free energy principle. We will then look at ways to reduce Bayesian inference to simple prediction adjustments based on precision-weighted prediction errors. This will provide a natural entry point to the field of active inference, a framework for modelling and programming the behaviour of agents negotiating their continued existence in a given environment. Under active inference, an agent uses Bayesian inference to choose its actions such that they minimize the free energy of its model of the environment. We will look at how an agent can infer the state of the environment and its own internal control states in order to generate appropriate actions.


  • To understand the reduction of Bayesian inference to precision-weighting of
    prediction errors
  • To understand the free energy principle and the modelling framework of
    active inference
  • To know the principles of Bayesian inference and model selection, and to understand their application to a given data set.


  • Friston, K. J., Daunizeau, J., & Kiebel, S. J. (2009). Reinforcement Learning
    or Active Inference? PLoS ONE, 4(7), e6421.
  • Mathys, C., Lomakina, E.I., Daunizeau, J., Iglesias, S., Brodersen, K.H.,
    Friston, K.J., & Stephan, K.E. (2014). Uncertainty in perception and the
    Hierarchical Gaussian Filter. Frontiers in Human Neuroscience, 8:825.
  • Mathys, C., Daunizeau, J., Friston, K.J., Stephan, K.E., 2011. A Bayesian
    foundation for individual learning under uncertainty. Front. Hum. Neurosci. 5,
  • Friston, K. (2009). The free-energy principle: A rough guide to the brain? Trends in Cognitive Sciences, 13(7), 293–301.


Christoph Mathys is Associate Professor of Cognitive Science at Aarhus University. Originally a theoretical physicist, he worked in the IT industry for several years before doing a PhD in information technology at ETH Zurich and a master’s degree in psychology and psychopathology at the University of Zurich. During his graduate studies, he developed the hierarchical Gaussian filter (HGF), a generic hierarchical Bayesian model of inference in volatile environments. Based on this, he develops and maintain the HGF Toolbox, a Matlab-based free software package for the analysis of behavioural and neuroimaging experiments. His research focus is on the hierarchical message passing that supports inference in the brain, and on failures of inference that lead to psychopathology.

Affiliation: sissa