Reference Work Entry

Encyclopedia of Neuroscience

pp 355-359

Bayesian Statistics (with Particular Focus on the Motor System)

  • Konrad KördingAffiliated withInstitute of Neurology


Probabilistic inference; Statistical inference; Bayesian inference; Antonym: Frequentist statistics


As our sensors are not perfect and do not provide information about all the properties of the world, we are faced with sensory uncertainty. Moreover, our muscles also produce noisy outputs and so we are also faced with motor uncertainty. Bayesian statistics is the systematic way of dealing with uncertainty by expressing its many forms in terms of probability.

Description of the Theory

Bayesian statistics can be used to infer the states of variables that are not directly measured, a process called Bayesian inference. “For example, when we see a tennis ball (observed variable) and we know from experience how they usually fly (prior knowledge) then Bayesian statistics allows us to calculate how likely the ball will land at any given position on the field (unobserved variable).” The way inference is done is the following:

(i) The prior ...

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