Bayes rule in perception, action and cognition
Cognition and intelligent behaviour are fundamentally tied to the ability to survive in an uncertain and changing environment. Our only access to knowledge about the world is through our senses which provide information that is usually corrupted by random fluctuations, termed noise, and may provide ambiguous information about the possible states of the environment. Moreover, when we act on the world through our motor system, the commands we send to our muscles are also corrupted by variability or noise. This combined sensory and motor variability limits the precision with which we can perceive and act on the world. Here we will review the framework of Bayesian decision theory, which has emerged as a principled approach to handle uncertain information in an attempt to behave optimally, and how this framework can be used to understand sensory, motor and cognitive processes. Bayesian Theory is named after Thomas Bayes (Figure 1) who was an 18th century English Presbyterian minister. He is only known to have published two works during his life, of which only one dealt with mathematics in which he defended the logical foundation of Isaac Newton's methods against contemporary criticism. After Bayes death, his friend Richard Price found an interesting mathematical proof among Bayes' papers and sent the paper to the Editor of the Philosophical Transactions of the Royal Society stating " I now send you an essay which I have found among the papers of our deceased friend Mr Bayes, and which, in my opinion, has great merit.... " The paper was subsequently published in 1764 as " Essay towards solving a problem in the doctrine of chances. " In the latter half of the 20 th century Bayesian approaches have become a mainstay of statistics and a more general framework has now emerged, termed Bayesian decision theory (BDT). Bayesian decision theory incorporates two main components: Bayesian statistics and decision theory: Bayesian statistics Bayesian statistics is a framework for making inferences based on uncertain information. The fundamental idea is that probabilities can be used to represent the degree of belief in different propositions and therefore the rules of probability can be used to update beliefs based on new information. For example, imagine you are a doctor and see a patient who you believe may have a particular disease. The strength of this belief can be represented by a real number between 0 and 1, which reflects the probability that we …