Beyond Bayes: On the Need for a Unified and Jaynesian Definition of Probability and Information within Neuroscience
Received: 9 December 2011 / Revised: 3 March 2012 / Accepted: 9 April 2012 / Published: 20 April 2012
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It has been proposed that the general function of the brain is inference, which corresponds quantitatively to the minimization of uncertainty (or the maximization of information). However, there has been a lack of clarity about exactly what this means. Efforts to quantify information
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It has been proposed that the general function of the brain is inference, which corresponds quantitatively to the minimization of uncertainty (or the maximization of information). However, there has been a lack of clarity about exactly what this means. Efforts to quantify information have been in agreement that it depends on probabilities (through Shannon entropy), but there has long been a dispute about the definition of probabilities themselves. The “frequentist” view is that probabilities are (or can be) essentially equivalent to frequencies, and that they are therefore properties of a physical system, independent of any observer of the system. E.T. Jaynes developed the alternate “Bayesian” definition, in which probabilities are always conditional on a state of knowledge through the rules of logic, as expressed in the maximum entropy principle. In doing so, Jaynes and others provided the objective means for deriving probabilities, as well as a unified account of information and logic (knowledge and reason). However, neuroscience literature virtually never specifies any definition of probability, nor does it acknowledge any dispute concerning the definition. Although there has recently been tremendous interest in Bayesian approaches to the brain, even in the Bayesian literature it is common to find probabilities that are purported to come directly and unconditionally from frequencies. As a result, scientists have mistakenly attributed their own information to the neural systems they study. Here I argue that the adoption of a strictly Jaynesian approach will prevent such errors and will provide us with the philosophical and mathematical framework that is needed to understand the general function of the brain. Accordingly, our challenge becomes the identification of the biophysical basis of Jaynesian information and logic. I begin to address this issue by suggesting how we might identify a probability distribution over states of one physical system (an “object”) conditional only on the biophysical state of another physical system (an “observer”). The primary purpose in doing so is not to characterize information and inference in exquisite, quantitative detail, but to be as clear and precise as possible about what it means to perform inference and how the biophysics of the brain could achieve this goal.