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Bayesian approaches to brain function investigate the capacity of the nervous system to operate in situations of uncertainty in a fashion that is close to the optimal prescribed by
Bayesian statistics Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, ...
. This term is used in
behavioural sciences Behavioral sciences explore the cognitive processes within organisms and the behavioral interactions between organisms in the natural world. It involves the systematic analysis and investigation of human and animal behavior through naturalisti ...
and neuroscience and studies associated with this term often strive to explain the brain's cognitive abilities based on statistical principles. It is frequently assumed that the nervous system maintains internal
probabilistic model A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, ...
s that are updated by neural processing of sensory information using methods approximating those of
Bayesian probability Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification o ...
.


Origins

This field of study has its historical roots in numerous disciplines including machine learning, experimental psychology and
Bayesian statistics Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, ...
. As early as the 1860s, with the work of
Hermann Helmholtz Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Association, ...
in experimental psychology the brain's ability to extract perceptual information from sensory data was modeled in terms of probabilistic estimation. The basic idea is that the nervous system needs to organize sensory data into an accurate internal model of the outside world. Bayesian probability has been developed by many important contributors.
Pierre-Simon Laplace Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized ...
, Thomas Bayes, Harold Jeffreys, Richard Cox and Edwin Jaynes developed mathematical techniques and procedures for treating probability as the degree of plausibility that could be assigned to a given supposition or hypothesis based on the available evidence. In 1988 Edwin Jaynes presented a framework for using Bayesian Probability to model mental processes. It was thus realized early on that the Bayesian statistical framework holds the potential to lead to insights into the function of the nervous system. This idea was taken up in research on unsupervised learning, in particular the Analysis by Synthesis approach, branches of machine learning. In 1983
Geoffrey Hinton Geoffrey Everest Hinton One or more of the preceding sentences incorporates text from the royalsociety.org website where: (born 6 December 1947) is a British-Canadian cognitive psychologist and computer scientist, most noted for his work on a ...
and colleagues proposed the brain could be seen as a machine making decisions based on the uncertainties of the outside world. During the 1990s researchers including Peter Dayan, Geoffrey Hinton and Richard Zemel proposed that the brain represents knowledge of the world in terms of probabilities and made specific proposals for tractable neural processes that could manifest such a Helmholtz Machine.


Psychophysics

A wide range of studies interpret the results of psychophysical experiments in light of Bayesian perceptual models. Many aspects of human perceptual and motor behavior can be modeled with Bayesian statistics. This approach, with its emphasis on behavioral outcomes as the ultimate expressions of neural information processing, is also known for modeling sensory and motor decisions using Bayesian decision theory. Examples are the work of Landy, Jacobs, Jordan, Knill, Kording and Wolpert, and Goldreich.


Neural coding

Many theoretical studies ask how the nervous system could implement Bayesian algorithms. Examples are the work of Pouget, Zemel, Deneve, Latham, Hinton and Dayan. George and Hawkins published a paper that establishes a model of cortical information processing called
hierarchical temporal memory Hierarchical temporal memory (HTM) is a biologically constrained machine intelligence technology developed by Numenta. Originally described in the 2004 book ''On Intelligence'' by Jeff Hawkins with Sandra Blakeslee, HTM is primarily used today for ...
that is based on Bayesian network of Markov chains. They further map this mathematical model to the existing knowledge about the architecture of cortex and show how neurons could recognize patterns by hierarchical Bayesian inference.


Electrophysiology

A number of recent electrophysiological studies focus on the representation of probabilities in the nervous system. Examples are the work of Shadlen and Schultz.


Predictive coding

Predictive coding In neuroscience, predictive coding (also known as predictive processing) is a theory of brain function which postulates that the brain is constantly generating and updating a "mental model" of the environment. According to the theory, such a ment ...
is a neurobiologically plausible scheme for inferring the causes of sensory input based on minimizing prediction error. These schemes are related formally to Kalman filtering and other Bayesian update schemes.


Free energy

During the 1990s some researchers such as
Geoffrey Hinton Geoffrey Everest Hinton One or more of the preceding sentences incorporates text from the royalsociety.org website where: (born 6 December 1947) is a British-Canadian cognitive psychologist and computer scientist, most noted for his work on a ...
and
Karl Friston Karl John Friston FRS FMedSci FRSB (born 12 July 1959) is a British neuroscientist and theoretician at University College London. He is an authority on brain imaging and theoretical neuroscience, especially the use of physics-inspired stati ...
began examining the concept of free energy as a calculably tractable measure of the discrepancy between actual features of the world and representations of those features captured by neural network models. A synthesis has been attempted recently by
Karl Friston Karl John Friston FRS FMedSci FRSB (born 12 July 1959) is a British neuroscientist and theoretician at University College London. He is an authority on brain imaging and theoretical neuroscience, especially the use of physics-inspired stati ...
, in which the Bayesian brain emerges from a general principle of free energy minimisation. In this framework, both action and perception are seen as a consequence of suppressing free-energy, leading to perceptual and active inference and a more embodied (enactive) view of the Bayesian brain. Using
variational Bayes Variational Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning. They are typically used in complex statistical models consisting of observed variables (usually ...
ian methods, it can be shown how
internal models Internal may refer to: *Internality as a concept in behavioural economics *Neijia, internal styles of Chinese martial arts *Neigong or "internal skills", a type of exercise in meditation associated with Daoism *''Internal (album)'' by Safia, 2016 ...
of the world are updated by sensory information to minimize free energy or the discrepancy between sensory input and predictions of that input. This can be cast (in neurobiologically plausible terms) as predictive coding or, more generally, Bayesian filtering. According to Friston:Friston K, Stephan KE.
Free energy and the brain
Synthese. 2007. 159:417–458
"The free-energy considered here represents a bound on the surprise inherent in any exchange with the environment, under expectations encoded by its state or configuration. A system can minimise free energy by changing its configuration to change the way it samples the environment, or to change its expectations. These changes correspond to action and perception, respectively, and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment implies that the system’s state and structure encode an implicit and probabilistic model of the environment."
This area of research was summarized in terms understandable by the layperson in a 2008 article in New Scientist that offered a unifying theory of brain function.Huang Gregory (2008)
"Is This a Unified Theory of the Brain?"
'' New Scientist''. May 23, 2008.
Friston makes the following claims about the explanatory power of the theory:
"This model of brain function can explain a wide range of anatomical and physiological aspects of brain systems; for example, the hierarchical deployment of cortical areas, recurrent architectures using forward and backward connections and functional asymmetries in these connections. In terms of synaptic physiology, it predicts associative plasticity and, for dynamic models, spike-timing-dependent plasticity. In terms of electrophysiology it accounts for classical and extra-classical receptive field effects and long-latency or endogenous components of evoked cortical responses. It predicts the attenuation of responses encoding prediction error with perceptual learning and explains many phenomena like repetition suppression, mismatch negativity and the P300 in electroencephalography. In psychophysical terms, it accounts for the behavioural correlates of these physiological phenomena, e.g.,
priming Priming may refer to: * Priming (agriculture), a form of seed planting preparation, in which seeds are soaked before planting * Priming (immunology), a process occurring when a specific antigen is presented to naive lymphocytes causing them to ...
, and global precedence."
"It is fairly easy to show that both perceptual inference and learning rest on a minimisation of free energy or suppression of prediction error."


See also

*
Bayesian cognitive science Bayesian cognitive science, also known as computational cognitive science, is an approach to cognitive science concerned with the rational analysis of cognition through the use of Bayesian inference and cognitive modeling. The term "computational ...
* Cognitive architecture *
Computational neuroscience Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematical models, computer simulations, theoretical analysis and abstractions of the brain to u ...
*
Free energy principle The free energy principle is a mathematical principle in biophysics and cognitive science that provides a formal account of the representational capacities of physical systems: that is, why things that exist look as if they track properties of the ...
*
Quantum cognition Quantum cognition is an emerging field which applies the mathematical formalism of quantum theory to model cognitive phenomena such as information processing by the human brain, language, decision making, human memory, concepts and conceptual re ...
*
Two-alternative forced choice Two-alternative forced choice (2AFC) is a method for measuring the sensitivity of a person, child or infant, or animal to some particular sensory input, stimulus, through that observer's pattern of choices and response times to two versions of the ...


References


External links


Universal Darwinism – Karl Friston
{{DEFAULTSORT:Bayesian approaches to brain function * Cognitive neuroscience Brain Probabilistic models