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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 ( or ) 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 ...
. This term is used in
behavioural sciences Behavioural science is the branch of science concerned with human behaviour.Hallsworth, M. (2023). A manifesto for applying behavioural science. ''Nature Human Behaviour'', ''7''(3), 310-322. While the term can technically be applied to the st ...
and
neuroscience Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions, and its disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, ...
and studies associated with this term often strive to explain the
brain The brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It consists of nervous tissue and is typically located in the head (cephalization), usually near organs for ...
'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 ( or ) 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 quant ...
.


Origins

This field of study has its historical roots in numerous disciplines including
machine learning Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task ( ...
,
experimental psychology Experimental psychology is the work done by those who apply Experiment, experimental methods to psychological study and the underlying processes. Experimental psychologists employ Research participant, human participants and Animal testing, anim ...
and
Bayesian statistics Bayesian statistics ( or ) 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 ...
. As early as the 1860s, with the work of
Hermann Helmholtz Hermann Ludwig Ferdinand von Helmholtz (; ; 31 August 1821 – 8 September 1894; "von" since 1883) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The ...
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 polymath, a scholar whose work has been instrumental in the fields of physics, astronomy, mathematics, engineering, statistics, and philosophy. He summariz ...
,
Thomas Bayes Thomas Bayes ( , ; 7 April 1761) was an English statistician, philosopher and Presbyterian minister who is known for formulating a specific case of the theorem that bears his name: Bayes' theorem. Bayes never published what would become his m ...
,
Harold Jeffreys Sir Harold Jeffreys, FRS (22 April 1891 – 18 March 1989) was a British geophysicist who made significant contributions to mathematics and statistics. His book, ''Theory of Probability'', which was first published in 1939, played an importan ...
, Richard Cox and
Edwin Jaynes Edwin Thompson Jaynes (July 5, 1922 – April 30, 1998) was the Wayman Crow Distinguished Professor of Physics at Washington University in St. Louis. He wrote extensively on statistical mechanics and on foundations of probability and statistical ...
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 Edwin Thompson Jaynes (July 5, 1922 – April 30, 1998) was the Wayman Crow Distinguished Professor of Physics at Washington University in St. Louis. He wrote extensively on statistical mechanics and on foundations of probability and statistical ...
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 Unsupervised learning is a framework in machine learning where, in contrast to supervised learning, algorithms learn patterns exclusively from unlabeled data. Other frameworks in the spectrum of supervisions include weak- or semi-supervision, wh ...
, in particular the Analysis by Synthesis approach, branches of
machine learning Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task ( ...
. In 1983
Geoffrey Hinton Geoffrey Everest Hinton (born 1947) is a British-Canadian computer scientist, cognitive scientist, and cognitive psychologist known for his work on artificial neural networks, which earned him the title "the Godfather of AI". Hinton is Univer ...
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 toda ...
that is based on Bayesian network of
Markov chain In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally ...
s. 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 men ...
is a neurobiologically plausible scheme for inferring the causes of sensory input based on minimizing prediction error. These schemes are related formally to
Kalman filter In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unk ...
ing and other Bayesian update schemes.


Free energy

During the 1990s some researchers such as
Geoffrey Hinton Geoffrey Everest Hinton (born 1947) is a British-Canadian computer scientist, cognitive scientist, and cognitive psychologist known for his work on artificial neural networks, which earned him the title "the Godfather of AI". Hinton is Univer ...
and Karl Friston 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, 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 Bayesian methods, it can be shown how internal models 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 ''New Scientist'' is a popular science magazine covering all aspects of science and technology. Based in London, it publishes weekly English-language editions in the United Kingdom, the United States and Australia. An editorially separate organ ...
that offered a unifying theory of brain function.Huang Gregory (2008)
"Is This a Unified Theory of the Brain?"
''
New Scientist ''New Scientist'' is a popular science magazine covering all aspects of science and technology. Based in London, it publishes weekly English-language editions in the United Kingdom, the United States and Australia. An editorially separate organ ...
''. 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 The mismatch negativity (MMN) or mismatch field (MMF) is a component of the event-related potential (ERP) to an odd stimulus in a sequence of stimuli. It arises from electrical activity in the brain and is studied within the field of cognitive neu ...
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 d ...
, 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 *
Cognitive architecture A cognitive architecture is both a theory about the structure of the human mind and to a computational instantiation of such a theory used in the fields of artificial intelligence (AI) and computational cognitive science. These formalized models ...
*
Computational neuroscience Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of  neuroscience which employs mathematics, computer science, theoretical analysis and abstractions of the brain to understand th ...
* Free energy principle * Quantum cognition *
Two-alternative forced choice Two-alternative forced choice (2AFC) is a method for measuring the sensitivity of a person or animal to some particular sensory input, stimulus, through that observer's pattern of choices and response times to two versions of the sensory input. Fo ...


References


External links


Universal Darwinism – Karl Friston
{{DEFAULTSORT:Bayesian approaches to brain function Computational neuroscience Cognitive neuroscience
Brain The brain is an organ (biology), organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It consists of nervous tissue and is typically located in the head (cephalization), usually near organs for ...
Probabilistic models