Mathematical models and real applications

A growing body of evidence suggests that animals and particularly humans are capable of mathematically optimal Bayesian inference and that the brain is a sort of Bayesian inference machine. Recent work describing how a neural network could store and manipulate probability distributions lends further support to the hypothesis.

The EU-funded project 'Biological mechanisms for Bayesian inference' (BMBISAMJOHNSON) set out to investigate the topic, developing neural network models in which Bayesian inference is integrated with other brain functions such as working memory or information processing.

Gradual strengthening of the connections (synapses) between two neurons is the neurobiological substrate of long-term memory as, for example, in learning to ride a bike. However, many cognitive functions, including inference, short-term memory and sensory memory, occur on much smaller timescales.

The team developed the concept of cluster reverberations in which small groups of neurons receive signals from each other to account for many of the characteristics of such functions. Researchers suggested a mechanism by which it could support optimal human inference from uncertain sensory information.

Scientists went on to conduct numerous other mathematical investigations of topics covering very diverse fields of interest. From plant-pollinator networks and financial institutions to sampling bias in public health research to a hotly debated topic regarding food web stability, researchers developed new concepts and identified novel network properties that explain how the world works.

The methods and algorithms developed along with the emerging network properties that have been identified will find broad application in mathematics, economics, biology and medicine.