Baysian Approaches

Kun Guo, PhD

Reader in Cognitive Neuroscience

School of Psychology

University of Lincoln

Quantitative Methods 2011

Example

Visual system interprets incoming retinal signals in the context of existing knowledge of the world.

Some issues within this process: (1) signals are corrupted by variability of noise; (2) uncertainity in computation.

Brain represents sensory information probabilistically, in the form of probability distribution.

Ideal Bayesian Inference Observer: assigning probabilities to any degree of belief abouth the state of the world.

Posterior ≈ Prior × Likelihood : Visual perception (Bayesian posterior probability of a scene) ≈ Prior probability of the state × Current input from the eye

Vision is an act of interpretationVision is an act of interpretation

Thomas Bayes (1701 – 1761): English mathematician

“An essay towards solving a problem in the doctrine of chances” was read to Royal Society in 1763 (doctrine of chance ~ theory of probability).

Posterior ≈ Prior × Likelihood: a method of statistical inference to calculate the impact of evidence on beliefs. The probability is interpreted as a degree of belief (conditional probability distribution) rather than frequency. In application, the initial degree of belief is called prior and the updated degree of belief is called posterior.

Widely applied in Science, Engineering, Medicine and Law, especially after 1950s.

Bayes’ TheoremBayes’ Theorem

P(A|B): posterior, the degree of belief in A after B is observed.

P(A): prior, the degree of belief in A before B is observed.

P(B|A)/P(B): likelihood, impact of B on the degree of belief in A.

Bayesian InferenceBayesian Inference

Landing light

Time

Predictor 1

Predictor 2

Predictor 3

Target

200 ms

Predictor 4

FP

Stimulus sequence comprised four collinear bars (predictors) which appeared successively towards the foveal region, followed by a target bar with same or different orientation.

Guo et al. (2004) Effects on orientation perception of manipulating the spatiotemporal prior probability of stimuli. Vision Research 44: 2349-2358

Applying Bayesian Inference in Vision researchApplying Bayesian Inference in Vision research

Stimulus demonstration – non-collinear trial

Applying Bayesian Inference in Vision researchApplying Bayesian Inference in Vision research

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Spatiotemporal structure of the priors

Applying Bayesian Inference in Vision researchApplying Bayesian Inference in Vision research

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Spatiotemporal structure of the priors

Applying Bayesian Inference in Vision researchApplying Bayesian Inference in Vision research

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Spatiotemporal structure of the priors

Applying Bayesian Inference in Vision researchApplying Bayesian Inference in Vision research

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Real orientation

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Distribution of perceived

orientation difference

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Psychophysical

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Noisy brain

Representation

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Guo et al., (2004) Vision Res. 44: 2349-2358

normal sequence — higher expectation of co-linearity — sharper prior distribution

Applying Bayesian Inference in Vision researchApplying Bayesian Inference in Vision researchFree parameters: width of prior, width of likelihood, co-linearity threshold, fitting error

Different spatiotemporal structure Different experimental frequency

Applying Bayesian Inference in Vision researchApplying Bayesian Inference in Vision research

Learning and reasoning

Language processing and acquisition

Memory

Vision

Sensorimotor control

Bayesian Applications in Bayesian Applications in Psychology & NeurosciencePsychology & Neuroscience

Reference: Trends in Cognitive Sciences, 2006, Vol 10(7), “Special issue: Probabilistic models of cognition”.