[day39 literature extensive reading] a Bayesian perspective on magnetic estimation

Read the literature ：

Petzschner, F. H., Glasauer, S., & Stephan, K. E. (2015). A Bayesian perspective on magnitude estimation. trends in cognitive sciences, 19(5), 285-293. 

Links to Literature ：

https://www.cell.com/trends/cognitive-sciences/fulltext/S1364-6613(15)00050-9?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS1364661315000509%3Fshowall%3Dtrue

Abstract

we discuss a unifying Bayesian framework for understanding biases in magnitude estimation and enable a re-interpretation of a range of established psychophysical findings.

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Theories of magnitude estimation

Bayesian accounts of magnitude estimation have the potential to provide a more general explanation that covers a wide set of behavioral characteristics and transcends any specific modality.

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A Bayesian framework for magnitude estimation

In Beyesian framework, a generative model combines a priori information (prior) with noisy sensory input (likelihood), weighing the two information sources by their relative uncertainty to produce biased magnitude judgments (posterior).

 

→ The higher the uncertainty (variance) of the prior, the more posterior depends on the likelihood.

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Links between classical and generative models of magnitude estimation

Regarding magnitude estimation as Bayesian perceptual inference is capable of reconciling the seemingly incompatible theories about perceptual function fπ→s  by Weber-Fechner (logarithmic form) and Stevens (power-function form).

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The utility of a Bayesian framework for future psychophysical and neuroimaging studies

Larger quantities in the non-temporal domain (such as space) are associated with longer durations, which may because the statistical co-occurrence of different magnitudes reliably reflects properties ofvthe physical world that link different magnitudes (such as time and space) and a global prior reflecting these probabilistic relations might lead to coupled estimates of different physical magnitudes.