Magnitude estimation in humans

Anyone who has climbed a mountain before knows that the perceived
distance walked depends on more than just its physical length. This
intriguing relationship between physical and experienced magnitudes
has fascinated researchers across various disciplines for more than
200 years. Part of the enthusiasm is driven by the fact that,
although magnitudes, as well as the sensory organs with which we
measure them, differ in so many ways, there are unifying principles
in behavior common to all types of magnitudes estimated. In this
thesis, the general characteristics of human magnitude estimation
are studied in the case of visual path integration. The aim is to
clarify the role of a-priori knowledge on the estimate of magnitude
and to provide a unifying mathematical framework that explains the
behavior. In particular, we investigated human linear and angular
displacement estimation in different experimental situations with
varying experience-dependent and abstract a-priori knowledge. We
find systematic behavioral characteristics that are omnipresent in
magnitude estimation studies, like the range effect, the regression
effect or scalar variability. These characteristics are explained
by a general model that combines a logarithmic scaling of
magnitudes according to the Weber-Fechner law with the concept of
Bayesian inference. The model incorporates apriori knowledge about
the stimulus and updates this knowledge on a trial-by-trial basis.
The resulting iterative Bayesian estimation accounts for the
aforementioned behavioral characteristics and provides a link
between the two most well-known laws in psychophysics: the
Weber-Fechner and Stevens’ powerlaw. This work provides substantial
evidence that magnitude estimation is not purely driven by
sensation but underlies perceptual estimation processes that
exploit and incorporate different types of information sources, in
particular short-term prior experience. The proposed mathematical
framework is likely applicable to magnitude estimation across
different modalities and consequently contributes to a unifying
account of the behavior.