Bayesian combination of two-dimensional location estimates.
We extend a Bayesian method for combining estimates of means and variances from independent cues in a spatial cue-combination paradigm. In a typical cue-combination experiment, subjects estimate a value on a single dimension-for example, depth-on the basis of two different cues, such as retinal disparity and motion. The mathematics for this one-dimensional case is well established. When the variable to be estimated has two dimensions, such as location (which has both x and y values), then the one-dimensional method may be inappropriate due to possible correlations between x and y and the fact that the dimensions may be inseparable. A cue-combination task for location involves people or animals estimating xy locations under two single-cue conditions and in a condition in which both cues are combined. We present the mathematics for the two-dimensional case in an analogous manner to the one-dimensional case and illustrate them using a numeric example. Our example involves locations on maps, but the method illustrated is relevant for any task for which the estimated variable has two or more dimensions.
Department of Psychology, University of Alberta, Edmonton, Alberta, Canada. alinda@ualberta.ca
Alinda
A
Friedman
Elliot A
EA
Ludvig
Eric L G
EL
Legge
Quoc C
QC
Vuong
D001499:Bayes Theorem; D003463:Cues; D003867:Depth Perception; D006801:Humans; D008297:Male; D008954:Models, Biological; D062206:Spatial Analysis; D013037:Spatial Behavior / Q000502:physiology*; D015357:Vision Disparity / Q000502:physiology