Bayesian combination of two-dimensional location estimates

Behav Res Methods. 2013 Mar;45(1):98-107. doi: 10.3758/s13428-012-0241-x.


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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Bayes Theorem*
  • Cues*
  • Depth Perception
  • Humans
  • Male
  • Models, Biological*
  • Spatial Analysis*
  • Spatial Behavior / physiology*
  • Vision Disparity / physiology