Dissecting Bayes: Using influence measures to test normative use of probability density information derived from a sample
Fig 2
Parametric decision making based on a sample.
A. Bivariate Gaussian PDF (referred to as the "population"). The population PDF is not known to the decision maker. B. The decision maker is given only a sample P1,⋯,PN of size N drawn from the Gaussian. C. The Gaussian parametric decision maker reduces a large number of sample values to the values of a small number of parameters. For the bivariate Gaussian, the sample is often reduced to five parameters that are estimates of population parameters
(referred to as "statistics"). D. The normative decision maker then makes decisions based only on these statistics, ignoring any "accidental" structure in the sample not captured by the parameters. For convenience in presentation we assume throughout that the Gaussian pdf is elongated (anisotropic) so that there there are exactly two orthogonal axes of symmetry. The excluded possibility is that the Gaussian is isotropic (circularly symmetric). All the Gaussian pdfs used in the experiment were anisotropic, vertically elongated.