Handbook of Psychology, Volume 4: Experimental Psychology

102 Foundations of Visual Perception

gain function in Figure 4.4). When it is used as a prescriptive
framework, it is called an ideal observer.
Observers in the laboratory, or parts of the visual system,
are not subject to prescriptions. What they actually do is
shown in Figure 4.5, which is a descriptive framework: how
observers (or, more generally, systems) actually make deci-
sions (Kubovy & Healy, 1980; Tanner & Sorkin, 1972).
The diagram identifies four opportunities for the observer
to deviate from the normative model:

1.Observers do not know the likelihood function or the prior
probabilities unless they learned them. They are unlikely
to have learned them perfectly; that is why we have
replaced the “likelihood function” and the “prior distribu-
tions” of Figure 4.4 with their subjective counterparts.

2.Instead of combining the “likelihood function” and the

“prior distributions” by using Bayes’s rule, we assume

that the observer has a computer that combines the subjec-

tive counterparts of these two sources of information. This

computer may not follow Bayes’s rule.

3.The subjective gain function may not simply reflect the

payoffs. Participants in an experiment may not only desire

to maximize gain; they may also be interested in exploring

the effect of various response strategies.

4.Instead of combining the “posterior distribution” with the

“gain function” in a way that will maximize gain, we as-

sume that the observer has a biaser that combines the sub-

jective counterparts of these two sources of information.

Problems with Threshold Theories

We have seen that the ROC curve for high-threshold theory is

linear. Such ROC curves are never observed. Let us consider

an example. In the animal behavior literature, a widely

accepted theory of discrimination was equivalent to high-

threshold theory. Cook and Wixted (1997) put this theory to a

test in a study of six pigeons performing a texture discrimi-

nation. On each trial the pigeons were show one of many po-

tential texture patterns on a computer screen (Figure 4.6).

In some of these patterns all the texture elements were iden-

tical in shape and color. Such patterns were called Same (Fig-

ure 4.6D). In the other patterns some of the texture elements

Observer’s

Likelihood

Function

Observer’s

Prior

Distributions

Observer’s

Posterior

Distribution

Observer’s

Gain

Function

Response

Previous

Stimuli

Bayes’s

Theorem

Decision

Rule

Learning

or Evolution Simulus Computer Biaser

Payoffsor

Ecological

Contingencies

Figure 4.5 Bayesian inference (descriptive).

Likelihood

Function

Prior

Distributions

Posterior

Distribution

Gain

Function

Response

Bayes’s

Theorem

Decision

Rule

Stimulus

Figure 4.4 Bayesian inference (prescriptive).