On probabilistic categorization: The Markovian observer

Abstract

A normative model (the Markovian observer) is described for a numerical decision task (an analogue of signal detection) in which the sequence of stimuli instantiates a two-state Markov chain. The expected-value observer of classical signal detection theory is a special case of the Markovian observer. An experiment is also described in which subjects performed the numerical detection task for different Markov chains of stimuli. Neither the ordinary expected-value observer nor the Markovian observer adequately described the performance of actual subjects, particularly when the stimulus sequence was random. A modification of the Markovian observer (the Markovian observer "ignorant" of the transition probabilities governing the stimulus sequence), similar to Kubovy and Healy's ideal-learner model, was simulated on a computer and provided a good qualitative fit to the data, especially to the distribution of violations of signal detection theory's single-criterion rule.

Signal detection by human observers: A cutoff reinforcement learning model of categorization decisions under uncertainty.

“…In each trial, the experimenter randomly chooses one of the two states (sources) in line with the relevant preset prior probabilities. Then the DM observes a stimulus drawn from the 3 Treisman (1987) studied signal detection without feedback; Ashby and Gott (1988) examined two-dimensional stimuli; Ward et al (1988) evaluated the effect of sequential dependencies between stimuli; and Busemeyer and Myung (1992) addressed situations in which complex decision rules may be required.…”

“…Among the experimental results accounted for by the suggested model are Kubovy and Healy's (1977) main findings (described in detail subsequently), which could not be accounted for by the models proposed before their study. More recent theoretical work (Ashby & Gott, 1988;Busemeyer & Myung, 1992;Treisman, 1987;Ward, Livingston, & Joseph, 1988) has focused on more complex categorization tasks and ignored Kubovy and Healy's basic findings) Cognitive Game Theoretic Analysis of Classical SDT Cognitive game theoretic research (Erev & Roth, in press;Roth & Erev, 1995) suggests that it is convenient to decompose models of choice behavior into three major submodels. The first (sub)model is the abstraction of the incentive and information structure.…”

“…Among the experimental results accounted for by the suggested model are Kubovy and Healy's (1977) main findings (described in detail subsequently), which could not be accounted for by the models proposed before their study. More recent theoretical work (Ashby & Gott, 1988; Busemeyer & Myung, 1992; Treisman, 1987; Ward, Livingston, & Joseph, 1988) has focused on more complex categorization tasks and ignored Kubovy and Healy's basic findings 3…”

Two response processes in a guessing task

“…As they get accustomed to the task, they are likely to guess in such a way as to match the pattern of F;« -R" differences with that of F"-l -F" differences in order to raise the proportion of correct responses. To support the validity of the dynamic processes in a signal detection task, I can adduce a learning model for the response process in a signal detection task (Dorfman & Biderman, 1971;Dorfman et al, 1975;Friedman et al, 1968;Ward, 1973;Ward, Livingston, & Li, 1988). The learning model is based on the assumption that the response process operating in a signal detection task is dynamic.…”

Dynamically structured holographic memory : a hybrid of discrete and distributed representation

“…This model is consistent with a large amount of psychological research showing that when sequential dependencies exist, people can often detect and exploit them (e.g., Estes, 1972;Restle, 1966;Rose & Vitz, 1966;Vitz & Todd, 1967). It also explains why people tend to do poorly on tasks that are truly random; they persist in trying to predict the outcomes even though doing so results in sub-optimal results (e.g., Gazzaniga, 1998;Ward, 1973;Ward, Livingston, & Li, 1988). used neural networks to examine the possibility that people play games by attempting to detect and exploit sequential dependencies in their opponent's play.…”