The asymptotic distribution of response probabilities in the Audley-Jonckheere learning model

The asymptotic distributions of response probabilities in the Audley-Jonckheere learning model, as applied to the two-choice learning situation, are described for (1) the experimenter-controlled events model, (2) the subject-controlled events model, and (3) the experimenter-subject-controlled events model.     

Some asymptotic properties of Luce's beta learning model

This paper studies asymptotic properties of Luce's beta model. Asymptotic results are given for the two-operator and four-operator cases of contingent and noncontingent reinforcement.This research was supported in part by the Group Psychology Branch of the Office of Naval Research and in part by the Rockefeller Foundation.     

The asymptotic distribution for the two-absorbing-barrier beta model

For the two-absorbing-barrier specialization of Luce's beta learning model, the asymptotic distribution of the response probability has all its density atp = 0 andp = 1. The functional equation for the amount of the density atp = 1 is investigated in this paper.Abstracted from a portion of the author's doctoral dissertation, University of Pennsylvania, June 1960. The author is indebted to Prof. B. Epstein and to Prof. Robert R. Bush, his dissertation supervisor, for the valuable help and encouragement received from them.The author is grateful to the Moore School for the support extended to him during his doctoral studies. He also wishes to thank D. Parkhill and N. Finkelstein of General Dynamics for their encouragement of his work.     

Symmetric limiting distributions of response probabilities

Necessary and sufficient conditions for the symmetry of the limiting distributions of response probabilities are derived for the Bush and Mosteller two experimenter-controlled events learning model [Bush and Mosteller, 1955].     

The asymptotic posterior normality of the latent trait in an IRT model

It has long been part of the item response theory (IRT) folklore that under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Under very general and nonrestrictive nonparametric assumptions, we make this claim rigorous for a broad class of latent models.This research was partially supported by Office of Naval Research Cognitive and Neural Sciences Grant N0014-J-90-1940, 442-1548, National Science Foundation Mathematics Grant NSF-DMS-91-01436, and the National Center for Supercomputing Applications. We wish to thank Kumar Joag-dev and Zhiliang Ying for enlightening suggestions concerning the proof of the basic result.The authors wish to thank Kumar Joag-Dev, Brian Junker, Bert Green, Paul Holland, Robert Mislevy, and especially Zhiliang Ying for their useful comments and discussions.     

Implicit learning of fifth- and sixth-order sequential probabilities

Serial reaction time (SRT) task studies have established that people can implicitly learn sequential contingencies as complex as fourth-order probabilities. The present study examined people’s ability to learn fifth-order (Experiment 1) and sixth-order (Experiment 2) probabilities. Remarkably, people learned fifth- and sixth-order probabilities. This suggests that the implicit sequence learning mechanism can operate over a range of at least seven sequence elements.     

Epistemic values and the value of learning

In addition to purely practical values, there are cognitive values which figure in scientific deliberations. One way of introducing cognitive values is to consider the cognitive value that accrues to the act of accepting a hypothesis. Although such values may have a role to play in the matter of theory acceptance, this does not exhaust their significance in scientific decision-making. This paper makes a plea for the consideration of epistemic value??cognitive value that attaches to a state of belief. I defend the notion of cognitive epistemic value against criticisms that have been raised against it. A stability requirement for epistemic value-functions is argued for on the basis of considerations of diachronic coherence. This requirement is sufficient for proving the Value of Learning Theorem, which says that the expected utility of cost-free learning cannot be negative. Under the assumption of stability, the expected cognitive epistemic value of undergoing a learning experience must also be non-negative.     

The role of response selection in sequence learning

We investigated the role of response selection in sequence learning in the serial reaction time (SRT) task, by manipulating stimulus-response compatibility. Under conditions in which other types of learning, like perceptual, response-based, and response-effect learning, were unaffected, sequence learning was better with an incompatible than with a compatible stimulus-response mapping. Stimulus discriminability, on the other hand, had no influence on the amount of sequence learning. This indicates that the compatibility effects cannot be accounted for by a different level of task difficulty. Relating our results to the dimensional overlap model (Kornblum, Hasbroucq, & Osman, 1990), which assumes that incompatible stimulus-response mappings require more controlled response selection than do compatible stimulus-response mapping, we suggest that sequence learning in the SRT task is particularly effective when response selection occurs in a controlled way.     

The role of response selection in sequence learning

We investigated the role of response selection in sequence learning in the serial reaction time (SRT) task, by manipulating stimulus–response compatibility. Under conditions in which other types of learning, like perceptual, response-based, and response-effect learning, were unaffected, sequence learning was better with an incompatible than with a compatible stimulus–response mapping. Stimulus discriminability, on the other hand, had no influence on the amount of sequence learning. This indicates that the compatibility effects cannot be accounted for by a different level of task difficulty. Relating our results to the dimensional overlap model (Kornblum, Hasbroucq, & Osman, 1990), which assumes that incompatible stimulus–response mappings require more controlled response selection than do compatible stimulus–response mapping, we suggest that sequence learning in the SRT task is particularly effective when response selection occurs in a controlled way.     

A sequence of limiting distributions of response probabilities

Explicit solutions are obtained for a sequence of limiting distributions of response probabilities for the two experimenter-controlled events learning model of Bush and Mosteller [2]. A generalization to thes experimenter-controlled events model is found.     

Subjective probabilities and values of socio-economic events at different degrees of uncertainty

Abstract.— The relationship between values (negative] positive) and subjective probabilities was studied. Stimuli consisted of unique socio-economic events represented in the political discussion in Finland. Uncertainty was measured as hesitation in estimating probabilities, The results indicated different relationships between values and probability estimates at different degrees of uncertainty. At certainty the relation was u-shaped, at some uncertainty the variables were nearly uncorrelated, and at uncertainty an linear relationship between values and subjective probabilities was found.     

A random support model of the calibration of subjective probabilities

A stochastic model of the calibration of subjective probabilities based on support theory (Rottenstreich and Tversky, 1997, Tversky and Koehler, 1994) is presented. This model extends support theory—a general representation of probability judgment—to the domain of calibration, the analysis of the correspondence between subjective and objective probability. The random support model can account for the common finding of overconfidence, and also predicts the form of the relationship between overconfidence and item difficulty (the “hard–easy effect”). The parameters of the model have natural psychological interpretations, such as discriminability between correct and incorrect hypotheses, and extremity of judgment. The random support model can be distinguished from other stochastic models of calibration by: (a) using fewer parameters, (b) eliminating the use of variable cutoffs by mapping underlying support directly into judged probability, (c) allowing validation of model parameters with independent assessments of support, and (d) applying to a wide variety of tasks by framing probability judgment in the integrative context of support theory.     

Implicit learning of first-, second-, and third-order transition probabilities

Most sequence-learning studies have confounded different types of information, making it difficult to know precisely what is learned. Addressing many of the confounds, the current study shows that people can learn 1st-, 2nd-, and 3rd-order transition probabilities. Measures directly assessing awareness of the probabilities show that the knowledge is implicit early in training and becomes explicit with extended training.     

The influence of NMDA receptors in the dorsomedial striatum on response reversal learning

In mammals, the dorsomedial striatum is one brain area shown to be critical for the flexible shifting of response patterns. At present, the neurochemical mechanisms that underlie learning during a shift in response patterns are unknown. The present study examined the effects of NMDA competitive antagonist, DL-2-amino-5-phosphonopentanoic acid (AP-5), injected into the dorsomedial striatum on the acquisition and reversal of a response discrimination. Male Long-Evans rats were tested across two consecutive days in a modified cross-maze. Rats received an infusion of either saline or AP-5 (5 or 25 nmol) 5 min prior to each test session. In the acquisition phase rats learned to turn in one direction (right or left) to receive a cereal reinforcement. In the reversal learning phase rats learned to turn in the opposite direction as in the acquisition phase. In both phases, criterion was achieved when a rat made 10 consecutive correct trials. Infusions of AP-5 did not impair acquisition, but impaired reversal learning of a response discrimination in a dose-dependent fashion. The reversal learning deficit induced by AP-5 resulted from reversions back to the originally learned response pattern following the initial shift. These results suggest that activation of NMDA receptors in the dorsomedial striatum are critical for the flexible shifting of response patterns by enhancing the reliable execution of a new response pattern under changing task contingencies.