On the effects of signaling reinforcer probability and magnitude in delayed matching to sample

Two experiments examined whether postsample signals of reinforcer probability or magnitude affected the accuracy of delayed matching to sample in pigeons. On each trial, red or green choice responses that matched red or green stimuli seen shortly before a variable retention interval were reinforced with wheat access. In Experiment 1, the reinforcer probability was either 0.2 or 1.0 for both red and green responses. Reinforcer probability was signaled by line or cross symbols that appeared after the sample had been presented. In Experiment 2, all correct responses were reinforced, and the signaled reinforcer durations were 1.0 s and 4.5 s. Matching was more accurate when larger or more probable reinforcers were signaled, independently of retention interval duration. Because signals were presented postsample, the effects were not the result of differential attention to the sample.     

An evidential support accumulation model of subjective probability

A model of cue-based probability judgment is developed within the framework of support theory. Cue diagnosticity is evaluated from experience as represented by error-free frequency counts. When presented with a pattern of cues, the diagnostic implications of each cue are assessed independently and then summed to arrive at an assessment of the support for a hypothesis, with greater weight placed on present than on absent cues. The model can also accommodate adjustment of support in light of the baserate or prior probability of a hypothesis. Support for alternatives packed together in a "residual" hypothesis is discounted; fewer cues are consulted in assessing support for alternatives as support for the focal hypothesis increases. Results of fitting this and several alternative models to data from four new multiple-cue probability learning experiments are reported.     

Absolute Probability Functions for Intuitionistic Propositional Logic

Provided here is a characterisation of absolute probability functions for intuitionistic (propositional) logic L, i.e. a set of constraints on the unary functions P from the statements of L to the reals, which insures that (i) if a statement A of L is provable in L, then P(A) = 1 for every P, L's axiomatisation being thus sound in the probabilistic sense, and (ii) if P(A) = 1 for every P, then A is provable in L, L's axiomatisation being thus complete in the probabilistic sense. As there are theorems of classical (propositional) logic that are not intuitionistic ones, there are unary probability functions for intuitionistic logic that are not classical ones. Provided here because of this is a means of singling out the classical probability functions from among the intuitionistic ones.     

A local model of concurrent performance

Concurrent procedures may be conceptualized as consisting of two pairs of schedules with only one pair operating at a time. One schedule of each pair arranges reinforcers for staying in the current alternative, and the other schedule arranges reinforcers for switching to the other alternative. These pairs alternate operation as the animal switches between choices. This analysis of the contingencies suggests that variables operating within an alternative produce behavior that conforms to the generalized matching law. Rats were exposed to one pair of stay and switch schedules in each condition, and the probabilities of reinforcement varied across conditions. Both run length and visit duration were power functions of the ratio of the probabilities of reinforcement for staying and switching. The local model, a model of performance on concurrent procedures, was derived from this power function. Performance on concurrent schedules was synthesized from the performances on the separate pairs. Both the generalized matching law and the local model fitted the synthesized concurrent performances. These results are consistent with the view that the contingencies in the alternative, the probability of stay and switch reinforcement, are responsible for performance consistent with the generalized matching law. These results are compatible with momentary maximizing and molar maximizing accounts of concurrent performance. Models of concurrent performance that posit comparisons among the alternatives are not easily applied to these results.     

Paradigms in Measure Theoretic Learning and in Informant Learning

We investigate many paradigms of identifications for classes of languages (namely: consistent learning, EX learning, learning with finitely many errors, behaviorally correct learning, and behaviorally correct learning with finitely many errors) in a measure-theoretic context, and we relate such paradigms to their analogues in learning on informants. Roughly speaking, the results say that most paradigms in measure-theoretic learning wrt some classes of distributions (called canonical) are equivalent to the corresponding paradigms for identification on informants.     

Using high-probability foods to increase the acceptance of low-probability foods

Studies have evaluated a range of interventions to treat food selectivity in children with autism and related developmental disabilities. The high-probability instructional sequence is one intervention with variable results in this area. We evaluated the effectiveness of a high-probability sequence using 3 presentations of a preferred food on increasing acceptance in a child with autism who refused a few specific foods. The high-probability sequence increased acceptance of 3 foods. We then systematically faded the intervention for 2 foods.     

Hierarchical models of simple mechanisms underlying confidence in decision making

Choice confidence is a central measure in psychological decision research, often being reported on a probabilistic scale. Simple mechanisms that describe the psychological processes underlying choice confidence, including those based on error and confirmation biases, have typically received support via fits to data averaged over subjects. While averaged data ease model development, they can also destroy important aspects of the confidence data distribution. In this paper, we develop a hierarchical model of raw confidence judgments using the beta distribution, and we implement two simple confidence mechanisms within it. We use Bayesian methods to fit the hierarchical model to data from a two-alternative confidence experiment, and we use a variety of Bayesian tools to diagnose shortcomings of the simple mechanisms that are overlooked when applied to averaged data. Bugs code for estimating the models is also supplied.     

Effects of time between trials on rats' and pigeons' choices with probabilistic delayed reinforcers

Parallel experiments with rats and pigeons examined reasons for previous findings that in choices with probabilistic delayed reinforcers, rats' choices were affected by the time between trials whereas pigeons' choices were not. In both experiments, the animals chose between a standard alternative and an adjusting alternative. A choice of the standard alternative led to a short delay (1 s or 3 s), and then food might or might not be delivered. If food was not delivered, there was an "interlink interval," and then the animal was forced to continue to select the standard alternative until food was delivered. A choice of the adjusting alternative always led to food after a delay that was systematically increased and decreased over trials to estimate an indifference point--a delay at which the two alternatives were chosen about equally often. Under these conditions, the indifference points for both rats and pigeons increased as the interlink interval increased from 0 s to 20 s, indicating decreased preference for the probabilistic reinforcer with longer time between trials. The indifference points from both rats and pigeons were well described by the hyperbolic-decay model. In the last phase of each experiment, the animals were not forced to continue selecting the standard alternative if food was not delivered. Under these conditions, rats' choices were affected by the time between trials whereas pigeons' choices were not, replicating results of previous studies. The differences between the behavior of rats and pigeons appears to be the result of procedural details, not a fundamental difference in how these two species make choices with probabilistic delayed reinforcers.     

Modeling the effect of reward amount on probability discounting

The present study with college students examined the effect of amount on the discounting of probabilistic monetary rewards. A hyperboloid function accurately described the discounting of hypothetical rewards ranging in amount from $20 to $10,000,000. The degree of discounting increased continuously with amount of probabilistic reward. This effect of amount was not due to changes in the rate parameter of the discounting function, but rather was due to increases in the exponent. These results stand in contrast to those observed with the discounting of delayed monetary rewards, in which the degree of discounting decreases with reward amount due to amount-dependent decreases in the rate parameter. Taken together, this pattern of results suggests that delay and probability discounting reflect different underlying mechanisms. That is, the fact that the exponent in the delay discounting function is independent of amount is consistent with a psychophysical scaling interpretation, whereas the finding that the exponent of the probability-discounting function is amount-dependent is inconsistent with such an interpretation. Instead, the present results are consistent with the idea that the probability-discounting function is itself the product of a value function and a weighting function. This idea was first suggested by Kahneman and Tversky (1979), although their prospect theory does not predict amount effects like those observed. The effect of amount on probability discounting was parsimoniously incorporated into our hyperboloid discounting function by assuming that the exponent was proportional to the amount raised to a power. The amount-dependent exponent of the probability-discounting function may be viewed as reflecting the effect of amount on the weighting of the probability with which the reward will be received.