Conditional Probability and Defeasible Inference

We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey–Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of non-monotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).Expectation is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability. The research of both authors was supported in part by a grant from NSF, and, for Parikh, also by support from the research foundation of CUNY.     

The precise time course of lexical activation: MEG measurements of the effects of frequency, probability, and density in lexical decision

Visually presented letter strings consistently yield three MEG response components: the M170, associated with letter-string processing (Tarkiainen, Helenius, Hansen, Cornelissen, & Salmelin, 1999); the M250, affected by phonotactic probability, (Pylkk?nen, Stringfellow, & Marantz, 2002); and the M350, responsive to lexical frequency (Embick, Hackl, Schaeffer, Kelepir, & Marantz, 2001). Pylkk?nen et al. found evidence that the M350 reflects lexical activation prior to competition among phonologically similar words. We investigate the effects of lexical and sublexical frequency and neighborhood density on the M250 and M350 through orthogonal manipulation of phonotactic probability, density, and frequency. The results confirm that probability but not density affects the latency of the M250 and M350; however, an interaction between probability and density on M350 latencies suggests an earlier influence of neighborhoods than previously reported.     

The Effects of Framing, Reflection, Probability, and Payoff on Risk Preference in Choice Tasks

A meta-analysis of Asian-disease-like studies is presented to identify the factors which determine risk preference. First the confoundings between probability levels, payoffs, and framing conditions are clarified in a task analysis. Then the role of framing, reflection, probability, type, and size of payoff is evaluated in a meta-analysis. It is shown that bidirectional framing effects exist for gains and for losses. Presenting outcomes as gains tends to induce risk aversion, while presenting outcomes as losses tends to induce risk seeking. Risk preference is also shown to depend on the size of the payoffs, on the probability levels, and on the type of good at stake (money/property vs human lives). In general, higher payoffs lead to increasing risk aversion. Higher probabilities lead to increasing risk aversion for gains and to increasing risk seeking for losses. These findings are confirmed by a subsequent empirical test. Shortcomings of existing formal theories, such as prospect theory, cumulative prospect theory, venture theory, and Markowitz's utility theory, are identified. It is shown that it is not probabilities or payoffs, but the framing condition, which explains most variance. These findings are interpreted as showing that no linear combination of formally relevant predictors is sufficient to capture the essence of the framing phenomenon.     

Interval estimation for the intraclass correlation in dirichlet-multinomial data

When the underlying distribution is discrete with a limited number of categories, methods for interval estimation of the intraclass correlation which assume normality are theoretically inadequate for use. On the basis of large sample theory, this paper develops an asymptotic closed-form interval estimate of the intraclass correlation for the case where there is a natural score associated with each category. This paper employs Monte Carlo simulation to demonstrate that when the underlying intraclass correlation is large, the traditional interval estimator which assumes normality can be misleading. We find that when the number of classes is 20, the interval estimator proposed here can generally perform reasonably well in a variety of situations. This paper further notes that the proposed interval estimator is invariant with respect to a linear transformation. When the data are on a nominal scale, an extension of the proposed method to account for this case, as well as a discussion on the relationship between the intraclass correlation and a kappa-type measure defined here and on the limitation of the corresponding kappa-type estimator are given.The authors wish to thank the Editor, the Associate Editor, and the three referees for many valuable comments and suggestions to improve the clarity of this paper. The works for the first, the third, and the fourth authors were partially supported by grant #R01AR43025-01 from the National Institute of Arthritis and Musculoskeletal and Skin Diseases.     

Effects of social context, reinforcer probability, and reinforcer magnitude on humans' choices to compete or not to compete.

In the first two experiments, subjects' choices to earn points (exchangeable for money) either by competing with a fictitious opponent or by not competing were studied. Buskist, Barry, Morgan, and Rossi's (1984) competitive fixed-interval schedule was modified to include a second response option, a noncompetitive fixed-interval schedule. After choosing to enter either option, the opportunity for reinforcers became available after the fixed-interval's duration had elapsed. Under the no-competition condition, points were always available after the interval had elapsed. Under the competition condition, points were available based on a predetermined probability of delivery. Experiments 1 and 2 examined how reinforcer probabilities and reinforcer magnitudes affected subjects' choices to compete. Several general conclusions can be made about the results: (a) Strong preferences to compete were observed at high and moderate reinforcer probabilities; (b) competing was observed even at very low reinforcer probabilities; (c) response rates were always higher in the competition component than in the no-competition component; and (d) response rates and choices to compete were insensitive to reinforcer-magnitude manipulations. In Experiment 3, the social context of this choice schedule was removed to determine whether the high levels of competing observed in the first two experiments were due to a response preference engendered by the social context provided by the experimenters through instructions. In contrast to the first two experiments, these subjects preferred the 60-s fixed-interval schedule (formerly the no-competition option), indicating that the instructions themselves were responsible for the preference to compete. This choice paradigm may be useful to future researchers interested in the effects of other independent variables (e.g., drugs, social context, instructions) on competitive behavior.     

Reinforcement contingencies as discriminative stimuli: II. Effects of changes in stimulus probability.

Three pigeons were trained on a matching procedure involving a sample component and a choice component. Responding in the sample component, according to either a differential-reinforcement-of-low-rate schedule on some trials or a differential-reinforcement-of-other-behavior schedule on other trials, produced access to the choice component in which each of two keys was illuminated with a unique color. The correct choice response was defined by the contingency that was met to produce the choice. The food hopper operated for 1.5 seconds following an appropriate sample response and for 3 seconds following a correct choice response. A signal-detection analysis showed that variations in the probability of presentation of the different contingencies systematically affected response bias but not sensitivity to the contingencies as stimuli. Substitution of a blackout for food at the end of the sample component did not differentially affect performance, but elimination of the delay between sample and choice components generally increased the sensitivity measure. The findings suggest a role for reinforcement contingency discrimination in schedule-controlled responding.     

Binary action based estimation of propensities

An observer is to make inference statements about a quantityp, called apropensity and bounded between 0 and 1, based on the observation thatp does or does not exceed a constantc. The propensityp may have an interpretation as a proportion, as a long-run relative frequency, or as a personal probability held by some subject. Applications in medicine, engineering, political science, and, most especially, human decision making are indicated. Bayes solutions for the observer are obtained based on prior distributions in the mixture of beta distribution family; these are then specialized to power-function prior distributions. Inference about logp and log odds is considered. Multiple-action problems are considered in which the focus of inference shifts to theprocess generating the propensitiesp, both in the case of a process parameter known to the subject and unknown. Empirical Bayes techniques are developed for observer inference aboutc when is known to the subject. A Bayes rule, a minimax rule and a beta-minimax rule are constructed for the subject when he is uncertain about.This research was partially supported by the Defense Advanced Research Projects Agency of the Department of Defense and was monitored by ONR under Contract No. N00014-77-C-0095. Any opinions, findings, conclusions or recommendations expressed herein are those of the author and do not necessarily reflect the views of the Defense Advanced Research Projects Agency, the Office of Naval Research, or Carnegie-Mellon University.     

The role of intermittent food in the induction of attack in pigeons

The present experiments evaluated whether transitions in reinforcer probability are necessary to induce attack in pigeons. In Experiment I, three of six pigeons exposed to response-contingent constant-probability food schedules and a photograph of a conspecific as a target exhibited sustained postreinforcement attack on the target. The postreinforcement pattern of attack developed over the course of the experiment and was accompanied by a reduction in the rate of postreinforcement key pecking and an increase in the postreinforcement pause in key pecking. These effects on key pecking resulted in unprogrammed variations in the probability of reinforcement which may have been responsible for the induction of attack. In Experiment II, the attack-inducing properties of a constant-probability response-independent food schedule were compared to a periodic food schedule matched for overall rate of food delivery and to a no-food condition. In addition to attack, the spatial location of the subjects was monitored during each interfood interval. The periodic and aperiodic food schedules generated very different patterns of spatial location. Postfood attack was induced by both food schedules, although the constant-probability schedule induced attack in fewer birds. The no-food condition was not effective in inducing attack in any birds. These experiments indicate that intermittent food schedules without reductions in reinforcer probability are sufficient to induce attack in some pigeons, although not as effective as schedules with transitions in reinforcer probability.     

Choice with probabilistic reinforcement: effects of delay and conditioned reinforcers.

Two experiments measured pigeons' choices between probabilistic reinforcers and certain but delayed reinforcers. In Experiment 1, a peck on a red key led to a 5-s delay and then a possible reinforcer (with a probability of .2). A peck on a green key led to a certain reinforcer after an adjusting delay. This delay was adjusted over trials so as to estimate an indifference point, or a duration at which the two alternatives were chosen about equally often. In all conditions, red houselights were present during the 5-s delay on reinforced trials with the probabilistic alternative, but the houselight colors on nonreinforced trials differed across conditions. Subjects showed a stronger preference for the probabilistic alternative when the houselights were a different color (white or blue) during the delay on nonreinforced trials than when they were red on both reinforced and nonreinforced trials. These results supported the hypothesis that the value or effectiveness of a probabilistic reinforcer is inversely related to the cumulative time per reinforcer spent in the presence of stimuli associated with the probabilistic alternative. Experiment 2 tested some quantitative versions of this hypothesis by varying the delay for the probabilistic alternative (either 0 s or 2 s) and the probability of reinforcement (from .1 to 1.0). The results were best described by an equation that took into account both the cumulative durations of stimuli associated with the probabilistic reinforcer and the variability in these durations from one reinforcer to the next.     

Hyperbolic modeling and assessment of hypothetical health behaviors during a viral outbreak using crowdsourced samples

The COVID-19 pandemic provided an opportunity to investigate factors related to public response to public health measures, which could help better prepare implementation of similar measures for inevitable future pandemics. To understand individual and environmental factors that influence likelihood in engaging in personal and public health measures, three crowdsourced convenience samples from Amazon Mechanical Turk (MTurk) completed likelihood-discounting tasks of engaging in health behaviors given a variety of hypothetical viral outbreak scenarios. Experiment 1 assessed likelihood of mask wearing for a novel virus. Experiment 2 assessed vaccination likelihood based on efficacy and cost. Experiment 3 assessed likelihood of seeking health care based on number of symptoms and cost of treatment. Volume-based measures and three-dimensional modeling were used to analyze hypothetical decision making. Hypothetical public and personal health participation increased as viral fatality increased and generally followed a hyperbolic function. Public health participation was moderated by political orientation and trust in science, whereas treatment-seeking was only moderated by income. Analytic methods used in this cross-sectional study predicted population-level outcomes that occurred later in the pandemic and can be extended to various health behaviors.