Do Bettors Correctly Perceive Odds? Three Studies of How Bettors Interpret Betting Odds as Probabilistic Information

This paper reports on three studies investigating how accurately bettors (=people who regularly bet on sports events) interpret the probabilistic information implied by betting odds. All studies were based on data collected by web surveys prompting a total of 186 experienced bettors to convert sets of representative odds into frequency judgments. Bayesian statistical methods were used to analyze the data. From the results, the following conclusions were made: (i) On the whole, the bettors produced well‐calibrated judgments, indicating that they have realistic perceptions of odds. (ii) Bettors were unable to consciously adjust judgments for different margins. (iii) Although their interval judgments often covered the estimates implied by the odds, the bettors tended to overestimate the variation of expected profitable bets between months. The results are consistent with prior research showing that people tend to make accurate probability judgments when faced with tasks characterized by constant and clear feedback. Copyright © 2015 John Wiley & Sons, Ltd.     

A Duet for one

This paper considers communication in terms of inference about the behaviour of others (and our own behaviour). It is based on the premise that our sensations are largely generated by other agents like ourselves. This means, we are trying to infer how our sensations are caused by others, while they are trying to infer our behaviour: for example, in the dialogue between two speakers. We suggest that the infinite regress induced by modelling another agent – who is modelling you – can be finessed if you both possess the same model. In other words, the sensations caused by others and oneself are generated by the same process. This leads to a view of communication based upon a narrative that is shared by agents who are exchanging sensory signals. Crucially, this narrative transcends agency – and simply involves intermittently attending to and attenuating sensory input. Attending to sensations enables the shared narrative to predict the sensations generated by another (i.e. to listen), while attenuating sensory input enables one to articulate the narrative (i.e. to speak). This produces a reciprocal exchange of sensory signals that, formally, induces a generalised synchrony between internal (neuronal) brain states generating predictions in both agents. We develop the arguments behind this perspective, using an active (Bayesian) inference framework and offer some simulations (of birdsong) as proof of principle.     

Identifying expectations about the strength of causal relationships

When we try to identify causal relationships, how strong do we expect that relationship to be? Bayesian models of causal induction rely on assumptions regarding people’s a priori beliefs about causal systems, with recent research focusing on people’s expectations about the strength of causes. These expectations are expressed in terms of prior probability distributions. While proposals about the form of such prior distributions have been made previously, many different distributions are possible, making it difficult to test such proposals exhaustively. In Experiment 1 we used iterated learning—a method in which participants make inferences about data generated based on their own responses in previous trials—to estimate participants’ prior beliefs about the strengths of causes. This method produced estimated prior distributions that were quite different from those previously proposed in the literature. Experiment 2 collected a large set of human judgments on the strength of causal relationships to be used as a benchmark for evaluating different models, using stimuli that cover a wider and more systematic set of contingencies than previous research. Using these judgments, we evaluated the predictions of various Bayesian models. The Bayesian model with priors estimated via iterated learning compared favorably against the others. Experiment 3 estimated participants’ prior beliefs concerning different causal systems, revealing key similarities in their expectations across diverse scenarios.     

Increasing accuracy of rock-climbing techniques in novice athletes using expert modeling and video feedback

Several studies have examined the efficacy of behavior analytic coaching strategies in sports to increase performance fluency. Rock climbing is a multifaceted sport requiring mastery of several complex behavior chains in order to successfully navigate climbing surfaces. To date, most investigations have focused on the physiological aspects of rock climbing, as opposed to training specific rock-climbing movements. In this replication and extension, researchers used a multiple baseline design across skills to examine an expert video modeling plus video and verbal feedback training package on foundational rock-climbing skills of novice adult climbers. Results demonstrated that all participants showed an increase in accurate performance for all three skills that were targeted in the intervention.     

Clustering colors

Regier, Kay, and Khetarpal report the results of computer simulations that cluster color stimuli on the basis of their coordinates in CIELAB space, one of two commonly used perceptual color spaces. Regier and coauthors find partitions of those stimuli that are strikingly similar to the way actual color lexicons partition color space. They do not argue for the custom-made clustering method used in their simulations, nor for the assumption of CIELAB space. The present paper aims to answer the question to what extent their computational results depend on these assumptions. It does this by applying a great variety of known clustering methods to Regier et al.’s stimuli, and by assuming not only CIELAB space but also CIELUV space, the other main color space.     

Estimation and visualization of confusability matrices from adaptive measurement data

We present a simple but effective method based on Luce’s choice axiom [Luce, R.D. (1959). Individual choice behavior: A theoretical analysis. New York: John Wiley & Sons] for consistent estimation of the pairwise confusabilities of items in a multiple-choice recognition task with arbitrarily chosen choice-sets. The method combines the exact (non-asymptotic) Bayesian way of assessing uncertainty with the unbiasedness emphasized in the classical frequentist approach.We apply the method to data collected using an adaptive computer game designed for prevention of reading disability. A player’s estimated confusability of phonemes (or more accurately, phoneme-grapheme connections) and larger units of language is visualized in an easily understood way with color cues and explicit indication of the accuracy of the estimates. Visualization of learning-related changes in the player’s performance is considered.The empirical validity of the choice axiom is evaluated using the game data itself. The axiom appears to hold reasonably well although a small systematic violation is observable for the smallest choice-set sizes.     

Bayesian parameter estimation in the Expectancy Valence model of the Iowa gambling task

The purpose of the popular Iowa gambling task is to study decision making deficits in clinical populations by mimicking real-life decision making in an experimental context. Busemeyer and Stout [Busemeyer, J. R., & Stout, J. C. (2002). A contribution of cognitive decision models to clinical assessment: Decomposing performance on the Bechara gambling task. Psychological Assessment, 14, 253-262] proposed an “Expectancy Valence” reinforcement learning model that estimates three latent components which are assumed to jointly determine choice behavior in the Iowa gambling task: weighing of wins versus losses, memory for past payoffs, and response consistency. In this article we explore the statistical properties of the Expectancy Valence model. We first demonstrate the difficulty of applying the model on the level of a single participant, we then propose and implement a Bayesian hierarchical estimation procedure to coherently combine information from different participants, and we finally apply the Bayesian estimation procedure to data from an experiment designed to provide a test of specific influence.     

A longitudinal study of student-teacher relationship quality, difficult temperament, and risky behavior from childhood to early adolescence

This study examines the mediating role of student-teacher relationship quality (conflict and closeness) in grades 4, 5, and 6 on the relation between background characteristics, difficult temperament at age 4½ and risky behavior in 6th grade. The longitudinal sample of participants (N = 1156) was from the NICHD Study of Early Child Care and Youth Development. Structural equation modeling was used to estimate paths from (a) background characteristics to student-teacher relationship quality and risky behavior, (b) temperament to student-teacher relationship quality and risky behavior, and (c) student-teacher relationship quality to risky behavior. Findings indicate that students' family income, gender, receipt of special services, and more difficult temperament were associated with risky behavior. In addition, student-teacher conflict was a mediator. Students with more difficult temperaments were more likely to report risky behavior and to have conflict in their relationships with teachers. More conflict predicted more risky behavior. Closer student-teacher relationships were associated with less risky behavior. Results suggest negative relationships, specifically student-teacher relationships, may increase the risk that certain adolescents will engage in risky behavior.     

Learning letter names and sounds: Effects of instruction, letter type, and phonological processing skill

Preschool-age children (N = 58) were randomly assigned to receive instruction in letter names and sounds, letter sounds only, or numbers (control). Multilevel modeling was used to examine letter name and sound learning as a function of instructional condition and characteristics of both letters and children. Specifically, learning was examined in light of letter name structure, whether letter names included cues to their respective sounds, and children’s phonological processing skills. Consistent with past research, children receiving letter name and sound instruction were most likely to learn the sounds of letters whose names included cues to their sounds regardless of phonological processing skills. Only children with higher phonological skills showed a similar effect in the control condition. Practical implications are discussed.     

Distribution-free tests of stochastic dominance for small samples

One variable is said to “stochastically dominate” another if the probability of observations smaller than x is greater for one variable than the other, for all x. Inferring stochastic dominance from data samples is important for many applications of econometrics and experimental psychology, but little is known about the performance of existing inferential methods. Through simulation, we show that three of the most widely used inferential methods are inadequate for use in small samples of the size commonly encountered in many applications (up to 400 observations from each distribution). We develop two new inferential methods that perform very well in a limited, but practically important, case where the two variables are guaranteed not to be equal in distribution. We also show that extensions of these new methods, and an improved version of an existing method, perform quite well in the original, unlimited case.