Bayesian Explanation Research Articles

Bayesian Explanation of the Effects of Tactile Feedback on the Affective Evaluation of Switch Sounds

Bayesian Explanation of the Effects of Tactile Feedback on the Affective Evaluation of Switch Sounds

A Bayesian explanation of the irrationality of sexist and racist beliefs involving generic content

Various sexist and racist beliefs ascribe certain negative qualities to people of a given sex or race. Epistemic allies are people who think that in normal circumstances rationality requires the rejection of such sexist and racist beliefs upon learning of many counter-instances. This is a common view among philosophers and non-philosophers. But epistemic allies face three problems. First, sexist and racist beliefs often involve generic propositions. These sorts of propositions are notoriously resilient in the face of counter-instances. Second, background beliefs can enable one to explain away counter-instances to one’s beliefs, thus making it rational to retain one’s beliefs in generics in the face of many counter-instances. The final problem is that the kinds of judgements epistemic allies want to make about the irrationality of sexist and racist beliefs upon encountering many counter-instances is at odds with the judgements that we are inclined to make in seemingly parallel cases about the rationality of non-sexist and non-racist generic beliefs. Thus epistemic allies may end up having to give up on plausible normative supervenience principles. In what follows I explain how a Bayesian approach to the relation between evidence and belief can neatly untie these knots. The basic story is one of defeat: Bayesianism explains when one is required to become increasingly confident in chance propositions, and confidence in chance propositions can make belief in corresponding generics irrational.

A Bayesian explanation for the effect of incumbency

Incumbents appear to perform better in elections because they are incumbents, yet the most commonly proposed explanations for this phenomenon are unsatisfying. I introduce a new explanation that is simple, parsimonious, and largely consistent with empirical evidence. If voters lack perfect information about electoral candidates, incumbency is an informative signal of quality, and voters will update their beliefs accordingly. I formalize these claims with a decision-theoretic model where voters receive noisy signals of candidate quality, and I discuss several empirical phenomena consistent with this explanation. For example, when voters learn that their incumbent barely won office, they are less likely to support reelection and the effect of incumbency largely disappears.

A Bayesian perspective on Likert scales and central tendency.

The central tendency bias is a robust finding in data from experiments using Likert scales to elicit responses. The present paper offers a Bayesian perspective on this bias, explaining it as a natural outcome of how participants provide point estimates of probability distributions over the items on a Likert scale. Two studies are reported that support this Bayesian explanation.

Mindreading and endogenous beliefs in games

We argue that a Bayesian explanation of strategic choices in games requires introducing a psychological theory of belief formation. We highlight that beliefs in epistemic game theory are derived from the actual choice of the players, and cannot therefore explain why Bayesian rational players should play the strategy they actually chose. We introduce the players’ capacity of mindreading in a game theoretical framework with the simulation theory, and characterise the beliefs that Bayes rational players could endogenously form in games. We show in particular that those beliefs need not be ratifiable, and therefore that rational players can form action-dependent beliefs.

Optimal non-diagonal-type estimators in linear regression under the prediction error sum of squares criterion

ABSTRACTThis article considers the notion of the non-diagonal-type estimator (NDTE) under the prediction error sum of squares (PRESS) criterion. First, the optimal NDTE in the PRESS sense is derived theoretically and applied to the cosmetics sales data. Second, we make a further study to extend the NDTE to the general case of the covariance matrix of the model and then give a Bayesian explanation for this extension. Third, two remarks concerned with some potential shortcomings of the NDTE are presented and an alternative solution is provided and illustrated by means of simulations.

It does belong together: cross-modal correspondences influence cross-modal integration during perceptual learning.

Experiencing a stimulus in one sensory modality is often associated with an experience in another sensory modality. For instance, seeing a lemon might produce a sensation of sourness. This might indicate some kind of cross-modal correspondence between vision and gustation. The aim of the current study was to explore whether such cross-modal correspondences influence cross-modal integration during perceptual learning. To that end, we conducted two experiments. Using a speeded classification task, Experiment 1 established a cross-modal correspondence between visual lightness and the frequency of an auditory tone. Using a short-term priming procedure, Experiment 2 showed that manipulation of such cross-modal correspondences led to the creation of a crossmodal unit regardless of the nature of the correspondence (i.e., congruent, Experiment 2a or incongruent, Experiment 2b). However, a comparison of priming effects sizes suggested that cross-modal correspondences modulate cross-modal integration during learning, leading to new learned units that have different stability over time. We discuss the implications of our results for the relation between cross-modal correspondence and perceptual learning in the context of a Bayesian explanation of cross-modal correspondences.

Perceptual biases and cue weighting in perception of 3D slant from texture and stereo information

Multiple cues are typically available for perceiving the 3D slant of surfaces, and slant perception has been used as a test case for investigating cue integration. Previous evidence suggests that texture and stereo slant cues contribute in an optimal Bayesian manner. We tested whether a Bayesian model could also account for perceptual underestimation of slant from texture. One explanation proposed by Todd, Christensen, and Guckes (2010) is that slant from texture is based on an inaccurate optical variable. An alternative Bayesian explanation is that perceptual underestimation is due to the influence of frontal cues and/or a frontal prior, which is weighted according to the reliability of slant cues. We measured slant perception using a hand-alignment task for conditions that provided only texture, only stereo, or combined texture and stereo cues. Slant estimates from monocular texture showed large biases toward frontal, with proportionally more underestimation at low slants than high slants. Slant estimates from stereo alone were more accurate, and adding texture information did not reduce accuracy. These results are consistent with a frontal influence that is decreasingly weighted as slant information becomes more reliable. We also included conditions with small cue conflicts to measure the relative weighting of texture and stereo cues. Consistent with previous studies, texture had a significant effect on slant estimates in binocular conditions, and the relative weighting of texture increased with slant. In some cases, perceived slant from combined stereo and texture cues was higher than from either cue in isolation. Both the perceptual biases and the cue weights were generally consistent with a Bayesian model that optimally integrates texture and stereo slant cues with frontal cues and/or a frontal prior.

A unifying learning framework for building artificial game-playing agents

This paper investigates learning-based agents that are capable of mimicking human behavior in game playing, a central task in computational economics. Although computational economists have developed various game-playing agents, well-established machine learning methods such as graphical models have not been applied before. Leveraging probabilistic graphical models, this paper presents a novel sequential Bayesian network (SBN) framework for building artificial game-playing agents. We show that many existing agents, including reinforcement learning, fictitious play, and many of their variants, have a unified Bayesian explanation within the proposed SBN framework. Moreover, we discover that SBN can handle various important settings of game playing, allowing for a broad scope of its use in economics. SBN not only provides a unifying and satisfying framework to explain existing learning approaches in virtual economies, but also enables the development of new algorithms that are stronger or have fewer restrictions. In this paper, we derive a new algorithm, Hidden Markovian Play (HMP), from the generic SBN model to handle an important but difficult setting in which a player cannot observe the opponent's strategy and payoff. It leverages Markovian learning to infer unobservable information, leading to higher quality of the agents. Experiments on real-world field experiments in evaluating economies show that our HMP model outperforms the baseline algorithms for building artificial agents.

A predictive coding perspective on autism spectrum disorders

A predictive coding perspective on autism spectrum disorders

A Bayesian explanation of the ‘Uncanny Valley’ effect and related psychological phenomena

There are a number of psychological phenomena in which dramatic emotional responses are evoked by seemingly innocuous perceptual stimuli. A well known example is the ‘uncanny valley’ effect whereby a near human-looking artifact can trigger feelings of eeriness and repulsion. Although such phenomena are reasonably well documented, there is no quantitative explanation for the findings and no mathematical model that is capable of predicting such behavior. Here I show (using a Bayesian model of categorical perception) that differential perceptual distortion arising from stimuli containing conflicting cues can give rise to a perceptual tension at category boundaries that could account for these phenomena. The model is not only the first quantitative explanation of the uncanny valley effect, but it may also provide a mathematical explanation for a range of social situations in which conflicting cues give rise to negative, fearful or even violent reactions.

The Bayesian explanation of transmission failure

Even if our justified beliefs are closed under known entailment, there may still be instances of transmission failure. Transmission failure occurs when P entails Q, but a subject cannot acquire a justified belief that Q by deducing it from P. Paradigm cases of transmission failure involve inferences from mundane beliefs (e.g., that the wall in front of you is red) to the denials of skeptical hypotheses relative to those beliefs (e.g., that the wall in front of you is not white and lit by red lights). According to the Bayesian explanation, transmission failure occurs when (i) the subject’s belief that P is based on E, and (ii) P(Q|E) P(Q). No modifications of the Bayesian explanation are capable of accommodating such cases, so the explanation must be rejected as inadequate. Alternative explanations employing simple subjunctive conditionals are fully capable of capturing all of the paradigm cases, as well as those missed by the Bayesian explanation.

Overconfidence and underconfidence: When and why people underestimate (and overestimate) the competition

It is commonly held that people believe themselves to be better than others, especially for outcomes under their control. However, such overconfidence is not universal. This paper presents evidence showing that people believe that they are below average on skill-based tasks that are difficult. A simple Bayesian explanation can account for these effects and for their robustness: On skill-based tasks, people generally have better information about themselves than about others, so their beliefs about others’ performances tend to be more regressive (thus less extreme) than their beliefs about their own performances. This explanation is tested in two experiments that examine these effects’ robustness to experience, feedback, and market forces. The discussion explores the implications for strategic planning in general and entrepreneurial entry in particular.

Overconfidence and Underconfidence

It is commonly held that, especially for outcomes under their control, people believe themselves to be better than others. However, such overconfidence is not universal. This paper presents evidence showing that people believe that they are below average on skill-based tasks that are difficult. A simple Bayesian explanation can account for these effects and for their robustness: On skill-based tasks, people generally have better information about themselves than about others, so their beliefs about others' performances tend to be less extreme than their beliefs about their own performances. This explanation is tested in two experiments that examine these effects' robustness to experience, feedback, and market forces. The discussion explores the implications for strategic planning in general and entrepreneurial entry in particular.

1010-64 Left Ventricular Size Effects the Diagnostic Accuracy of SPECT Thallium-201 Perfusion Imaging in Both Men and Women

The diagnostic accuracy of SPECT TI-201 for coronary artery disease (CAD) is lower in women (F) than in men (M). Previous investigators have suggested a Bayesian explanation. More recently, it has been suggested that smaller left ventricular mass in women was the cause. The current study was undertaken to assess the effect of left ventricular size (LVsize) on the accuracy of SPECT TI-201. For this study patients who had either less than 5% pretest probability of CAD (nls) or had cardiac catheterization performed within 45 days of stress thallium testing without an intervening cardiac event (pts) were Identified. We excluded patients with pathologic Q waves, documented prior infarction, LBBB on EKG, prior CABG or non-ischemic cardiomyopathy. We Identified a total of 259 subjects (153 M, 106 F). Patients with <50% stenosis on cath were analyzed as nl. Twenty M and 20 F were taken from the nls and processed separately to create normal limits. Images were reconstructed with a Hanning filter. The fraction of the left ventricle less than 1, 2, 2.5, 3 and 4 standard deviations was calculated and used to calculate the area under the receiver operating characteristic (ROC) curves using the Dorfman maximum likelihood technique. A measure of left ventricular size was generated from short axis slice diameter and the number of slices. The number of stenosed vessels (2.0 ± 0.8 vs. 1.9 ± 0.9, P = NS) and worst stenosis (91 ± 12% vs. 89 ± 15%, p = NS) were similar for M and F. M exercised to higher workloads (estimated METS 6.7 ± 3.1 vs. 4.3 ± 2.3, p < 0.0001) but similar peak heart rates (HR) and percent of maximal predicted HR (133 ± 19 vs. 130 ± 22 and 78 ± 11% vs. 79 ± 13%, both p = NS). The LVsize was greater in men (105 vs. 79 p < 0.001). The area under the ROC curves for M was marginally greater than F (0.92 vs. 0.82 P = 0.10). LV size significantly affected accuracy; the ROC area for M and F with LVsize >75 was much greater than for those <75 (0.89 vs. 0.64 P = 0.007). There was no significant difference in accuracy between M and F with LVsize > 75 (0.91vs. 0.85, P = 0.47). We conclude that a small LVsize significantly reduces the accuracy of SPECT TI-201 in M and F, but since F have, on average, smaller LVsize, they are more likely to be affected.

Investigations of excess environmental risks around putative sources: statistical problems and a proposed test.

Individual reactions to a report which identifies an excess of risk near a putative source are determined mainly by some quoted significance level. One reaction, involving a commonly used 'coincidence' argument is given a simple Bayesian explanation. It is argued that interpretations of such reports should if possible allow both for data selection and for uncertainty in the null expectations underlying the significance levels. Tests are proposed, based on the first isotonic regression estimator under an order restriction, which allow for the effects of selecting a study region in the light of the data and have a simple form. Data on cancer incidence around two nuclear plants are used to illustrate.

Bayes' theorem in the trial process: Instructing jurors on the value of statistical evidence.

The use of statistics and probabilities as legal evidence has recently come under increased scrutiny. Judges' and jurors' ability to understand and use this type of evidence has been of special concern. Finkelstein and Fairley (1970) proposed introducing Bayes' theorem into the courtroom to aid the fact-finder evaluate this type of evidence. The present study addressed individuals' ability to use statistical information as well as their ability to understand and use an expert's Bayesian explanation of that evidence. One hundred and eighty continuing education students were presented with a transcript purportedly taken from an actual trial and were asked to make several subjective probabiliy judgments regarding blood-grouping evidence. The results extend to the trial process previous psychological research suggesting that individuals generally underutilize statistical information, as compared to a Bayesian model. In addition, subjects in this study generally ignored the expert's Bayesian explanation of the statistical evidence.