Philosophy and the practice of Bayesian statistics

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico‐deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.     

Discovering syntactic deep structure via Bayesian statistics

In the Bayesian framework, a language learner should seek a grammar that explains observed data well and is also a priori probable. This paper proposes such a measure of prior probability. Indeed it develops a full statistical framework for lexicalized syntax. The learner's job is to discover the system of probabilistic transformations (often called lexical redundancy rules) that underlies the patterns of regular and irregular syntactic constructions listed in the lexicon. Specifically, the learner discovers what transformations apply in the language, how often they apply, and in what contexts. It considers simpler systems of transformations to be more probable a priori. Experiments show that the learned transformations are more effective than previous statistical models at predicting the probabilities of lexical entries, especially those for which the learner had no direct evidence.     

Basic statistics and the inconsistency of multiple comparison procedures.

This paper has two main themes. First, the various statistical measures used in this journal are summarized and their interrelationships described by way of a flow chart. These are the pooled standard deviation, the pooled variance or mean square error (MSE), the standard error of each treatment mean (SEM) and of the difference between two treatment means (SED), and the least difference between two means which is significant at (e.g.) the 5% level of significance (LSD(5%)). The last three measures can be displayed as vertical bars in graphs, and the relationship between the lengths of these bars is graphically illustrated. It is suggested that the LSD is the most useful of these three measures. Second, when the experimenter has no prior hypotheses to be tested using analysis of variance "contrasts," a multiple comparison procedure (MCP) that examines all pair-wise differences between treatment means, may be appropriate. In this paper a fictitious experimental data set is used to compare several well-known McPs by focussing on a particular operating characteristic, the consistency of the results between an overall analysis of all treatments and an analysis of a subset of the experimental treatments. The procedure that behaves best according to this criterion is the unrestricted least significant difference (LSD) procedure. The unrestricted LSD is therefore recommended with the proviso that it be used as a method of generating hypotheses to be tested in subsequent experimentation, not as a method that attempts to simultaneously formulate and test hypotheses.     

Are there still things to do in Bayesian statistics?

From the outside, Bayesian statistics may seem like a closed little corner of probability. Once a prior is specified you compute! From the inside the field is filled with problems, conceptual and otherwise. This paper surveys some of what remains to be done and gives examples of the work in progress via a Bayesian peek into Feller volume I.This work had its origin in conversations with Marco Scarsini. Distance has prevented us from working things out jointly. This paper was presented at the workshop, we thank Eugenio Regazzini, Dominico Costantini and Maria Carla Galavotti for their help. Art Dempster, Carl Morris, John Pratt, Abner Shimony and Sandy Zabell raised interesting questions incorporated herein.     

Understanding associations between negatively biased attention and depression and social anxiety: positively biased attention is key

ABSTRACT

Background and objectives: Although research supports the premise that depressed and socially anxious individuals direct attention preferentially toward negative emotional cues, little is known about how attention to positive emotional cues might modulate this negative attention bias risk process. The purpose of this study was to determine if associations between attention biases to sad and angry faces and depression and social anxiety symptoms, respectively, would be strongest in individuals who also show biased attention away from happy faces.

Methods: Young adults (N?=?151; 79% female; M?=?19.63 years) completed self-report measures of depression and social anxiety symptoms and a dot probe task to assess attention biases to happy, sad, and angry facial expressions.

Results: Attention bias to happy faces moderated associations between attention to negatively valenced faces and psychopathology symptoms. However, attention bias toward sad faces was positively and significantly related to depression symptoms only for individuals who also selectively attended toward happy faces. Similarly, attention bias toward angry faces was positively and significantly associated with social anxiety symptoms only for individuals who also selectively attended toward happy faces.

Conclusions: These findings suggest that individuals with high levels of depression or social anxiety symptoms attend preferentially to emotional stimuli across valences.     

Representations for biased numerical judgments

Models are presented that introduce bias parameters into the numerical representations for ratio and interval judgments. An interval bias model is considered that has the capability of accounting for both interval and ratio judgments. A contrasting ratio bias model—a simple generalization of the classical model that accepts ratio judgments at face value—is also considered, and both models are tested with brightness data. The ratio estimation data lead to the conclusion that the constraints placed on the structure of the data by the classical model are too strong. In terms of goodness-of-fit and certain theoretical criteria, the interval bias model accounts for the ratio estimation data better than the ratio bias model. The interval estimation data are supportive of recent efforts directed toward the development of direct interval scaling theory.     

Perfectionism and statistics anxiety

The purpose of this study was to investigate the relationship between perfectionism and statistics anxiety, using a multivariate approach. Participants were 107 students enrolled in graduate-level research methodology courses. A canonical correlation analysis revealed that graduate students who hold unrealistic standards for significant others (i.e. other-oriented perfectionists) and those who maintain a perceived need to attain standards and expectations prescribed by significant others (i.e. socially-prescribed perfectionists) tend to have higher levels of statistics anxiety associated with interpretation anxiety, test and class anxiety, computational self-concept and fear of asking for help. The implications of these findings are discussed.     

Transfer of training emotionally biased interpretations

Non‐anxious college students first performed a semantic‐judgement task that was designed to train either threat‐related or threat‐unrelated interpretations of threat‐ambiguous homographs (e.g. mug). Next they performed an ostensibly separate transfer task of constructing personal mental images for single words, in a series that included new, threat‐ambiguous homographs. In two experiments, the number of threat‐related interpretations in the transfer task significantly increased following threat‐related experience during the training phase, compared to other training conditions. We conclude that interpretive biases typically shown by anxious people can be established in non‐anxious students in ways that generalize to novel tasks and materials. Copyright © 2003 John Wiley & Sons, Ltd.     

Attention is biased to near surfaces

It is thought that attention is allocated to figural items over adjacent ground stimuli. It is unclear which attribute of figures drives any previously observed attentional effects (e.g., nearness or shapedness). Moreover, it is unclear whether previous attentional effects are automatic or strategy driven. In the present series of experiments, we tested whether attention is allocated to the nearer of two surfaces under condition where near/far was not confounded with shaped/shapelessness. Using a temporal order judgment paradigm, in the first experiment, we showed that attention is allocated to the nearer of two surfaces. Furthermore, by using the stimuli themselves as the temporal order probe in Experiment 2, we found that this effect is independent of previous attentional allocation across the visual field. A third experiment ruled out the possibility that lateral inhibition by the pretarget backdrop was responsible for attentional bias toward near surfaces. Overall, our results converge to show that near surfaces attract attention.     

Accurate and biased perceptions of responsive support predict well-being

The current research examined effects of accurate and biased perceptions of romantic partners’ responsive support provision on perceivers’ well-being. Perceivers discussed a personal problem with their romantic partners (“targets”). Perceivers’ perceptions of targets’ responsive support following the discussion were related to external indicators of targets’ behavior, but these perceptions also were predicted by perceivers’ sentiments toward targets, suggesting that processes underlying perceivers’ perceptions were a blend of both accuracy and bias. In addition, both accurately perceived and biased perceptions of targets’ responsiveness predicted perceivers’ personal well-being (i.e., affect, coping, self-efficacy) and interpersonal well-being (i.e., more positive sentiments toward targets) immediately after the support interaction, 2 weeks later, and 6 months later. Results suggest that accurate and biased cognition during interpersonal interactions can have important consequences for perceivers’ personal and interpersonal well-being through effects on perceived partner responsiveness.     

Self-affirmation and the biased processing of threatening health-risk information

Self-affirming before reading about the link between alcohol and breast cancer promoted increased message acceptance among young women at higher risk. Differences were maintained on variables measured up to 1 month later. Relative to their nonaffirmed counterparts, higher risk, self-affirmed participants had higher ratings of risk, imagination, intention to reduce alcohol consumption, and negative affect, such as fear, while reading the leaflet. In contrast, there were no differences between the groups on measures of broader message acceptance (belief in the link, evidence strength). Thus, self-affirmation promoted acceptance of the personal relevance of the message, a critical step in the precaution adoption process. Overall, the findings support the view that self-affirmation in an unrelated domain can offset defensive processing of a threatening health message, promoting central route persuasion and producing consequential and durable increases in message acceptance.     

Health statistics

Facing the Figures: What is Really Happening to the NHS, by the BSSRS Radical Statistics Group, 1987, 191 pages, £3.95 (25 Horsell Road, London N5 1XL)     

Distraction from emotional information reduces biased judgements

Biases arising from emotional processes are some of the most robust behavioural effects in the social sciences. The goal of this investigation was to examine the extent to which the emotion regulation strategy of distraction could reduce biases in judgement known to result from emotional information. Study 1 explored lay views regarding whether distraction is an effective strategy to improve decision-making and revealed that participants did not endorse this strategy. Studies 2–5 focused on several established, robust biases that result from emotional information: loss aversion, desirability bias, risk aversion and optimistic bias. Participants were prompted to divert attention away from their feelings while making judgements, and in each study this distraction strategy resulted in reduced bias in judgement relative to control conditions. The findings provide evidence that distraction can improve choice across several situations that typically elicit robustly biased responses, even though participants are not aware of the effectiveness of this strategy.     

Economic inequality is linked to biased self-perception

People's self-perception biases often lead them to see themselves as better than the average person (a phenomenon known as self-enhancement). This bias varies across cultures, and variations are typically explained using cultural variables, such as individualism versus collectivism. We propose that socioeconomic differences among societies--specifically, relative levels of economic inequality--play an important but unrecognized role in how people evaluate themselves. Evidence for self-enhancement was found in 15 diverse nations, but the magnitude of the bias varied. Greater self-enhancement was found in societies with more income inequality, and income inequality predicted cross-cultural differences in self-enhancement better than did individualism/collectivism. These results indicate that macrosocial differences in the distribution of economic goods are linked to microsocial processes of perceiving the self.