In forecasting and decision making, people can and often do represent a degree of belief in some proposition. At least two separate constructs capture such degrees of belief: likelihoods capturing evidential balance and support capturing evidential weight. This paper explores the weight or justification that evidence affords propositions, with subjects communicating using a belief function in hypothetical legal situations, where justification is a relevant goal. Subjects evaluated the impact of sets of 1–3 pieces of evidence, varying in complexity, within a hypothetical legal situation. The study demonstrates the potential usefulness of this evidential weight measure as an alternative or complement to the more-studied probability measure. Subjects’ responses indicated that weight and likelihood were distinguished; that subjects’ evidential weight tended toward single elements in a targeted fashion; and, that there were identifiable individual differences in reactions to conflicting evidence. Specifically, most subjects reacted to conflicting evidence that supported disjoint sets of suspects with continued support in the implicated sets, although an identifiable minority reacted by pulling back their support, expressing indecisiveness. Such individuals would likely require a greater amount of evidence than the others to counteract this tendency in support. Thus, the study identifies the value of understanding evidential weight as distinct from likelihood, informs our understanding of the psychology of individuals’ judgments of evidential weight, and furthers the application and meaningfulness of belief functions as a communication language.

Bayesian statistics offers a normative description for how a person should combine their original beliefs (i.e., their priors) in light of new evidence (i.e., the likelihood). Previous research suggests that people tend to under-weight both their prior (base rate neglect) and the likelihood (conservatism), although this varies by individual and situation. Yet this work generally elicits people’s knowledge as single point estimates (e.g., x has a 5% probability of occurring) rather than as a full distribution. Here we demonstrate the utility of eliciting and fitting full distributions when studying these questions. Across three experiments, we found substantial variation in the extent to which people showed base rate neglect and conservatism, which our method allowed us to measure for the first time simultaneously at the level of the individual. While most people tended to disregard the base rate, they did so less when the prior was made explicit. Although many individuals were conservative, there was no apparent systematic relationship between base rate neglect and conservatism within each individual. We suggest that this method shows great potential for studying human probabilistic reasoning.

Scientific understanding of multitactic weed management systems (MTS) is complicated by (1) the large number of potential combinations among tactics, (2) potentially noisy and complex system behavior because of individually more moderate mortality events, and (3) possible transient system behavior of unknown duration. Therefore, decomposing the relative performance of MTS components is much more difficult than it is for single-tactic strategies (STS). Attempting to accommodate the increased complexity of system behavior while maintaining the generality of results requires analytical methods capable of accomplishing these tasks. We provide two examples of statistical procedures that may help gain understanding of MTS systems using previously published weed demographic time-series data. First, we demonstrate the use of mixed-effects models capable of representing and removing factors contributing uncontrolled variation to system behavior. Model selection criteria are used to highlight the importance of the increased flexibility the mixed-model framework provides. Second, by explicitly modeling the probabilistic process presumed to be generating the data, we demonstrate how different components of the MTS can be compared and how the methodology can facilitate integration of such information into a decision-making application.

Background: Distressing intrusive images are frequently experienced by sufferers from chronic and acute pain. The images (Index images) are correlated with elevations in anxiety, threat, and a cognition that the imaged event might actually happen. The over-estimation that having a negative cognition about an adverse event will increase the probability of the negative event occurring - the likelihood bias - has been observed in a variety of psychological disorders. Preliminary research indicated this cognitive bias might occur in pain sufferers. Aims: To investigate the occurrence of a cognitive likelihood bias associated with imagery in acute and chronic pain sufferers, and to relate the postulated cognitive bias to psychological characteristics of participants, and four other important cognitive responses to their Index images. Method: Fifty-nine pain sufferers completed a newly developed questionnaire (Image-Event-Fusion-pain: IEF-p) to assess cognitive likelihood bias in pain sufferers. The internal consistency, reliability, factor structure and validity of the scale were evaluated. Psychological measures to assess anxiety, depression, PTSD symptoms, and levels of mental defeat were administered. Results: The IEF-p was found to be psychometrically robust with satisfactory test-retest reliability, good internal consistency, single factor structure and criterion validity. The IEF-p was significantly correlated with four key cognitive appraisals of the Index Images (responsibility, likelihood, premonition, and threat). Three of these correlations were independent of depression. High cognitive bias scores were significantly associated with elevated levels of anxiety symptoms, depression, PTSD symptoms, and mental defeat. Conclusion: Pain Index images were significantly associated with cognitive bias (IEF-p), increased threat levels, and raised estimate of the likelihood of imaged events actually occurring. The results indicate the prevalence of a cognitive bias associated with pain imagery cognitions, comparable to that established with intrusive cognitions in OCD, notably Thought-Action- Fusion.

We formulate a localization property of wavelet coefficients for processes with stationary increments, in the estimation problem associated with the processes. A general setting for the estimation is adopted and examples that fit this setting are given. An evaluation of wavelet coefficient decay with respect to shift k∈ℕ is explicitly derived (only the asymptotic behavior, for large k, was previously known). It is this evaluation that makes it possible to establish the localization property of the wavelet coefficients. In doing so, it turns out that the theory of positive-definite functions plays an important role. As applications, we show that, in the wavelet coefficient domain, estimators that use a simple moment method are nearly as good as maximum likelihood estimators. Moreover, even though the underlying process is long-range dependent and process domain estimates imply the validity of a noncentral limit theorem, for the wavelet coefficient domain estimates we always obtain a central limit theorem with a small prescribed error.

Some simple methods of estimating inbreeding from tests on a random sample of individuals are discussed. These are mostly iterative procedures, converging to the maximum likelihood estimate, with algorithms for finding standard errors. But there are problems of interpretation, both from the statistical and biological points of view.

A flexible method based on maximum likelihood theory is introduced for the analysis of binary response data in twins. The method allows for explanatory variables such as age and sex, is free of the untestable distributional assumption of bivariate normality of liability, and makes more efficient use of the data available. The method is illustrated with preliminary data on drinking status in adult twins. Although there is some bias in the ascertainment of male dizygous twins, the results suggest that monozygous twins are more concordant than dizygous twins for drinking status.