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Methods for group comparisons using predicted probabilities and marginal effects on probabilities are developed for regression models for binary outcomes. Unlike approaches based on the comparison of regression coefficients across groups, the methods we propose are unaffected by the scalar identification of the coefficients and are expressed in the natural metric of the outcome probability. While we develop our approach using binary logit with two groups, we consider how our interpretive framework can be used with a broad class of regression models and can be extended to any number of groups. [ABSTRACT FROM AUTHOR]

For monodomain nematic elastomers, we construct generalised elastic–nematic constitutive models combining purely elastic and neoclassical-type strain energy densities. Inspired by recent developments in stochastic elasticity, we extend these models to stochastic–elastic–nematic forms, where the model parameters are defined by spatially independent probability density functions at a continuum level. To investigate the behaviour of these systems and demonstrate the effects of the probabilistic parameters, we focus on the classical problem of shear striping in a stretched nematic elastomer for which the solution is given explicitly. We find that, unlike the neoclassical case, where the inhomogeneous deformation occurs within a universal interval that is independent of the elastic modulus, for the elastic–nematic models, the critical interval depends on the material parameters. For the stochastic extension, the bounds of this interval are probabilistic, and the homogeneous and inhomogeneous states compete, in the sense that both have a a given probability to occur. We refer to the inhomogeneous pattern within this interval as 'likely striping'. [ABSTRACT FROM AUTHOR]

In large deformations, internally pressurised elastic spherical shells and tubes may undergo a limit-point, or inflation, instability manifested by a rapid transition in which their radii suddenly increase. The possible existence of such an instability depends on the material constitutive model. Here, we revisit this problem in the context of stochastic incompressible hyperelastic materials, and ask the question: what is the probability distribution of stable radially symmetric inflation, such that the internal pressure always increases as the radial stretch increases? For the classic elastic problem, involving isotropic incompressible materials, there is a critical parameter value that strictly separates the cases where inflation instability can occur or not. By contrast, for the stochastic problem, we show that the inherent variability of the probabilistic parameters implies that there is always competition between the two cases. To illustrate this, we draw on published experimental data for rubber, and derive the probability distribution of the corresponding random shear modulus to predict the inflation responses for a spherical shell and a cylindrical tube made of a material characterised by this parameter. [ABSTRACT FROM AUTHOR]

Accurate measurement and a cutoff probability with inferential statistics are not wholly compatible. Fisher understood this when he developed the F test to deal with measurement variability and to make judgments on manipulations that may be worth further study. Neyman and Pearson focused on modeled distributions whose parameters were highly determined and concluded that inferential judgments following an F test could be made with accuracy because the distribution parameters were determined. Neyman and Pearson's approach in the application of statistical analyses using alpha and beta error rates has played a dominant role guiding inferential judgments, appropriately in highly determined situations and inappropriately in scientific exploration. Fisher tried to explain the different situations, but, in part due to some obscure wording, generated a long standing dispute that currently has left the importance of Fisher's p<.05 criteria not fully understood and a general endorsement of the Neyman and Pearson error rate approach. Problems were compounded with power calculations based on effect sizes following significant results entering into exploratory science. To understand in a practical sense when each approach should be used, a dimension reflecting varying levels of certainty or knowledge of population distributions is presented. The dimension provides a taxonomy of statistical situations and appropriate approaches by delineating four zones that represent how well the underlying population of interest is defined ranging from exploratory situations to highly determined populations. [ABSTRACT FROM AUTHOR]

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Objective: To test whether the format in which women receive probabilistic information about breast cancer and mammography affects their comprehension.Methods: A convenience sample of 180 women received pre-assembled randomized packages containing a breast health information brochure, with probabilities presented in either verbal or numeric format, and four questionnaires. Enclosed questionnaires assessed women’s knowledge of breast health, socio-demographic/ clinical characteristics, comprehension of breast health information brochure and format preference.Results: Nearly two-thirds of the study participants reported a preference for the numeric format. However, the study results showed that comprehension was significantly higher among women who received probabilistic information in verbal format than those who received the information in numeric format. This higher degree of comprehension was sustained even if the verbal format was inconsistent with the respondents’ format preference, and even if the respondents’ educational background were relatively limited. Women’s comprehension was strongly associated with the interaction between received format and their format preferences as well as their education level and their perceived benefit of early detection of breast cancer.Conclusion: The study demonstrates that comprehension of information depends on: (1) women’s readiness to receive information; and (2) their education and numeracy skills in processing and interpreting probabilistic information, particularly, when presented in quantitative format. Attention must be paid to these factors when designing or communicating breast health information in order to ensure full comprehension of information, and to avoid any potential discrimination which people may face relating to their poor education or numeracy skills. Systematic investigation into the relationships among readiness, numeracy problems, and format preferences could help build effective guidelines for providing women with appropriate and comprehensible information. [ABSTRACT FROM AUTHOR]

Fundamental principles of precaution are legal maxims that ask for preventive actions, perhaps as contingent interim measures while relevant information about causality and harm remains unavailable, to minimize the societal impact of potentially severe or irreversible outcomes. Such principles do not explain how to make choices or how to identify what is protective when incomplete and inconsistent scientific evidence of causation characterizes the potential hazards. Rather, they entrust lower jurisdictions, such as agencies or authorities, to make current decisions while recognizing that future information can contradict the scientific basis that supported the initial decision. After reviewing and synthesizing national and international legal aspects of precautionary principles, this paper addresses the key question: How can society manage potentially severe, irreversible or serious environmental outcomes when variability, uncertainty, and limited causal knowledge characterize their decisionmaking? A decision–analytic solution is outlined that focuses on risky decisions and accounts for prior states of information and scientific beliefs that can be updated as subsequent information becomes available. As a practical and established approach to causal reasoning and decision-making under risk, inherent to precautionary decision-making, these (Bayesian) methods help deci- sion-makers and stakeholders because they formally account for probabilistic outcomes, new information, and are consistent and replicable. Rational choice of an action from among various alternatives–defined as a choice that makes preferred consequences more likely–requires accounting for costs, benefits and the change in risks associated with each candidate action. Decisions under any form of the pre- cautionary principle reviewed must account for the con- tingent nature of scientific information, creating a link to the decision–analytic principle of expected value of information (VOI), to show the relevance of new informa- tion, relative to the initial (and smaller) set of data on which the decision was based. We exemplify this see- mingly simple situation using risk management of BSE. As an integral aspect of causal analysis under risk, the methods developed in this paper permit the addition of non-linear, hormetic dose–response models to the current set of regulatory defaults such as the linear, non-threshold models. This increase in the number of defaults is an important improvement because most of the variants of the precautionary principle require cost–benefit balan- cing. Specifically, increasing the set of causal defaults accounts for beneficial effects at very low doses. We also show and conclude that quantitative risk assessment dominates qualitative risk assessment, supporting the extension of the set of default causal models. [ABSTRACT FROM AUTHOR]