Estimation of covariance functions by a fully data-driven model selection procedure and its application to Kriging spatial interpolation of real rainfall data

In this paper, we propose a data-driven model selection approach for the nonparametric estimation of covariance functions under very general moments assumptions on the stochastic process. Observing i.i.d replications of the process at fixed observation points, we select the best estimator among a set of candidates using a penalized least squares estimation procedure with a fully data-driven penalty function, extending the work in Bigot et al. (Electron J Stat 4:822–855, 2010). We then provide a practical application of this estimate for a Kriging interpolation procedure to forecast rainfall data.     

Measuring feelings about choices and risks: The Berlin Emotional Responses to Risk Instrument (BERRI)

We introduce a brief instrument specifically validated for measuring positive and negative feelings about risks—the Berlin Emotional Responses to Risk Instrument (BERRI). Based on seven studies involving diverse adults from three countries (n = 2120), the BERRI was found to robustly estimate anticipatory affective reactions derived from subjective evaluations of positive (i.e., assured, hopeful, and relieved) and negative emotions (i.e., anxious, afraid, and worried). The brief BERRI outperformed a 14-item assessment, uniquely tracking costs/benefits associated with cancer screening among men and women (Studies 1 and 2). Predictive validity was further documented in paradigmatic risky choice studies wherein options varied over probabilities and severities across six contexts (health, social, financial, technological, ethical, and environmental; Study 3). Studies 4–6, conducted during the Ebola epidemic and COVID-19 pandemic, indicated BERRI responses were sensitive to subtle effects caused by emotion-related framing manipulations presented in different cultures and languages (the United States, Spain, and Poland). Study 7 indicated BERRI responses remained stable for 2 weeks. Although the BERRI can provide an estimate of overall affect, choices were generally better explained by the unique influences of positive and negative affect. Overall, results suggest the novel, brief instrument can be an efficient tool for high-stakes research on decision making and risk communication.