Statistical detection of a rare class of objects in a two-class classification problem can pose several challenges. Because the class of interest is rare in the training data, there is relatively little information in the known class response labels for model building. At the same time the available explanatory variables are often moderately high dimensional. In the four assays of our drug-discovery application, compounds are active or not against a specific biological target, such as lung cancer tumor cells, and active compounds are rare. Several sets of chemical descriptor variables from computational chemistry are available to classify the active versus inactive class; each can have up to thousands of variables characterizing molecular structure of the compounds. The statistical challenge is to make use of the richness of the explanatory variables in the presence of scant response information. Our algorithm divides the explanatory variables into subsets adaptively and passes each subset to a base classifier. The various base classifiers are then ensembled to produce one model to rank new objects by their estimated probabilities of belonging to the rare class of interest. The essence of the algorithm is to choose the subsets such that variables in the same group work well together; we call such groups phalanxes.

Due to COVID-19, universities across Canada were forced to undergo a transition from classroom-based face-to-face learning and invigilated assessments to online-based learning and non-invigilated assessments. This study attempts to empirically measure the impact of COVID-19 on students’ marks from eleven science, technology, engineering, and mathematics (STEM) courses using a Bayesian linear mixed effects model fitted to longitudinal data. The Bayesian linear mixed effects model is designed for this application which allows student-specific error variances to vary. The novel Bayesian missing value imputation method is flexible which seamlessly generates missing values given complete data. We observed an increase in overall average marks for the courses requiring lower-level cognitive skills according to Bloom’s Taxonomy and a decrease in marks for the courses requiring higher-level cognitive skills, where larger changes in marks were observed for the underachieving students. About half of the disengaged students who did not participate in any course assessments after the transition to online delivery were in special support.

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The measurement of statistical evidence is of considerable current interest in fields where statistical criteria are used to determine knowledge. The most commonly used approach to measuring such evidence is through the use of p-values, even though these are known to possess a number of properties that lead to doubts concerning their validity as measures of evidence. It is less well known that there are alternatives with the desired properties of a measure of statistical evidence. The measure of evidence given by the relative belief ratio is employed in this paper. A relative belief multiple testing algorithm was developed to control for false positives and false negatives through bounds on the evidence determined by measures of bias. The relative belief multiple testing algorithm was shown to be consistent and to possess an optimal property when considering the testing of a hypothesis randomly chosen from the collection of considered hypotheses. The relative belief multiple testing algorithm was applied to the problem of inducing sparsity. Priors were chosen via elicitation, and sparsity was induced only when justified by the evidence and there was no dependence on any particular form of a prior for this purpose.

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