In this paper, a Bayesian nonparametric approach to the two-sample problem is proposed. Given two samples \(\text{X} = {X_1}, \ldots ,{X_{m1}}\;\mathop {\text~}\limits^{i.i.d.} F\) and \(Y = {Y_1}, \ldots ,{Y_{{m_2}}}\mathop {\text~}\limits^{i.i.d.} G\), with F and G being unknown continuous cumulative distribution functions, we wish to test the null hypothesis H₀: F = G. The method is based on computing the Kolmogorov distance between two posterior Dirichlet processes and comparing the results with a reference distance. The parameters of the Dirichlet processes are selected so that any discrepancy between the posterior distance and the reference distance is related to the difference between the two samples. Relevant theoretical properties of the procedure are also developed. Through simulated examples, the approach is compared to the frequentist Kolmogorov–Smirnov test and a Bayesian nonparametric test in which it demonstrates excellent performance.

The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a prior, checking the prior for bias, checking for prior-data conflict and estimation and hypothesis assessment inferences based on a measure of evidence. A long-standing anomalous example is resolved by this approach to inference and an application is made to a practical problem of considerable importance, which, among other novel aspects of the analysis, involves the development of a relevant elicitation algorithm.

A logistic regression model is a specialized model for product-binomial data. When a proper, noninformative prior is placed on the unrestricted model for the product-binomial model, the hypothesis H 0 of a logistic regression model holding can then be assessed by comparing the concentration of the posterior distribution about H 0 with the concentration of the prior about H 0. This comparison is effected via a relative belief ratio, a measure of the evidence that H 0 is true, together with a measure of the strength of the evidence that H 0 is either true or false. This gives an effective goodness of fit test for logistic regression.

Majority of the students now have access to portable devices that can provide countless information at their fingertips through various resources such as learning games and interactive applications. These resources allow immediate communication and interaction between students and instructors. In this paper, we study the effectiveness of using these resources in lectures on students’ academic performance and their level of understanding of the lecture topic. A survey was carried out for students, who have taken statistics courses at the University of Toronto, to analyze various factors of using technology in class. The results of the survey showed that a significant portion of students gained a deeper level of understanding using technology in class, thus allowing us to take advantage of technology in class to create a more immersive learning environment for students than traditional methods.

Extropy, a complementary dual of entropy, is considered in this paper. A Bayesian approach based on the Dirichlet process is proposed for the estimation of extropy. A goodness of fit test is also developed. Many theoretical properties of the procedure are derived. Several examples are discussed to illustrate the approach.

In the 1990s, educators advocated for projects in statistical courses to enrich student learning. Prior research showcases the positive impact of Project‐Based Learning (PBL), where students complete course‐driven projects. In agreement with this perspective, we implemented PBL methodologies within two statistical courses at a North American research‐intensive university: “Survey, Sampling, & Design” and “Experimental Design.” Students were invited to participate in an optional survey to share their opinions regarding the course project. Consistent with existing literature, our findings indicate that students hold favorable views towards course‐based projects, noticing benefits such as understanding real‐life applications, collaboration, and enhancing data analysis skills. Additionally, many students have incorporated the use of generative AI for their works, such as ChatGPT, and shared the advantages of such tools in their coursework. Drawing from our experiences, we propose strategies to enhance course projects and address concerns related to the overreliance of generative AI tools.