Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector

For the important classical problem of inference on a sparse high-dimensional normal mean vector, we propose a novel empirical Bayes model that admits a posterior distribution with desirable properties under mild conditions. In particular, our empirical Bayes posterior distribution concentrates on balls, centered at the true mean vector, with squared radius proportional to the minimax rate, and its posterior mean is an asymptotically minimax estimator. We also show that, asymptotically, the support of our empirical Bayes posterior has roughly the same effective dimension as the true sparse mean vector. Simulation from our empirical Bayes posterior is straightforward, and our numerical results demonstrate the quality of our method compared to others having similar large-sample properties.Comment: 18 pages, 3 figures, 3 table

Fostering Student Engagement: Four Strategies

In response to studies demonstrating that poor teaching was the cause of many students leaving math, science, and engineering programs, the American Society of Civil Engineers (ASCE) developed the ExCEEd(Excellence in Civil Engineering Education) Teaching Workshop. Several faculty from the UNLV Department of Civil & Environmental Engineering and Construction have attended the highly intensive five-day workshop. To evaluate the impact on student engagement, four basic instructional strategies from the ExCEEdworkshop, applicable to all fields, were tested and assessed during the Fall 2018 semester: Questioning techniques, physical models, instructor involvement, and group work.https://digitalscholarship.unlv.edu/btp_expo/1066/thumbnail.jp