An official website of the United States government
Summary Nan Laird has an enormous and growing impact on computational statistics. Her paper with Dempster and Rubin on the expectation‐maximisation (EM) algorithm is the second most cited paper in statistics. Her papers and book on longitudinal modelling are nearly as impressive. In this brief survey, we revisit the derivation of some of her most useful algorithms from the perspective of the minorisation‐maximisation (MM) principle. The MM principle generalises the EM principle and frees it from the shackles of missing data and conditional expectations. Instead, the focus shifts to the construction of surrogate functions via standard mathematical inequalities. The MM principle can deliver a classical EM algorithm with less fuss or an entirely new algorithm with a faster rate of convergence. In any case, the MM principle enriches our understanding of the EM principle and suggests new algorithms of considerable potential in high‐dimensional settings where standard algorithms such as Newton's method and Fisher scoring falter.
more »
« less
This content will become publicly available on December 1, 2026
Introduction to the Mathematical Legacy of Hel Braun
Abstract Hel Braun was an extraordinary mathematician. Chances are, however, that you are unfamiliar with her. A serendipitous encounter with archival documents set the author on a path to learning about Braun, her mathematical contributions, and surprising factors that helped shape her legacy and our understanding of mathematical knowledge more broadly.
more »
« less
- Award ID(s):
- 2302011
- PAR ID:
- 10653689
- Publisher / Repository:
- Mitteilungen der Deutschen Mathematiker-Vereinigung
- Date Published:
- Journal Name:
- Mitteilungen der Deutschen Mathematiker-Vereinigung
- Volume:
- 33
- Issue:
- 4
- ISSN:
- 0947-4471
- Page Range / eLocation ID:
- 268 to 275
- Subject(s) / Keyword(s):
- Hel Braun Helene Braun
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null; null; null (Ed.)Through participation in a research project on fostering creativity in calculus, two instructors showed shifts in their beliefs on teaching. Participation in the project entailed creating mathematical tasks designed to elicit creative responses from students. Support for task development included participation in weekly online professional development sessions. In this paper, we share one instructor’s shifts in beliefs as well as alignment of her pre-existing beliefs with pedagogical actions. Preliminary analysis of her entrance tickets to the professional development sessions and her exit interview indicates that this instructor a) shifted her previous beliefs about a perceived time pressure and b) manifested her existing beliefs into actions regarding multiple-approach tasks.more » « less
-
Ayalon, M; Koichu, B; Leikin, R; Rubel, L; Tabach, M (Ed.)We follow a beginning mathematics teacher, Olive, from the university-based course Mathematical Reasoning and Proving for Secondary Teachers through the supervised internship where Olive taught in her cooperating teacher’s classroom. By drawing upon Activity Theory, we compare her teaching within the two teaching settings, and we examine the opportunities for reasoning and proving she provided to her students in each teaching setting. As a prospective teacher, Olive provided her students opportunities for reasoning and proving. During the internship, these opportunities initially diminished due to institutional and contextual constraints. However, Olive gradually carved out unique paths to engage students with reasoning and proving as her teaching independence increased.more » « less
-
This study investigated how a middle school mathematics teacher positions herself and her students in the context of teaching Emergent Bilinguals. The teacher's discourses during the planning meetings and teaching sessions were analyzed through the lens of positioning theory. The strongest patterns in the teacher’s positioning were assessor and supporter, respectively. In the planning sessions, the teacher positioned herself as one who assesses EBs’ readiness in mathematics and English and revealed her views that her EBs were not currently ready to do many mathematical and linguistic tasks suggested by the researcher. However, her positioning EBs as capable problem-solvers was clear and consistent throughout all co-planning and co-teaching sessions.more » « less
-
Abstract This paper shares the experiences, engagement, and struggle of one young Indigenous Hawaiian woman as she grapples with her sense of disconnect with STEM while serving as a land protector on the Mauna Kea, the home of the Thirty Meter Telescope being built over the objection of the local Indigenous community. I examine her changing perspectives and connections to STEM through her engagement during a summer school enrichment class focused on science and technology learning in service of community goals. Findings indicate that her sense of agency and autonomy were greatly improved by engaging in a space where science and technology were tools serving her goals of protecting the Mauna Kea from further development.more » « less
