A Cornucopia of Maximum Likelihood Algorithms.
Classroom expositions of maximum likelihood estimation (MLE) rely on traditional calculus methods to construct analytic solutions. This creates in students a false sense of the ease with which MLE problems can be attacked. In a nod to reality, some teachers mention and apply Newton's method, Fisher...
| Published in: | American Statistician Vol. 79; no. 4; pp. 538 - 549 |
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| Main Authors: | , , |
| Format: | Article |
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Taylor & Francis Ltd
Nov2025
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| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=189286920&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 189286920 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 00031305 STT jtl: American Statistician issn: 00031305 maglogo: Y pubinfo: dt: Nov2025 vid: 79 iid: 4 pid: 377 pub: Taylor & Francis Ltd artinfo: ui: 189286920 10.1080/00031305.2025.2526535 ppf: 538 ppct: 11 formats: tig: atl: A Cornucopia of Maximum Likelihood Algorithms. aug: au: Lange, Kenneth Li, Xun-Jian Zhou, Hua affil: Departments of Computational Medicine, Human Genetics, and Statistics, University of California, Los Angeles, CA Department of Biostatistics, University of California, Los Angeles, CA Departments of Biostatistics and Computational Medicine, University of California, Los Angeles, CA su: Maximum likelihood statistics Expectation-maximization algorithms Newton-Raphson method Scientific language Optimization algorithms Calculus sug: subj: Maximum likelihood statistics Expectation-maximization algorithms Newton-Raphson method Scientific language Optimization algorithms Calculus keyword: Block ascent Convexity Maximum likelihood estimation MM principle Newton's method Profile likelihood Block ascent Convexity Maximum likelihood estimation MM principle Newton's method Profile likelihood ab: Classroom expositions of maximum likelihood estimation (MLE) rely on traditional calculus methods to construct analytic solutions. This creates in students a false sense of the ease with which MLE problems can be attacked. In a nod to reality, some teachers mention and apply Newton's method, Fisher scoring, and the expectation-maximization (EM) algorithm. Although preferable to leaving students in a state of ignorance, such brief expositions ultimately fail to expose the full body of relevant techniques. Some of these techniques extend more readily to high-dimensional data problems than Newton's method and scoring. The current paper emphasizes block ascent and descent, profile likelihoods, the minorization-maximization (MM) principle, and their creative combination. These themes are put to work in readable Julia code to solve several MLE problems. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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