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...

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Published in:American Statistician Vol. 79; no. 4; pp. 538 - 549
Main Authors: Lange, Kenneth, Li, Xun-Jian, Zhou, Hua
Format: Article
Published: Taylor & Francis Ltd Nov2025
Subjects:
Online Access:View this record in EBSCOhost
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      dt: Nov2025
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        10.1080/00031305.2025.2526535
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      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
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