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A Cornucopia of Maximum Likelihood Algorithms.

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Summary
This summary is machine-generated.

This study introduces advanced computational techniques for maximum likelihood estimation (MLE), moving beyond basic calculus. It highlights methods like block ascent and minorization-maximization for tackling complex, high-dimensional data problems more effectively.

Keywords:
MM principleNewton’s methodblock ascentconvexitymaximum likelihood estimationprofile likelihood

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Area of Science:

  • Statistics
  • Computational Statistics
  • Numerical Optimization

Background:

  • Traditional classroom teaching of maximum likelihood estimation (MLE) uses calculus, which can oversimplify problem-solving.
  • Existing supplementary methods like Newton's method, Fisher scoring, and EM algorithm offer limited scope, especially for high-dimensional data.
  • There's a need for more robust and scalable techniques in statistical inference education.

Purpose of the Study:

  • To present advanced computational techniques for maximum likelihood estimation (MLE).
  • To demonstrate the application of these methods to solve complex MLE problems.
  • To provide educators and students with practical alternatives to traditional calculus-based approaches.

Main Methods:

  • Emphasis on block ascent and descent algorithms.
  • Application of profile likelihoods for model simplification.
  • Integration of the minorization-maximization (MM) principle.
  • Creative combination of these techniques.
  • Implementation using readable Julia code.

Main Results:

  • Demonstration of how advanced methods can be practically applied to MLE problems.
  • Illustrates the effectiveness of block ascent, profile likelihoods, and MM principles.
  • Provides a computational framework in Julia for solving challenging estimation tasks.

Conclusions:

  • Advanced techniques like block ascent, profile likelihoods, and MM are crucial for modern MLE, especially with high-dimensional data.
  • These methods offer a more realistic and powerful approach compared to traditional calculus-based solutions.
  • The presented Julia code facilitates the learning and application of these advanced statistical inference techniques.