Mathematics Branches, Topics, and Sub-Topics

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62Cxx Decision theory

This subtopic introduces the core ideas in decision theory, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.

Specific topics

62C05 General considerations in statistical decision theory

Overview

General considerations in statistical decision theory. This topic covers statistical decision theory, optimal rules, admissibility, minimax principles, and Bayesian decision formulations.

Related Wikipedia Page

Wikipedia: Decision theory

Useful Links

Key Ideas

  • loss functions and risk
  • optimality and admissibility
  • minimax and Bayesian criteria

Typical Uses

Used to formalize and optimize statistical actions under uncertainty and competing criteria.

Applications

  • Hypothesis testing design
  • Sequential and adaptive decisions
  • Machine learning decision frameworks

References

Recommended Textbooks

62C07 Complete class results in statistical decision theory

Overview

Complete class results in statistical decision theory. This topic covers statistical decision theory, optimal rules, admissibility, minimax principles, and Bayesian decision formulations.

Related Wikipedia Page

Wikipedia: Decision theory

Useful Links

Key Ideas

  • loss functions and risk
  • optimality and admissibility
  • minimax and Bayesian criteria

Typical Uses

Used to formalize and optimize statistical actions under uncertainty and competing criteria.

Applications

  • Hypothesis testing design
  • Sequential and adaptive decisions
  • Machine learning decision frameworks

References

Recommended Textbooks

62C10 Bayesian problems; characterization of Bayes procedures

Overview

Bayesian problems; characterization of Bayes procedures. This topic covers statistical decision theory, optimal rules, admissibility, minimax principles, and Bayesian decision formulations.

Related Wikipedia Page

Wikipedia: Decision theory

Useful Links

Key Ideas

  • loss functions and risk
  • optimality and admissibility
  • minimax and Bayesian criteria

Typical Uses

Used to formalize and optimize statistical actions under uncertainty and competing criteria.

Applications

  • Hypothesis testing design
  • Sequential and adaptive decisions
  • Machine learning decision frameworks

References

Recommended Textbooks

62C12 Empirical decision procedures; empirical Bayes procedures

Overview

Empirical decision procedures; empirical Bayes procedures. This topic covers statistical decision theory, optimal rules, admissibility, minimax principles, and Bayesian decision formulations.

Related Wikipedia Page

Wikipedia: Decision theory

Useful Links

Key Ideas

  • loss functions and risk
  • optimality and admissibility
  • minimax and Bayesian criteria

Typical Uses

Used to formalize and optimize statistical actions under uncertainty and competing criteria.

Applications

  • Hypothesis testing design
  • Sequential and adaptive decisions
  • Machine learning decision frameworks

References

Recommended Textbooks

62C15 Admissibility in statistical decision theory

Overview

Admissibility in statistical decision theory. This topic covers statistical decision theory, optimal rules, admissibility, minimax principles, and Bayesian decision formulations.

Related Wikipedia Page

Wikipedia: Decision theory

Useful Links

Key Ideas

  • loss functions and risk
  • optimality and admissibility
  • minimax and Bayesian criteria

Typical Uses

Used to formalize and optimize statistical actions under uncertainty and competing criteria.

Applications

  • Hypothesis testing design
  • Sequential and adaptive decisions
  • Machine learning decision frameworks

References

Recommended Textbooks

62C20 Minimax procedures

Overview

Minimax procedures. This topic covers statistical decision theory, optimal rules, admissibility, minimax principles, and Bayesian decision formulations.

Related Wikipedia Page

Wikipedia: Decision theory

Useful Links

Key Ideas

  • loss functions and risk
  • optimality and admissibility
  • minimax and Bayesian criteria

Typical Uses

Used to formalize and optimize statistical actions under uncertainty and competing criteria.

Applications

  • Hypothesis testing design
  • Sequential and adaptive decisions
  • Machine learning decision frameworks

References

Recommended Textbooks

62C25 Compound decision problems

Overview

Compound decision problems. This topic covers statistical decision theory, optimal rules, admissibility, minimax principles, and Bayesian decision formulations.

Related Wikipedia Page

Wikipedia: Decision theory

Useful Links

Key Ideas

  • loss functions and risk
  • optimality and admissibility
  • minimax and Bayesian criteria

Typical Uses

Used to formalize and optimize statistical actions under uncertainty and competing criteria.

Applications

  • Hypothesis testing design
  • Sequential and adaptive decisions
  • Machine learning decision frameworks

References

Recommended Textbooks