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Entropy Maximization

In: Statistical Decision Problems

Author

Listed:
  • Michael Zabarankin

    (Stevens Institute of Technology)

  • Stan Uryasev

    (University of Florida)

Abstract

The previous chapter showed that given independent observations of a random variable X, the probability distribution of X can be estimated based on the maximum likelihood principle. However, if no observations of X are available, but some integral characteristics of the distribution of X are known, for example, mean μ and standard deviation σ, the main principle for finding the distribution in question is, arguably, the one of maximum entropy. This principle, also known as MaxEnt, originated from the information theory and statistical mechanics (see [22]) and determines the “most unbiased” probability distribution for X subject to any constraints on X (prior information). Nowadays, it is widely used in financial engineering and statistical decision problems [4, 11, 56]. Estimation of probability distributions through entropy maximization and through relative entropy minimization subject to various constraints on unknown distributions is the subject of this chapter.

Suggested Citation

  • Michael Zabarankin & Stan Uryasev, 2014. "Entropy Maximization," Springer Optimization and Its Applications, in: Statistical Decision Problems, edition 127, chapter 0, pages 53-70, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-8471-4_5
    DOI: 10.1007/978-1-4614-8471-4_5
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