Statistics

In General > s.a. game theory; probability [distributions].
* Idea:
$ Average:
* Superstatistics: Superpositions of different statistics on different time or spatial scales.

Concepts and Techniques > s.a. correlations [correlation functions].
* Frequency distribution:

P(f; p) = exp{–(N/2) (f_j – p_j)² / f_j} .

* Exchangeable random variables: A more general concept than that of independent variables, for which one can obtain distributions analogous to the binomial or Poisson distributions; They account, e.g., for the fact that animals in the same litter behave more similarly than across litters (the corresponding variables are exchangeable but not independent) [@ George & Bowman Biometrics(95)].

Parameter Estimation or Statistical Inference
* Idea: Using experimental data/outcomes to estimate the probability distribution that generated them.
@ General references: Earman 92; Vapnik 98, 99.
@ Quantum: Brody & Hughston PRL(96) [geometrical]; Bogdanov phy/02, qp/03-in.
@ Statistical complexity: Rissanen 89.
@ Continuous distributions, field theory method: Bialek et al PRL(96); Holy PRL(97); Periwal PRL(97)ht, NPB(99); van Hameren et al NPB(99) [discrepancies and Fermions]; Bialek et al NC(01)phy/00; Nemenman & Bialek PRE(02)cm/00.

General References > s.a. statistics and error analysis in physics.
@ Problems: Bassett et al 00.
@ Differential geometry methods: Amari 85; Murray & Rice 93.

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 16 jun 2008