Statistics  

In General > s.a. game theory; probability [distributions]; statistics and error analysis in physics.
* Idea:
* Superstatistics: Superpositions of different statistics on different time or spatial scales; > s.a. markov processes.
@ Problems: Bassett et al 00.
@ Differential geometry methods: Amari 85; Murray & Rice 93.
> Online resources: see Wikipedia page.

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

P(f; p) = exp{–(N/2) (fjpj)2 / fj} .

* 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)].
$ Mean: The (arithmetic) mean of a collection of n numbers aj is AM({a}):= (a1 + ... + an)/n; If the numbers have weights (probabilities) pj, satisfying (pj + ... + pj) = 1, then the mean becomes AM({a};{p} ):= (p1a1 + ... + pnan)/n; In the case of a continuous variable x with probability density p(x), the mean value of x is ∫dx p(x) x, and the mean value of a function f(x) is ∫dx p(x) f(x).
@ References: Mukhopadhyay 08 [multivariate analysis]; Bertin & Györgyi JSM(10)-a1006 [extreme-value statistics, renormalization flow].
> Online resources: see Wikipedia page on average [arithmetic, geometric, harmonic mean].

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; Edwards 06; Gupta & Kabe 11 [sample surveys].
@ Quantum: Brody & Hughston PRL(96) [geometrical]; Bogdanov phy/02, qp/03-conf; Kumagai & Hayashi CMP(13)-a1110 [quantum analogues of chi-square, t and F tests].
@ Statistical complexity: Rissanen 98.
@ 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.


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