Statistics| 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.
@ Related topics: news sn(19)apr [the debate on 'statistical significance'].
> Online resources:
see Wikipedia page;
Good Calculators site [statistics calculators].
Concepts and Techniques
> s.a. correlations [correlation functions]; Median.
* Frequency distribution:
P(f; p) = exp{−(N/2) (fj − pj)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.
* Duhem-Quine problem:
Hypothesis testing is always conditional on a bundle of real auxiliary assumptions.
@ 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.
@ Hypothesis testing:
Liu & Adams a1812 [and Bertrand's question].
@ 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.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 30 apr 2020