Statistics and Error Analysis in Physics  

In General: Data, Fluctuations and Errors > s.a. particle statistics [spin-statistics]; probability in physics.
* Statistical uncertainties: They vanish in general for Nobs → , except for certain systems said to possess non-averaging properties, as in random media.
@ General references: Hacking 90; Roe 92; > s.a. statistics.
@ Related topics: Levy a0804 [use of the median vs the mean in physics].

Experimental Errors > s.a. physics teaching.
* Types: Can be statistical/random or systematic; Errors in reading measuring instruments can be either type.
* Combining uncertainties: There is no universally accepted prescription for combining statistical and systematic errors into one number, so they are usually given separately; In terms of probabilities, the only way to deal with issues like this one is to abandon the frequentist view in favor of "degrees of belief".
* Variance:
* Confidence interval:
* Error propagation: The rule

u = [i (u/xi)2 i2]1/2

applies to variances of random, uncorrelated variables, not to confidence intervals.
@ Error analysis: Taylor 97; Silverman et al AJP(04) [error propagation].

Data Analysis, Inference
@ Bayesian: Sivia 96 [II]; Lemm 03; James 06.
@ Related topics: Sorkin IJTP(83)ap/05 [Occam's razor and goodness of fit]; Maltoni & Schwetz PRD(03)hp [compatibility of data sets]; Gould ap/03 [linear fits]; Pilla et al PRL(05)phy [signal in noisy background].

Specific Areas and Topics > s.a. correlations; stochastic processes.
@ In quantum mechanics: Rylov qp/01; Rajeev MPLA(03).
@ In astrophysics/cosmology: Szapudi ap/00-in [variances of correlations]; Hill ap/01-in [Bayesian statistics in detection]; Feigelson & Babu ap/04-in; Verde a0712-ln; > s.a. observational cosmology.

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 21 jun 2008