Normal Distribution Error Propagation
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Error Propagation Calculator
the company Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags Users Badges error propagation physics Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only error propagation chemistry takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Error Propagation up vote 3 down vote favorite I come from a physics background where the only error propagation I've dealt with was in the lab using the simple formulas found here. So
Error Propagation Square Root
if I have some function that I am interested in, $f$, and it depends on variable $y$ with some standard deviation $\sigma_y$, then I can compute $\sigma_f$ using one of the above formulas. From what I understand though, these formulas depend on the probability law for $y$ being a normal distribution. However, quite often, this is not the case and the probability law for $y$ may be some arbitrary distribution. So my question is, given that we know that the probability distribution function (or uncertainty) for $y$ is not a normal distribution, what are the ways to propagate this uncertainty to $f(y)$? normal-distribution error uncertainty share|improve this question edited Nov 8 '15 at 3:52 Sean Easter 4,76921236 asked Nov 11 '14 at 15:28 symmetric 162 add a comment| 3 Answers 3 active oldest votes up vote 1 down vote From what I understand though, these formulas depend on the probability law for y being a normal distribution. This is not true: In the first three formulas, the results follow from properties of variance that apply regardless of distribution. (And the fact
of errors is essential to be able to judge the relevance of observed trends. Below, a brief definition of the main concepts and a discussion of generic ways to obtain error estimates is provided. [1] [2] Of course, any particular error propagation inverse measuring device generally requires specific techniques. Contents 1 The measurement process 2 Calibration 3 propagated error calculus Error estimate (experimental error known) 4 Systematic and random errors 5 Error estimate (experimental error unknown) 6 Test of statistical validity
Error Propagation Excel
of the model 7 Fluctuations and noise 8 Non-Gaussian statistics 9 Integrated data analysis 10 Summary 11 References The measurement process The measuring device performs measurements on a physical system P. As a result, http://stats.stackexchange.com/questions/123561/error-propagation it produces estimates of a set of physical parameters {p}. One may think of p as loose numbers (e.g., a confinement time), data along a spatial chord at a single time (e.g., a Thomson scattering profile), data at a point in space with time resolution (e.g., magnetic field fluctuations from a Mirnov coil), or data having both time and space resolution (e.g., tomographic data from Soft X-Ray arrays). The actual http://wiki.fusenet.eu/wiki/Error_propagation measurement hardware does not deliver the parameters {p} directly, but produces a set of numbers {s}, usually expressed in Volts, Amperes, or pixels. Calibration The first task of the experimentalist is to translate the measured signals {s} into the corresponding physical parameters {p}. The second task is to provide error estimates (discussed below). Generally, the translation of {s} into {p} requires having a (basic) model for the experiment studied and its interaction with the measuring device. In the simplest cases, the relation between {s} and {p} is linear (e.g. conversion of the measured voltages from Mirnov coils to magnetic fields). Taking s and p to be vectors, such a conversion can be written as $ p = A \cdot(s - b), $ where A is a (possibly diagonal) calibration matrix and b a vector for offset correction. However, in fusion science it is more common that the conversion from s to p involves some (non-linear) numerical modelling of the physical (and measurement) system. In this case, rather than assuming a linear relation, one assumes a non-linear map Mp between s and p: p = Mp(s). The subscript p indicates that Mp may depend on p. In principle, determining p from s now requires an iterative numerical approach. The
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