Posts tagged ‘measurement error’

Lost in Translation: Measurement Error

You would think that something like “measurement error” is a well-defined concept, and everyone knows what it means. Not so. I have so far counted at least 3 different interpretations of what it means.

Suppose you have measurements X={Xi, i=1..N} of a quantity whose true value is, say, X0. One can then compute the mean and standard deviation of the measurements, E(X) and σX. One can also infer the value of a parameter θ(X), derive the posterior probability density p(θ|X), and obtain confidence intervals on it.

So here are the different interpretations:

  1. Measurement error is σX, or the spread in the measurements. Astronomers tend to use the term in this manner.
  2. Measurement error is X0-E(X), or the “error made when you make the measurement”, essentially what is left over beyond mere statistical variations. This is how statisticians seem to use it, essentially the bias term. To quote David van Dyk

    For us it is just English. If your measurement is different from the real value. So this is not the Poisson variability of the source for effects or ARF, RMF, etc. It would disappear if you had a perfect measuring device (e.g., telescope).

  3. Measurement error is the width of p(θ|X), i.e., the measurement error of the first type propagated through the analysis. Astronomers use this too to refer to measurement error.

Who am I to say which is right? But be aware of who you may be speaking with and be sure to clarify what you mean when you use the term!

[Q] systematic error

What is systematic error? Can it be modeled statistically? Is it random? Is it fixed? Is it a bias? Is it …? Continue reading ‘[Q] systematic error’ »

my first AAS. V. measurement error and EM

While discussing different view points on the term, clustering, one of the conversers led me to his colleague’s poster. This poster (I don’t remember its title and abstract) was my favorite from all posters in the meeting. Continue reading ‘my first AAS. V. measurement error and EM’ »

[ArXiv] Swift and XMM measurement errors, Sep. 8, 2007

From arxiv/astro-ph:0708.1208v1:
The measurement errors in the Swift-UVOT and XMM-OM by N.P.M. Kuin and S.R. Rosen

The probability distribution of photon counts from the Optical Monitor on XMM Newton satellite (XMM-OM) and the UVOT on the Swift satellite follows a binomial distribution due to detector characteristics. Incident count rate was derived as a function of the measured count rate, which was shown to follow a binomial distribution.
Continue reading ‘[ArXiv] Swift and XMM measurement errors, Sep. 8, 2007’ »