Mar 6th, 2009| 03:42 pm | Posted by hlee

Ah ha~ Once I questioned, “what is systematic error?” (see [Q] systematic error.) Thanks to L. Lyons’ work discussed in [ArXiv] Particle Physics, I found this paper, titled **Systematic Errors** describing the concept and statistical inference related to **systematic errors** in the field of particle physics. It, gladly, shares lots of similarity with high energy astrophysics. Continue reading ‘systematic errors’ »

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Comment
Jan 2nd, 2009| 11:24 pm | Posted by vlk

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={X*_{i}, i=1..N} of a quantity whose true value is, say, *X*_{0}. One can then compute the mean and standard deviation of the measurements, *E(X)* and *σ*_{X}. 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:

- Measurement error is
*σ*_{X}, or the spread in the measurements. Astronomers tend to use the term in this manner.
- Measurement error is
*X*_{0}-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).

- 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!

Jun 20th, 2008| 11:02 pm | Posted by hlee

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’ »

Apr 24th, 2008| 02:56 pm | Posted by vlk

There is a new report from Bernabei et al. (arXiv:0804.2741) of the direct detection of the effects of Dark Matter that is causing a lot of buzz. (The Bad Astronomer has a good summary.) They find yearly modulation in their detected scintillation rate that matches what you would expect if the Earth were rushing through Galactic Dark Matter as it goes around the Sun. They have worked out the significance of the modulation to be 8.2 sigma. Significant! But significant of what? Continue reading ‘Is 8-sigma significant enough for you?’ »