The AstroStat Slog » Earth http://hea-www.harvard.edu/AstroStat/slog Weaving together Astronomy+Statistics+Computer Science+Engineering+Intrumentation, far beyond the growing borders Fri, 09 Sep 2011 17:05:33 +0000 en-US hourly 1 http://wordpress.org/?v=3.4 Is 8-sigma significant enough for you? http://hea-www.harvard.edu/AstroStat/slog/2008/dark-matter-modulation/ http://hea-www.harvard.edu/AstroStat/slog/2008/dark-matter-modulation/#comments Thu, 24 Apr 2008 18:56:58 +0000 vlk http://hea-www.harvard.edu/AstroStat/slog/?p=279 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?

I am no expert on this in a hundred and one different ways. But I feel kinda sorry for the DAMA group. Certainly, at 8-sigma, it is easy to accept that there is modulation. But is this modulation proof of Dark Matter? Astronomers in general are extremely suspicious of any yearly modulations, as we have learnt from hard experience that it is an extremely common source of systematic error. Essentially, the Earth is a poorly calibrated detector, and it has diurnal and annual cycles, and these invariably show up in everything. So when the signal you are looking for goes exactly like the first thing you try to catch and eliminate, what price statistical significance?

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Kepler and the Art of Astrophysical Inference http://hea-www.harvard.edu/AstroStat/slog/2008/kepler-inference/ http://hea-www.harvard.edu/AstroStat/slog/2008/kepler-inference/#comments Wed, 16 Apr 2008 22:49:18 +0000 vlk http://hea-www.harvard.edu/AstroStat/slog/?p=270 I recently discovered iTunesU, and I have to confess, I find it utterly fascinating. By golly, it is everything that they promised us that the internet would be. Informative, entertaining, and educational. What are the odds?!? Anyway, while poking around the myriad lectures, courses, and talks that are now online, I came across a popular Physics lecture series at UMichigan which listed a talk by one of my favorite speakers, Owen Gingerich. He had spoken about The Four Myths of the Copernican Revolution last November. It was, how shall we say, riveting.

Owen talks in detail about how the Copernican model came to supplant the Ptolemaic model. In particular, he describes how Kepler went from Ptolemaic epicycles to elliptical orbits. Contrary to general impression, Kepler did not fit ellipses to Tycho Brahe’s observations of Mars. The ellipticity is far too small for it to be fittable! But rather, he used logical reasoning to first offset Earth’s epicyle away from the center in order to avoid the so-called Martian Catastrophe, and then used the phenomenological constraint of the law of equal areas to infer that the path must be an ellipse.

This process, along with Galileo’s advocacy for the heliocentric system, demonstrates a telling fact about how Astrophysics is done in practice. Hyunsook once lamented that astronomers seem to be rather trigger happy with correlations and regressions, and everyone knows they don’t constitute proof of anything, so why do they do it? Owen says about 39 1/2 minutes into the lecture:

Here we have the fourth of the myths, that Galileo’s telescopic observations finally proved the motion of the earth and thereby, at last, established the truth of the Copernican system.

What I want to assure you is that, in general, science does not operate by proofs. You hear that an awful lot, about science looking for propositions that can be falsified, that proof plays this big role.. uh-uh. It is coherence of explanation, understanding things that are well-knit together; the broader the framework of knitting the things together, the more we are able to believe it.

Exactly! We build models, often with little justification in terms of experimental proof, and muddle along trying to make it fit into a coherent narrative. This is why statistics is looked upon with suspicion among astronomers, and why for centuries our mantra has been “if it takes statistics to prove it, it isn’t real!”

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