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stefano-meschiari / Systemic2

Systemic is a C library for modeling exoplanetary radial velocities, with an R binding and a full GUI IDE.
http://www.stefanom.org/?systemic
GNU General Public License v3.0
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Question about Chi Square and KS p-value computations in Systemic #11

Open ddellaro opened 9 years ago

ddellaro commented 9 years ago

I presume these tests are computed by comparing the actual radial velocity data sample against the orbital element fit curve (used as the "theoretical" distribution), and that the null hypothesis is that the sample data is a valid "subset" of the theoretical distribution. Is this correct? If not, can you help me clarify how Systemic implements these tests?

Thanks, Devin Della-Rose

ddellaro commented 9 years ago

So in looking at your PASP 2009 Paper I, equation (2) on pg. 1018, it appears your Keplerian fit indeed serves as the "parent" or "theoretical" distribution in the Chi-Square test. That leads me to another question--in your tutorial, the user fits the data for HD 115617. Once three planets have been added, your Chi-Square value is about 1760, and the degrees of freedom is 166 ( = 183 - 17). The corresponding critical value at the 99 percent confidence level is about 211. So I conclude that the null hypothesis must be strongly rejected, i.e., the sample data for HD 115617 is not consistent with the fit. This also seems to be reflected in the KS p-value, which is practically zero (3.7e-13). Is my thinking correct here, and if so, how does one use Systemic to obtain a good fit for HD 115617?? By the way, I encounter this same issue in other data sets included with Systemic (such as Tau Bootis, which we are also observing from the Air Force Academy Observatory with our echelle spectrograph).

Thanks very much for your time & patience with my questions, Devin