Aug 27th, 2008| 07:50 am | Posted by vlk
UChicago, my alma mater, is doing alright for itself in the spacecraft naming business.
First there was Edwin Hubble (S.B. 1910, Ph.D. 1917).
Then came Arthur Compton (the “MetLab”).
Followed by Subramanya Chandrasekhar (Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics).
And now, Enrico Fermi.
Tags:
CGRO,
Chandra,
Compton,
CXO,
Fermi,
GLAST,
HST,
Hubble,
observatory,
UChicago,
University of Chicago Category:
Astro,
gamma-ray,
High-Energy,
News,
Optical,
X-ray |
Comment
Aug 20th, 2008| 01:00 pm | Posted by vlk
I still remember my first class as a new grad student. As a cocky Physics graduate, I was quite sure I knew plenty of astronomy. Astro 301, class 1, and it took all of 20 minutes of talk about stellar magnitudes to put that notion to permanent rest. So, for the sake of our stats colleagues, here’s a brief primer on one of the basic building blocks of astronomy. Continue reading ‘Magnitude [Eqn]’ »
Aug 13th, 2008| 01:00 pm | Posted by vlk
Differential Emission Measures (DEMs) are a summary of the temperature structure of the outer atmospheres (aka coronae) of stars, and are usually derived from a select subset of line fluxes. They are notoriously difficult to estimate. Very few algorithms even bother to calculate error envelopes on them. They are also subject to numerous systematic uncertainties which can play havoc with proper interpretation. But they are nevertheless extremely useful since they allow changes in coronal structures to be easily discerned, and observations with one instrument can be used to derive these DEMs and these can then be used to predict what is observable with some other instrument. Continue reading ‘Differential Emission Measure [Eqn]’ »
Tags:
DEM,
Differential Emission Measure,
EotW,
Equation,
Equation of the Week,
stellar coronae Category:
Astro,
High-Energy,
Jargon,
Spectral,
Stars,
X-ray |
2 Comments
Aug 13th, 2008| 12:59 pm | Posted by vlk
I grew up in an environment that glamourized mathematical equations. Equations adorned a text like jewelry, set there to dazzle, and often to outshine the text that they were to illuminate. Needless to say, anything I wrote was dense, opaque, and didn’t communicate what it set out to. It was not until I saw a Reference Frame essay by David Mermin on how to write equations (1989, Physics Today, 42, p9) that I realized that equations should be treated as part of the text. You should be able to read them. David Mermin set out 3 rules for writing out equations, which I’ve tried to follow diligently (if not always successfully) since then. Continue reading ‘I Like Eq’ »
Tags:
1989,
David Mermin,
EotW,
Equation,
Equation of the Week,
formatting,
Physics Today,
Quotes Category:
Jargon,
Languages,
Meta,
Quotes |
2 Comments
Aug 6th, 2008| 01:00 pm | Posted by vlk
As mentioned before, background subtraction plays a big role in astrophysical analyses. For a variety of reasons, it is not a good idea to subtract out background counts from source counts, especially in the low-counts Poisson regime. What Bayesians recommend instead is to set up a model for the intensity of the source and the background and to infer these intensities given the data. Continue reading ‘Background Subtraction, the Sequel [Eqn]’ »
Tags:
background,
background marginalization,
background subtraction,
EotW,
Equation,
Equation of the Week Category:
Astro,
Bayesian,
Data Processing,
High-Energy,
Imaging,
Jargon,
Stat |
Comment
Jul 30th, 2008| 01:00 pm | Posted by vlk
I have noticed that our statistician collaborators are often confused by our units. (Not a surprise; I, too, am constantly confused by our units.) One of the biggest culprits is the unit of energy, [keV], Continue reading ‘keV vs keV [Eqn]’ »
Tags:
Angstrom,
Boltzmann,
EotW,
Equation,
Equation of the Week,
erg,
Kelvin,
keV,
Planck,
temperature,
units,
wavelength Category:
Astro,
High-Energy,
Jargon,
X-ray |
1 Comment
Jul 23rd, 2008| 01:00 pm | Posted by vlk
With the LHC coming on line anon, it is appropriate to highlight the Banff Challenge, which was designed as a way to figure out how to place bounds on the mass of the Higgs boson. The equations that were to be solved are quite general, and are in fact the first attempt that I know of where calibration data are directly and explicitly included in the analysis. Continue reading ‘The Banff Challenge [Eqn]’ »
Jul 16th, 2008| 01:00 pm | Posted by vlk
The Χ2 distribution plays an incredibly important role in astronomical data analysis, but it is pretty much a black box to most astronomers. How many people know, for instance, that its form is exactly the same as the γ distribution? A Χ2 distribution with ν degrees of freedom is
p(z|ν) = (1/Γ(ν/2)) (1/2)ν/2 zν/2-1 e-z/2 ≡ γ(z;ν/2,1/2) , where z=Χ2.
Continue reading ‘chi-square distribution [Eqn]’ »
Jul 14th, 2008| 11:55 pm | Posted by vlk
Hyunsook recently said that she wished that there were “some astronomical data depositories where no data reduction is required but one can apply various statistical analyses to the data in the depository to learn and compare statistical methods”. With the caveat that there really is no such thing (every dataset will require case specific reduction; standard processing and reduction are inadequate in all but the simplest of cases), here is a brief list: Continue reading ‘Reduced and Processed Data’ »
Tags:
ADC,
astro catalogs,
Cast,
CDF-S,
Chandra,
datasets,
HEASARC,
Penn State,
reduced,
standard processing,
W3Browse Category:
Astro,
Data Processing,
Misc |
4 Comments
Jul 9th, 2008| 01:00 pm | Posted by vlk
The Kaplan-Meier (K-M) estimator is the non-parametric maximum likelihood estimator of the survival probability of items in a sample. “Survival” here is a historical holdover because this method was first developed to estimate patient survival chances in medicine, but in general it can be thought of as a form of cumulative probability. It is of great importance in astronomy because so much of our data are limited and this estimator provides an excellent way to estimate the fraction of objects that may be below (or above) certain flux levels. The application of K-M to astronomy was explored in depth in the mid-80′s by Jurgen Schmitt (1985, ApJ, 293, 178), Feigelson & Nelson (1985, ApJ 293, 192), and Isobe, Feigelson, & Nelson (1986, ApJ 306, 490). [See also Hyunsook's primer.] It has been coded up and is available for use as part of the ASURV package. Continue reading ‘Kaplan-Meier Estimator (Equation of the Week)’ »
Tags:
censored,
EotW,
Equation,
Equation of the Week,
Feigelson,
Isobe,
Kaplan-Meier,
maximum likelihood,
Nelson,
Schmitt,
survival analysis,
upper limit Category:
Frequentist,
Jargon,
Methods,
Stat |
13 Comments
Jul 2nd, 2008| 01:00 pm | Posted by vlk
Astrophysics, especially high-energy astrophysics, is all about counting photons. And this, it is said, naturally leads to all our data being generated by a Poisson process. True enough, but most astronomers don’t know exactly how it works out, so this derivation is for them. Continue reading ‘Poisson Likelihood [Equation of the Week]’ »
Jun 25th, 2008| 01:00 pm | Posted by vlk
For a discipline that relies so heavily on images, it is rather surprising how little use astronomy makes of the vast body of work on image analysis carried out by mathematicians and computer scientists. Mathematical morphology, for example, can be extremely useful in enhancing, recognizing, and extracting useful information from densely packed astronomical
images.
The building blocks of mathematical morphology are two operators, Erode[I|Y] and Dilate[I|Y], Continue reading ‘Open and Shut [Equation of the Week]’ »
Jun 19th, 2008| 03:13 pm | Posted by vlk
You all may have heard that GLAST launched on June 11, and the mission is going smoothly. Via Josh Grindlay comes news that Steve Ritz, the GLAST Project Scientist at GSFC, is keeping a weblog dedicated to it at
http://blogs.nasa.gov/cm/blog/GLAST
and intends to post status reports and related information on it.
Jun 18th, 2008| 01:00 pm | Posted by vlk
From Protassov et al. (2002, ApJ, 571, 545), here is a formal expression for the Likelihood Ratio Test Statistic,
TLRT = -2 ln R(D,Θ0,Θ)
R(D,Θ0,Θ) = [ supθεΘ0 p(D|Θ0) ] / [ supθεΘ p(D|Θ) ]
where D are an independent data sample, Θ are model parameters {θi, i=1,..M,M+1,..N}, and Θ0 form a subset of the model where θi = θi0, i=1..M are held fixed at their nominal values. That is, Θ represents the full model and Θ0 represents the simpler model, which is a subset of Θ. R(D,Θ0,Θ) is the ratio of the maximal (technically, supremal) likelihoods of the simpler model to that of the full model.
Continue reading ‘Likelihood Ratio Test Statistic [Equation of the Week]’ »
Tags:
EotW,
Equation,
Equation of the Week,
F-test,
likelihood,
likelihood ratio test,
LRT,
Protassov,
Rostislav Protassov Category:
Fitting,
Jargon,
Stat |
2 Comments
Jun 11th, 2008| 01:00 pm | Posted by vlk
High-resolution astronomical spectroscopy has invariably been carried out with gratings. Even with the advent of the new calorimeter detectors, which can measure the energy of incoming photons to an accuracy of as low as 1 eV, gratings are still the preferred setups for hi-res work below energies of 1 keV or so. But how do they work? Where are the sources of uncertainty, statistical or systematic?
Continue reading ‘Grating Dispersion [Equation of the Week]’ »
Tags:
Bragg's Law,
Chandra,
diffraction,
dispersion,
EotW,
Equation,
Equation of the Week,
grating,
LETG,
Rowland Circle Category:
Astro,
Jargon,
Spectral |
2 Comments