Weaving together Astronomy+Statistics+Computer Science+Engineering+Intrumentation, far beyond the growing borders
Archive for the ‘Spectral’ Category.
The full description is given http://cxc.harvard.edu/ciao3.4/ahelp/bayes.html about “bayes” under sherpa/ciao[1]. Some sentences kept bothering me and here’s my account for the reason given outside of quotes. Continue reading ‘It bothers me.’ »
RMF. It is a wørd to strike terror even into the hearts of the intrepid. It refers to the spread in the measured energy of an incoming photon, and even astronomers often stumble over what it is and what it contains. It essentially sets down the measurement error for registering the energy of a photon in the given instrument.
Thankfully, its usage is robustly built into analysis software such as Sherpa or XSPEC and most people don’t have to deal with the nitty gritty on a daily basis. But given the profusion of statistical software being written for astronomers, it is perhaps useful to go over what it means. Continue reading ‘Redistribution’ »
Without signal processing courses, the following equation should be awfully familiar to astronomers of photometry and handling data:
Terms are in order, camera response (c_k), light source (l), spectral radiance by l (r), filter (f), sensitivity (α), and noise (n_k), where Λ indicates the range of the spectrum in which the camera is sensitive.
Or simplified to 
where φ denotes the combined illuminant and the spectral sensitivity of the k-th channel, which goes by augmented spectral sensitivity. Well, we can skip spectral radiance r, though. Unfortunately, the sensitivity α has multiple layers, not a simple closed function of λ in astronomical photometry.
Or 
Inverting Θ and finding a reconstruction operator such that r=inv(Θ)c_k leads spectral reconstruction although Θ is, in general, not a square matrix. Otherwise, approach from indirect reconstruction. Continue reading ‘[tutorial] multispectral imaging, a case study’ »
The following footnotes are from one of Prof. Babu’s slides but I do not recall which occasion he presented the content.
– In the XSPEC packages, the parametric bootstrap is command FAKEIT, which makes Monte Carlo simulation of specified spectral model.
– XSPEC does not provide a nonparametric bootstrap capability.
Continue reading ‘Parametric Bootstrap vs. Nonparametric Bootstrap’ »
Like spherical cows, true blackbodies do not exist. Not because “black objects are dark, duh”, as I’ve heard many people mistakenly say — black here simply refers to the property of the object where no wavelength is preferentially absorbed or emitted, and all the energy input to it is converted into radiation. There are many famous astrophysical cases which are very good approximations to perfect blackbodies — the 2.73K microwave background radiation left over from the early Universe, for instance. Even the Sun is a good example. So it is often used to model the emission from various objects. Continue reading ‘Blackbody Radiation [Eqn]’ »
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]’ »
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]’ »
Since I learned Hubble’s tuning fork[1] for the first time, I wanted to do classification (semi-supervised learning seems more suitable) galaxies based on their features (colors and spectra), instead of labor intensive human eye classification. Ironically, at that time I didn’t know there is a field of computer science called machine learning nor statistics which do such studies. Upon switching to statistics with a hope of understanding statistical packages implemented in IRAF and IDL, and learning better the contents of Numerical Recipes and Bevington’s book, the ignorance was not the enemy, but the accessibility of data was. Continue reading ‘[ArXiv] 5th week, Apr. 2008’ »
Why is it that detection of emission lines is more reliable than that of absorption lines?
That was one of the questions that came up during the recent AstroStat Special Session at HEAD2008. When you look at the iconic Figure 1 from Protassov et al (2002), which shows how the null distribution of the Likelihood Ratio Test (LRT) and how it holds up for testing the existence of emission and absorption lines. The thin vertical lines are the nominal F-test cutoffs for a 5% false positive rate. The nominal F-test is too conservative in the former case (figures a and b; i.e., actual existing lines will not be recognized as such), and is too anti-conservative in the latter case (figure c; i.e., non-existent lines will be flagged as real). Continue reading ‘The Flip Test’ »
Astronomers have developed their ways of processing signals almost independent to but sometimes collaboratively with engineers, although the fundamental of signal processing is same: extracting information. Doubtlessly, these two parallel roads of astronomers’ and engineers’ have been pointing opposite directions: one toward the sky and the other to the earth. Nevertheless, without an intensive argument, we could say that somewhat statistics has played the medium of signal processing for both scientists and engineers. This particular issue of IEEE signal processing magazine may shed lights for astronomers interested in signal processing and statistics outside the astronomical society.
IEEE Signal Processing Magazine Jul. 2007 Vol 24 Issue 4: Bootstrap methods in signal processing
This link will show the table of contents and provide links to articles; however, the access to papers requires IEEE Xplore subscription via libraries or individual IEEE memberships). Here, I’d like to attempt to introduce some articles and tutorials.
Continue reading ‘Signal Processing and Bootstrap’ »
One of the big problems that has come up in recent years is in how to represent the uncertainty in certain estimates. Astronomers usually present errors as +-stddev on the quantities of interest, but that presupposes that the errors are uncorrelated. But suppose you are estimating a multi-dimensional set of parameters that may have large correlations amongst themselves? One such case is that of Differential Emission Measures (DEM), where the “quantity of emission” from a plasma (loosely, how much stuff there is available to emit — it is the product of the volume and the densities of electrons and H) is estimated for different temperatures. See the plots at the PoA DEM tutorial for examples of how we are currently trying to visualize the error bars. Another example is the correlated systematic uncertainties in effective areas (Drake et al., 2005, Chandra Cal Workshop). This is not dissimilar to the problem of determining the significance of a “feature” in an image (Connors, A. & van Dyk, D.A., 2007, SCMA IV). Continue reading ‘Dance of the Errors’ »
The chi2 bias can affect the results of the X-ray spectral fitting and it
can be demonstrated in a simple way. The described simulations can be done
in Sherpa or XSPEC, the two software packages that allow for simulating the X-ray
spectra using a function called “fakeit”.
Here I assume an absorbed power law model with the sets of 3 parameters
(absorption column, photon index, and normalization) to simulate Chandra X-ray
spectrum given the instrument calibration files (RMF/ARF) and the Poisson noise.
The resulting simulated X-ray spectrum contains the model predicted counts with
the Poisson noise. This spectrum is then fit with the absorbed power law model to get
the best fit parameter values for NH, photon index and normalization.
I simulate 1000 spectra and fit each of them using different statistics: chi2 data variance,
chi2 model variance and Cash/C-statistics.
The next step is to plot the simulated distributions of the parameters and compare them
to the assumed values for the simulations. The figure shows the distribution of the photon
index parameter obtain from the fit of the spectra generated for the assumed simulated value
of 1.267. The chi2 bias is evident in this analysis, while the
CSTAT and Cash statistics based on the likelihood behave well. chi2 model variance
underestimates the simulated value, chi2 data variance overestimates this parameter.
From arxiv/math.st: 0708.0499v1
Inference for mixtures of symmetric distributions by Hunter, Wang, and Hettmansperger, Annals of Statistics, 2007, Vol.35(1), pp.224-251.
Continue reading ‘[ArXiv] Identifiability and mixtures of distributions, Aug. 3, 2007’ »
During the International X-ray Summer School, as a project presentation, I tried to explain the inadequate practice of χ^2 statistics in astronomy. If your best fit is biased (any misidentification of a model easily causes such bias), do not use χ^2 statistics to get 1σ error for the 68% chance of capturing the true parameter.
Later, I decided to do further investigation on that subject and this paper came along: Astrostatistics: Goodness-of-Fit and All That! by Babu and Feigelson.
Continue reading ‘Astrostatistics: Goodness-of-Fit and All That!’ »
From arxiv/astro-ph:0707.1891v1
The Geneva-Copenhagen Survey of the Solar neighborhood II. New uvby calibrations and rediscussion of stellar ages, the G dwarf problem, age-metalicity diagram, and heating mechanisms of the disk by Holmberg, Nordstrom, and Andersen
Researchers, including scientists from CHASC, working on color magnitude diagrams to infer ages, metalicities, temperatures, and other physical quantities of stars and stellar clusters may find this paper useful.
Continue reading ‘[ArXiv] Geneva-Copenhagen Survey, July 13, 2007’ »