Archive for the ‘Spectral’ Category.

#### [ArXiv] classifying spectra

[arXiv:stat.ME:0910.2585]
Variable Selection and Updating In Model-Based Discriminant Analysis for High Dimensional Data with Food Authenticity Applications
by Murphy, Dean, and Raftery

Classifying or clustering (or semi supervised learning) spectra is a very challenging problem from collecting statistical-analysis-ready data to reducing the dimensionality without sacrificing complex information in each spectrum. Not only how to estimate spiky (not differentiable) curves via statistically well defined procedures of estimating equations but also how to transform data that match the regularity conditions in statistics is challenging.
Continue reading ‘[ArXiv] classifying spectra’ »

Soon it’ll not be qualified for [MADS] because I saw some abstracts with the phrase, compressed sensing from arxiv.org. Nonetheless, there’s one publication within refereed articles from ADS, so far.

Title:Compressed sensing imaging techniques for radio interferometry

Speaking of XAtlas from my previous post I tried another visualization tool called Parallel Coordinates on these Capella observations and two stars with multiple observations (AL Lac and IM Peg). As discussed in [MADS] Chernoff face, full description of the catalog is found from XAtlas website. The reason for choosing these stars is that among low mass stars, next to Capella (I showed 16), IM PEG (HD 21648, 8 times), and AR Lac (although different phases, 6 times) are most frequently observed. I was curious about which variation, within (statistical variation) and between (Capella, IM Peg, AL Lac), is dominant. How would they look like from the parametric space of High Resolution Grating Spectroscopy from Chandra? Continue reading ‘[MADS] Parallel Coordinates’ »

#### worse than the Drake eq.

I was reading the June 2009 IMS bulletin on my way to Korea for the 1st IMS-APRM meeting. Then, I was in half shock and in half sadness. Something unlike than the Drake equation had happened. Continue reading ‘worse than the Drake eq.’ »

I cannot remember when I first met Chernoff face but it hooked me up instantly. I always hoped for confronting multivariate data from astronomy applicable to this charming EDA method. Then, somewhat such eager faded, without realizing what’s happening. Tragically, this was mainly due to my absent mind. Continue reading ‘[MADS] Chernoff face’ »

#### 4754 d.f.

I couldn’t believe my eyes when I saw 4754 degrees of freedom (d.f.) and chi-square test statistic 4859. I’ve often enough seen large degrees of freedom from journals in astronomy, several hundreds to a few thousands, but I never felt comfortable at these big numbers. Then with a great shock 4754 d.f. appeared. I must find out why I feel so bothered at these huge degrees of freedom. Continue reading ‘4754 d.f.’ »

#### It bothers me.

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.’ »

1. Note that the current sherpa is beta under ciao 4.0 not under ciao 3.4 and a description about “bayes” from the most recent sherpa is not available yet, which means this post needs updates one new release is available[]

#### Redistribution

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’ »

#### [tutorial] multispectral imaging, a case study

Without signal processing courses, the following equation should be awfully familiar to astronomers of photometry and handling data:
$$c_k=\int_\Lambda l(\lambda) r(\lambda) f_k(\lambda) \alpha(\lambda) d\lambda +n_k$$
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 $$c_k=\int_\Lambda \phi_k (\lambda) r(\lambda) d\lambda +n_k$$
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 $$c_k=\Theta r +n$$
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’ »

#### Parametric Bootstrap vs. Nonparametric Bootstrap

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.

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 Measure [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]’ »

#### Grating Dispersion [Equation of the Week]

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]’ »

#### [ArXiv] 5th week, Apr. 2008

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’ »