The AstroStat Slog

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’ »

In order to understand a learning procedure statistically it is necessary to identify two important aspects: its structural model and its error model. The former is most important since it determines the function space of the approximator, thereby characterizing the class of functions or hypothesis that can be accurately approximated with it. The error model specifies the distribution of random departures of sampled data from the structural model.

Continue reading ‘A Quote on Model’ »

People of experience would say very differently and wisely against what I’m going to discuss now. This post only combines two small cross sections of each branch of two trees, astronomy and statistics. Continue reading ‘survey and design of experiments’ »

The CfA is celebrating the 100th anniversary of the discovery of the Cepheid period-luminosity relation on Nov 6, 2008. See http://www.cfa.harvard.edu/events/2008/leavitt/ for details.

[Update 10/03] For a nice introduction to the story of Henrietta Swan Leavitt, listen to this Perimeter Institute talk by George Johnson: http://pirsa.org/06050003/

Is there an objective method to combine measurements of the same quantity obtained with different instruments?

Suppose you have a set of N₁ measurements obtained with one detector, and another set of N₂ measurements obtained with a second detector. And let’s say you wanted something as simple as an estimate of the mean of the quantity (say the intensity) being measured. Let us further stipulate that the measurement errors of each of the points is similar in magnitude and neither instrument displays any odd behavior. How does one combine the two datasets without appealing to subjective biases about the reliability or otherwise of the two instruments? Continue reading ‘[Q] Objectivity and Frequentist Statistics’ »

To my personal thoughts, the history of astronomy is more interesting than the history of statistics. This may change tomorrow. Harvard statistics department (chair Xiao-Li Meng) organizes a symposium titled

Quintessential Contributions:
Celebrating Major Birthdays of Statistical Ideas and Their Inventors
When: Saturday, September 27, 2008, 9:45 AM - 5:00 PM
Where: Radcliffe Gymnasium, 18 Mason Street, Cambridge, MA

Continue reading ‘Quintessential Contributions’ »

Another deduced conclusion from reading preprints listed in arxiv/astro-ph is that astronomers tend to confuse classification and clustering and to mix up methodologies. They tend to think any algorithms from classification or clustering analysis serve their purpose since both analysis algorithms, no matter what, look like a black box. I mean a black box as in neural network, which is one of classification algorithms. Continue reading ‘Classification and Clustering’ »

I’ve been joking about the astronomers’ fashion in writing Markov chain Monte Carlo (MCMC). Frequently, MCMC was represented by Monte Carlo Markov Chain in astronomical journals. I was curious about the history of this new creation. Overall, I thought it would be worth to learn more about the history of MCMC and this paper was up in arxiv: Continue reading ‘A History of Markov Chain Monte Carlo’ »

Astronomers tend to think in Bayesian way, but their Bayesian implementation is very limited. OpenBUGS, WinBUGS, GeoBUGS (BUGS for geostatistics; for example, modeling spatial distribution), R2WinBUGS (R BUGS wrapper) or PyBUGS (Python BUGS wrapper) could boost their Bayesian eagerness. Oh, by the way, BUGS stands for Bayesian inference Using Gibbs Sampling. Continue reading ‘BUGS’ »

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’ »

Physicists believe that the Gaussian law has been proved in mathematics while mathematicians think that it was experimentally established in physics — Henri Poincare

Continue reading ‘Why Gaussianity?’ »

Talking about limits in Numerical Recipes in my PyIMSL post, I couldn’t resist checking materials, particularly updates in the new edition of Numerical Recipes by Press, et al. (2007). Continue reading ‘NR, the 3rd edition’ »

I didn’t realize this post was sitting for a month during which I almost neglected the slog. As if great books about probability and information theory for statisticians and engineers exist, I believe there are great statistical physics books for physicists. On the other hand, relatively less exist that introduce one subject to the other kind audience. In this regard, I thought the lecture note can be useful.

[arxiv:physics.data-an:0808.0012]
Lectures on Probability, Entropy, and Statistical Physics by Ariel Caticha
Abstract:

Continue reading ‘A lecture note of great utility’ »

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]’ »

Diab Jerius follows up on LOESS techniques with a very nice summary update and finds LOCFIT to be very useful, but there are still questions about how it deals with measurement errors and combining observations from different experiments:

Continue reading ‘loess and lowess and locfit, oh my’ »