The AstroStat Slog

The first issue of this year’s IMS bulletin has an obituary, from which the following is quoted. Continue reading ‘Circumspect frequentist’ »

I wonder what Fisher, Neyman, and Pearson would say if they see “Technique” after “Likelihood Ratio” instead of “Test.” A presenter’s saying “Likelihood Ratio Technique” for source identification, I couldn’t resist checking it out not to offend founding fathers of the likelihood principle in statistics since “Technique” sounded derogatory to be attached with “Likelihood” to my ears. I thank, above all, the speaker who kindly gave me the reference about this likelihood ratio technique. Continue reading ‘Likelihood Ratio Technique’ »

You would think that something like “measurement error” is a well-defined concept, and everyone knows what it means. Not so. I have so far counted at least 3 different interpretations of what it means.

Suppose you have measurements X={X_i, i=1..N} of a quantity whose true value is, say, X₀. One can then compute the mean and standard deviation of the measurements, E(X) and σ_X. One can also infer the value of a parameter θ(X), derive the posterior probability density p(θ|X), and obtain confidence intervals on it.

So here are the different interpretations:

1. Measurement error is σ_X, or the spread in the measurements. Astronomers tend to use the term in this manner.
2. Measurement error is X₀-E(X), or the “error made when you make the measurement”, essentially what is left over beyond mere statistical variations. This is how statisticians seem to use it, essentially the bias term. To quote David van Dyk
   

   For us it is just English. If your measurement is different from the real value. So this is not the Poisson variability of the source for effects or ARF, RMF, etc. It would disappear if you had a perfect measuring device (e.g., telescope).

3. Measurement error is the width of p(θ|X), i.e., the measurement error of the first type propagated through the analysis. Astronomers use this too to refer to measurement error.

Who am I to say which is right? But be aware of who you may be speaking with and be sure to clarify what you mean when you use the term!

We have seen the word “bipartisan” often during the election and during the on-going recession period. Sometimes, I think that the bipartisanship is not driven by politicians but it’s driven by media, commentator, and interpreters. Continue reading ‘Bipartisanship’ »

Almost two year long scrutinizing some publications by astronomers gave me enough impression that astronomers live in the Gaussian world. You are likely to object this statement by saying that astronomers know and use Poisson, binomial, Pareto (power laws), Weibull, exponential, Laplace (Cauchy), Gamma, and some other distributions.^[1] This is true. I witness that these distributions are referred in many publications; however, when it comes to obtaining “BEST FIT estimates for the parameters of interest” and “their ERROR (BARS)”, suddenly everything goes back to the Gaussian world.^[2]

Borel Cantelli Lemma (from Planet Math): because of mathematical symbols, a link was made but any probability books have the lemma with proofs and descriptions.

Continue reading ‘Borel Cantelli Lemma for the Gaussian World’ »

1. It is a bit disappointing fact that not many mention the t distribution, even though less than 30 observations are available.[↩]
2. To stay off this Gaussian world, some astronomers rely on Bayesian statistics and explicitly say that it is the only escape, which is sometimes true and sometimes not – I personally weigh more that Bayesians are not always more robust than frequentist methods as opposed to astronomers’ discussion about robust methods.[↩]

There will be a special session at the 213th AAS meeting on meaning from surveys and population studies (SPS). Until then, it might be useful to pull out some interesting and relevant papers and questions/challenges as a preliminary to the meeting. I will not list astronomical catalogs and surveys only, which are literally countless these days but will bring out some if they change the way how science is performed with a description of the catalog (the best example would be SDSS, Sloan Digital Sky Survey, to my knowledge). Continue reading ‘[SPS] Testing Completeness’ »

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[↩]

Personally, it was a highly anticipated symposium at CfA because I was fascinated about the female computers’ (or astronomers’) contributions that occurred here about a century ago even though at that time women were not considered as scientists but mere assistants for tedious jobs. Continue reading ‘after “Thanks to Henrietta Leavitt”’ »

[9/30/2008]

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/

[Update 11/06] The full program is now available. The symposium begins at Noon today.

The notions of missing data are overall different between two communities. I tend to think missing data carry as good amount of information as observed data. Astronomers…I’m not sure how they think but my impression so far is that a missing value in one attribute/variable from a object/observation/informant, all other attributes related to that object become useless because that object is not considered in scientific data analysis or model evaluation process. For example, it is hard to find any discussion about imputation in astronomical publication or statistical justification of missing data with respect to inference strategies. On the contrary, they talk about incompleteness within different variables. Putting this vague argument with a concrete example, consider a catalog of multiple magnitudes. To draw a color magnitude diagram, one needs both color and magnitude. If one attribute is missing, that star will not appear in the color magnitude diagram and any inference methods from that diagram will not include that star. Nonetheless, one will trying to understand how different proportions of stars are observed according to different colors and magnitudes. Continue reading ‘missing data’ »

I’ve talked about IMSL on my pyIMSL post, which is a commercial scientific library. There is a GNU version of IMSL, GSL. Finding GSL is the courtesy of Jiangang, who was the author of the poster that I most liked from the 212th AAS, (see My first AAS. V. measurement error and EM and his comment.) Continue reading ‘GSL – GNU Scientific Library’ »

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’ »

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’ »

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’ »