The AstroStat Slog

So far, I didn’t complain much related to my “statistician learning astronomy” experience. Instead, I’ve been trying to emphasize how fascinating it is. I hope that more statisticians can join this adventure when statisticians’ insights are on demand more than ever. However, this positivity seems not working so far. In two years of this slog’s life, there’s no posting by a statistician, except one about BEHR. Statisticians are busy and well distracted by other fields with more tangible data sets. Or compared to other fields, too many obstacles and too high barriers exist in astronomy for statisticians to participate. I’d like to talk about these challenges from my ends.^[1]

The biggest challenge for a statistician to use astronomical data is the lack of mercy for nonspecialists’ accessing data including format, quantification, and qualification^[2] ; and data analysis systems. IDL is costly although it is used in many disciplines and other tools in astronomy are hardly utilized for different projects.^[3] In that regards, I welcome astronomers using python to break such exclusiveness in astronomical data analysis systems.

Even if data and software issues are resolved, there’s another barrier to climb. Validation. If you have a catalog, you’ll see variables of measures, and their errors typically reflecting the size of PSF and its convolution to those metrics. If a model of gaussian assumption applied, in order to tabulate power law index, King’s, Petrosian’s, or de Vaucouleurs’ profile index, and numerous metrics, I often fail to find any validation of gaussian assumptions, gaussian residuals, spectral and profile models, outliers, and optimal binning. Even if a data set is publicly available, I also fail to find how to read in raw data, what factors must be considered, and what can be discarded because of unexpected contamination occurred like cosmic rays and charge over flows. How would I validate raw data that are read into a data analysis system is correctly processed to match values in catalogs? How would I know all entries in catalog are ready for further scientific data analysis? Are those sources real? Is p-value appropriately computed?

I posted an article about Chernoff faces applied to Capella observations from Chandra. Astronomers already processed the raw data and published a catalog of X-ray spectra. Therefore, I believe that the information in the catalog is validated and ready to be used for scientific data analysis. I heard that repeated Capella observation is for the calibration. Generally speaking, in other fields, targets for calibration are almost time invariant and exhibit consistency. If Capella is a same star over the 10 years, the faces in my post should look almost same, within measurement error; but as you saw, it was not consistent at all. Those faces look like observations were made toward different objects. So far I fail to find any validation efforts, explaining why certain ObsIDs of Capella look different than the rest. Are they real Capella? Or can I use this inconsistent facial expression as an evidence that Chandra calibration at that time is inappropriate? Or can I conclude that Capella was a wrong choice for calibration?

Due to the lack of quantification procedure description from the raw data to the catalog, what I decided to do was accessing the raw data and data processing on my own to crosscheck the validity in the catalog entries. The benefit of this effort is that I can easily manipulate data for further statistical inference. Although reading and processing raw data may sound easy, I came across another problem, lack of documentation for nonspecialists to perform the task.

A while ago, I talked about read.table() in R. There are slight different commands and options but without much hurdle, one can read in ascii data in various styles easily with read.table() for exploratory data analysis and confirmatory data analysis with R. From my understanding, statisticians do not spend much time on reading in data nor collecting them. We are interested in methodology to extract information of the population based on sample. While the focus is methodology, all the frustrations with astronomical data analysis softwares occur prior to investigating the best method. The level of frustration reached to the extend of terminating my eagerness for more investigation about inference tools.

In order to assess those Capella observations, thanks to its on-site help, I evoke ciao. Beforehand, I’d like to disclaim that I exemplify ciao to illustrate the culture difference that I experienced as a statistician. It was used to discuss why I think that astronomical data analysis systems are short of documentations and why that astronomical data processing procedures are lack of validation. I must say that I confront very similar problems when I tried to learn astronomical packages such as IRAF and AIPS. Ciao happened to be at handy when writing this post.

In order to understand X-ray data, not only image data files, one also needs effective area (arf), redistribution matrix (rmf), and point spread function (psf). These files are called by calibration data files. If the package was developed for general users, like read.table() I expect there should be a homogenized/centralized data including calibration data reading function with options. Instead, there were various kinds of functions one can use to read in data but the description was not enough to know which one is doing what. What is the functionality of these commands? Which one only stores names of data file? Which one reconfigures the raw data reflecting up to date calibration file? Not knowing complete data structures and classes within ciao, not getting the exact functionality of these data reading functions from ahelp, I was not sure the log likelihood that I computed is appropriate or not.

For example, there are five different ways to associate an arf: read_arf(), load_arf(), set_arf(), get_arf(), and unpack_arf() from ciao. Except unpack_arf(), I couldn’t understand the difference among these functions for accessing an arf^[4] Other softwares including XSPEC that I use, in general, have a single function with options to execute different level of reading in data. Ciao has an extensive web documentation without a tutorial (see my post). So I read all ahelp “commands” a few times. But I still couldn’t decide which one to use for my work to read in arfs and rmfs (I happened to have many calibration data files).

[Note that above links may not work since ciao documentation website evolves quickly. Some might be routed to different links so please, check this website for other data reading commands: cxc.harvard.edu/sherpa/ahelp/index_alphabet.html].

So, I decide to seek for a help through cxc help desk several months back. Their answers are very reliable and prompt. My question was “what are the difference among read_xxx(), load_xxx(), set_xxx(), get_xxx(), and unpack_xxx(), where xxx can be data, arf, rmf, and psf?” The answer to this question was that

You can find detailed explanations for these Sherpa commands in the “ahelp” pages of the Sherpa website:

http://cxc.harvard.edu/sherpa/ahelp/index_alphabet.html

This is a good answer but a big cultural shock to a statistician. It’s like having an answer like “check http://www.r-project.org/search.html and http://cran.r-project.org/doc/FAQ/R-FAQ.html” for IDL users to find out the difference between read.table() and scan(). Probably, for astronomers, all above various data reading commands are self explanatory like R having read.table(), read.csv(), and scan(). Disappointingly, this answer was not I was looking for.

Well, thanks to this embezzlement, hesitation, and some skepticism, I couldn’t move to the next step of implementing fitting methods. At the beginning, I was optimistic when I found out that Ciao 4.0 and up is python compatible. I thought I could do things more in statistically rigorous ways since I can fake spectra to validate my fitting methods. I was thinking about modifying the indispensable chi-square method that is used twice for point estimation and hypothesis testing that introduce bias (a link made to a posting). My goal was make it less biased and robust, less sensitive iid Gaussian residual assumptions. Against my high expectation, I became frustrated at the first step, reading and playing with data to get a better sense and to develop a quick intuition. I couldn’t even make a baby step to my goal. I’m not sure if it a good thing or not, but I haven’t been completely discouraged. Also, time helps gradually to overcome this culture difference, the lack of documentation.

What happens in general is that, if a predecessor says, use “set_arf(),” then the apprentice will use “set_arf()” without doubts. If you begin learning on your own purely relying on documentations, I guess at some point you have to make a choice. One can make a lucky guess and move forward quickly. Sometimes, one can land on miserable situation because one is not sure about his/her choice and one cannot trust the features appeared after these processing. I guess it is natural to feel curiosity about what each of these commands is doing to your data and what information is carried over to the next commands in analysis procedures. It seems righteous to know what command is best for the particular data processing and statistical inference given the data. What I found is that such comparison across commands is missing in documentations. This is why I thought astronomical data analysis systems are short of mercy for nonspecialists.

Another thing I observed is that there seems no documentation nor standard procedure to create the repeatable data analysis results. My observation of astronomers says that with the same raw data, the results by scientist A and B are different (even beyond statistical margins). There are experts and they have knowledge to explain why results are different on the same raw data. However, not every one can have luxury of consulting those few experts. I cannot understand such exclusiveness instead of standardizing the procedures through validations. I even saw that the data that A analyzed some years back can be different from this year’s when he/she writes a new proposal. I think that the time for recreating the data processing and inference procedure to explain/justify/validate the different results or to cover/narrow the gap could have not been wasted if there are standard procedures and its documentation. This is purely a statistician’s thought. As the comment in where is ciao X?^[5] not every data analysis system has to have similar design and goals.

Getting lost while figuring out basics (handling, arf, rmf, psf, and numerous case by case corrections) prior to applying any simple statistics has been my biggest obstacle in learning astronomy. The lack of documenting validation methods often brings me frustration. I wonder if there’s any astronomers who lost in learning statistics via R, minitab, SAS, MATLAB, python, etc. As discussed in where is ciao X? I wish there is a centralized tutorial that offers basics, like how to read in data, how to do manipulate datum vector and matrix, how to do arithmetics and error propagation adequately not violating assumptions in statistics (I don’t like the fact that the point estimate of background level is subtracted from observed counts, random variable when the distribution does not permit such scale parameter shifting), how to handle and manipulate fits format files from Chandra for various statistical analysis, how to do basic image analysis, how to do basic spectral analysis, and so on with references^[6]

1. This is quite an overdue posting. Links and associated content can be outdated.[↩]
2. For the classification purpose, data with clear distinction between response and predictor variables so called a training data set must be given. However, I often fail to get processed data sets for statistical analysis. I first spend time to read data and question what is outlier, bias, or garbage. I’m not sure how to clean and extract numbers for statistical analysis and every sub-field in astronomy have their own way to clean to be fed into statistics and scatter plots. For example, image processing is still executed case by case via trained eyes of astronomers. On the other hand, in medical imaging diagnosis specialists offer training sets with which scientists in computer vision develop algorithms for classification. Such collaboration yields accelerated, automatic but preliminary diagnosis tools. A small fraction of results from these preliminary methods still can be ambiguous, i.e. false positive or false negative. Yet, when such ambiguous cancerous cell images at the decision boundaries occur, specialists like trained astronomers scrutinize those images to make a final decision. As medical imaging and its classification algorithms resolve the issue of expert shortage under overflowing images, I wish astronomers adopt their strategies to confront massive streaming images and to assist sparse trained astronomers[↩]
3. Something I like to see is handling background statistically in high energy astrophysics. When simulating a source, background can be simulated as well via Makov Random field, kriging, and other spatial statistics methods. In reality, background is subtracted once in measurement space and the random nature of background is not interactively reflected. Regardless of available statistical methodology to reflect the nature of background, it is difficult to implement it for trial and validation because those tools are not compatible for adding statistical modules and packages.[↩]
4. A Sherpa expert told me there is an FAQ (I failed to locate previously) on this matter. However, from data analysis perspective like a distinction between data.structure, vector, matrix, list and other data types in R, the description is not sufficient for someone who wants to learn ciao and to perform scientific (both deterministic or stochastic) data analysis via scripting i.e. handling objects appropriately. You might want to read comparing commands in Sharpa from Shepa FAQ[↩]
5. I know there is ciaox. Apart from the space between ciao and X, there is another difference that astronomers do not care much compared to statisticians: the difference between X and x. Typically, the capital letter is for random variable and lower case letters for observation or value[↩]
6. By the way, there are ciao workshop materials available that could function as tutorials. Please, locate them if needed.[↩]