I often feel irksome whenever I see a function being normalized over a feasible parameter space and it being used as a probability density function (pdf) for further statistical inference. In order to be a suitable pdf, normalization has to be done over a measurable space not over a feasible space. Such practice often yields biased best fits (biased estimators) and improper error bars. On the other hand, validating a measurable space under physics seems complicated. To be precise, we often lost in translation. Continue reading ‘A short note on Probability for astronomers’ »
Archive for 2009
Because of blogging and projects I worked on, I happened to collect quite many publications in Astronomy. The collection is biased toward my personal interests. However, these authors discussed statistics in a wide range. So, I felt my astronomical bibliography can be useful to slog audience. Some areas could match your interests. Or your own name can be found. Continue reading ‘astronomy bibliography’ »
Please, IMS Bulletin, v.38 (10) check p.11 of this pdf file for the whole article. Continue reading ‘From Terence’s stuff: You want proof?’ »
When I begin to subscribe arXiv/astro-ph and arXiv/stat, although only for a year I listed astro-ph papers featuring relatively advanced statistics, I also kept more papers relevant to astrostatistics beyond astro-ph or introducing hot topics in statistics and computer science for astronomical data applications. While creating my own arXiv as follows, I had a hope to write up short introductions of statistics that are unlikely known to most of astronomers (like my MADS) and matching subjects/targets in astronomy. I thought such effort could spawn new collaborations or could expand understanding of statistics among astronomers (see Magic Crystal). Well, I couldn’t catch up the growth rate and it’s about time to terminate the hope. However, I thought some papers can be useful to some slog subscribers. I hope they do. Continue reading ‘arxiv list’ »
He was one of the frequently cited statisticians in this slog because of his influence in statistics. It is extremely difficult to avoid his textbooks and his establishment of theoretical statistics when one begins to comprehend and to appreciate the modern theoretical statistics. To me, Testing Statistical Hypotheses and Theory of Point Estimation are two pillars of graduate statistical education. In addition, Elements of Large Sample Theory and Nonparametrics: Statistical Methods Based on Ranks are also eye openers. Continue reading ‘Erich Lehmann’ »
by Emanuel Parzen in Statistical Science 2004, Vol 19(4), pp.652-662 JSTOR
I teach that statistics (done the quantile way) can be simultaneously frequentist and Bayesian, confidence intervals and credible intervals, parametric and nonparametric, continuous and discrete data. My first step in data modeling is identification of parametric models; if they do not fit, we provide nonparametric models for fitting and simulating the data. The practice of statistics, and the modeling (mining) of data, can be elegant and provide intellectual and sensual pleasure. Fitting distributions to data is an important industry in which statisticians are not yet vendors. We believe that unifications of statistical methods can enable us to advertise, “What is your question? Statisticians have answers!”
I couldn’t help liking this paragraph because of its bitter-sweetness. I hope you appreciate it as much as I did.
I was told to stay away from python and I’ve obeyed the order sincerely. However, I collected the following stuffs several months back at the instance of hearing about import inference and I hate to see them getting obsolete. At that time, collecting these modules and getting through them could help me complete the first step toward the quest Learning Python (the first posting of this slog). Continue reading ‘some python modules’ »
by P.I.Good and J.W.Hardin. Publisher’s website
My astronomer neighbor mentioned this book a while ago and quite later I found intriguing quotes. Continue reading ‘Quotes from Common Errors in Statistics’ »
As a part of exploring spatial distribution of particles/objects, not to approximate via Poisson process or Gaussian process (parametric), nor to impose hypotheses such as homogenous, isotropic, or uniform, various nonparametric methods somewhat dragged my attention for data exploration and preliminary analysis. Among various nonparametric methods, the one that I fell in love with is tessellation (state space approaches are excluded here). Computational speed wise, I believe tessellation is faster than kernel density estimation to estimate level sets for multivariate data. Furthermore, conceptually constructing polygons from tessellation is intuitively simple. However, coding and improving algorithms is beyond statistical research (check books titled or key-worded partially by computational geometry). Good news is that for computation and getting results, there are some freely available softwares, packages, and modules in various forms. Continue reading ‘[ArXiv] Voronoi Tessellations’ »
I’m very sure that Fortran is one of the major scientific programming languages. Many functions, modules, and libraries are written in this language. Without being aware of, these routines are ported into many script languages. However, I become curious whether Fortran is still the major force in astronomy or statistics, compared to say 20 years ago (10 seems too small). Continue reading ‘Do people use Fortran?’ »
I watched a movie in which one of the characters said, “country A has nukes with 80% chance” (perhaps, not 80% but it was a high percentage). One of the statements in that episode is that people will not eat lettuce only if the 1% chance of e coli is reported, even lower. Therefore, with such a high percentage of having nukes, it is right to send troops to A. This episode immediately brought me a thought about astronomers’ null hypothesis probability and their ways of concluding chi-square goodness of fit tests, likelihood ratio tests, or F-tests.
First of all, I’d like to ask how you would like to estimate the chance of having nukes in a country? What this 80% implies here? But, before getting to the question, I’d like to discuss computing the chance of e coli infection, first. Continue reading ‘The chance that A has nukes is p%’ »
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’ »
Astronomers rely on scatter plots to illustrate correlations and trends among many pairs of variables more than any scientists. Pages of scatter plots with regression lines are often found from which the slope of regression line and errors bars are indicators of degrees of correlation. Sometimes, too many of such scatter plots makes me think that, overall, resources for drawing nice scatter plots and papers where those plots are printed are wasted. Why not just compute correlation coefficients and its error and publicize the processed data for computing correlations, not the full data, so that others can verify the computation results for the sake of validation? A couple of scatter plots are fine but when I see dozens of them, I lost my focus. This is another cultural difference. Continue reading ‘Scatter plots and ANCOVA’ »
- This is not an assuring absolute statement but a personal impression after reading articles of various fields in addition to astronomy. My readings of other fields tell that many rely on correlation statistics but less scatter plots by adding straight lines going through data sets for the purpose of imposing relationships within variable pairs[↩]
Although a bit of time has elapsed since my post space weather, saying that logistic regression is used for prediction, it looks like still true that logistic regression is rarely used in astronomy. Otherwise, it could have been used for the similar purpose not under the same statistical jargon but under the Bayesian modeling procedures. Continue reading ‘[MADS] logistic regression’ »