| DATE |
Description | |
|---|---|---|
Mon Aug 29 |
topics_to_cover_2011. Intro to to the course: outline, contents, rationale. You should know the contents of my website "UNIX, EMACS, AND LATEX" . If you are going to use IDL, you should know the contents of "IDL PROCEDURES and INSTRUCTIONAL HANDOUTS", and you should download my entire IDL procedure library and follow the README instructions. We discussed the material in managing_computers.notes. You should have a BACKUP SCHEME that utilizes more than a single external hard drive, and you should use RSYNC or a more sophisticated Equilvalent. | |
Wed Aug 31 |
lect2. Color: RGB, CMYK. Graph issues: color contrast, line thickness, character size and font, Colorblind men. Importing graphs and figures into PowerPoint, and related issues. bpidl : issues with graphs and plots; colored symbols; use of textoidl for math/Greei in IDL. why PostScript is so wonderful. | |
Wed Sep 7 | lect4.ps ; ididl ; newdimensionalcolor ; projections ; tim robishaw's IDL display.pro . We discuss images, annotating, multidimensional color on both on X and PS; Visual classes: Pseudocolor, Truecolor, Directcolor. Color tables. Using color in plots. Color images: one-dimensional, two-d, and three-d. Projections of the spherical sky onto paper (and, also, healpix). Use of Tim Robishaw's display.pro in IDL | |
PROBLEM |
hiproj.ps : A 2d image of HI with a stereographic projection. HERE is the LAB fits file, and here is the IDL procedure to read it called getsp.pro | |
READING |
DO READING on monovariate PDFs: TRUMPLER/WEAVER 1.11-1.15 inclusive. DO READING on using transformaations to generate random numbers of a desired functional form: Cowan 3.1, 3.2, 3.3. | |
Mon Sep 12 |
Monovariate PDFs. Basics, Examples, transformations. Random number generating, Monte Carlo basics. | |
Wed Sep 14 |
NO CLASS! Carl's out of town. | |
READING |
DO READING: BIVARIATE PDFS AND THEIR TRANSORMATIONS: TRUMPLER AND WEAVER, sections 1.31, 1.33, 1.34; COWAN, section 3.2. | |
Mon Sep 19 |
Bivariate PDFs. Basics, Examples, transformations Bivariate PDFs and their transformations. Examples: PDF of thickness of randomly oriented disks; PDF of sum of two variables with different PDFs. The very important case of PDF of sqrt of sum of squares of 2 variables. | |
READING |
DO READING on famous/important PDFs: COWAN chapter 2. (2.1, 2.2, 2.3, 2.5, 2.6, 2.7). DO READING : Numerical Recipes (NR) on the chi-square test and the Kolmogoroff-Smirnoff test. | |
Wed Sep 21 |
Famous/important PDFs: binomial, poisson, Gaussian, log-normal, chi-squared | |
PROBLEM |
poissondiff_problem.ps : DO THIS PROBLEM!! due Wednesday, Sep 28. | |
Mon Sep 26 |
Introduction to Maximum Entropy and information. MaxEnt as applied to monovariate PDFs. The Lebesgue measure and the Shannon-James Entropy. The Poisson PDF as the MaxEnt PDF for a counting experiment. READING: SIVIA, pages 118-125. | |
Wed Sep 28 |
Finish MaxEnt as applied to monovariate PDFs. Discrete PDFs (i.e., data histograms). Parent and sample populations, mean, variance, median, chi-square and KS tests. READING for chi-square and KS: Numerical Recipes, section 14.3 (section title: "Are Two Distributions Different?") | |
Mon Oct 03 |
Introduction to Bayesian techniques. Read pdfinfo.ps and bring it to class. | |
Wed Oct 05 |
More Introduction to Bayesian techniques. Read pdfinfo.ps and bring it to class. | |
READING |
pdfinfo.ps : READ THIS! (What we've been covering in class about Bayesian parameter estimation; it will help with the PROBLEM below!! | |
PROBLEM |
pol_prob.ps : DO THIS PROBLEM (on deriving linear polarization from Stokes (Q,U)!! due Wednesday, Oct 19. | |
Mon Oct 10 | Multivariate Gaussian statistics. Covariance, correlation, uncertainties of those in a sample. Discrete distributions: mean, variance, variance of variance, variance of correlation coefficients. | |
READING |
DO READING: Error propagation, COWAN SECTION 1.6. Diagonalizing the covariance matrix, COWAN SECTION 1.7. | |
Wed Oct 12 |
Error propagation including covariance. Eigenvector diagonalizing the covariance matrix. | |
Mon Oct 17 |
Maximum Likelihood (ML) for Gaussian statistics; Least squares I: Fundamentals, multivariate fitting. | |
READING |
lsfit_2008.ps lsfit_2008.pdf I recommend printing this 66-page handout on Least-squares fitting. I'll refer to it in classs, aand we will gradually work our way through the entire thing... | |
Wed Oct 19 |
Illustrative example of least-squares: a polynomial fit. covariance. orthogonal functions; legendre fit. formulating least squares properly: two examples. Looking at the matrices to chase down problems. Proof (and conditions required) for the covariance matrix to reflect the true covariance. | |
Mon Oct 24 |
Chauvenet's criterion. Nonlinear least-squares fitting using Taylor expansion. Multiple minima. Levenberg-Marquardt/Craig Markwardt's mpfit.pro. Numerical derivatives: accuracy considerations in computing. | |
Wed Oct 26 |
Chi-square fitting and weighted fitting. Covariance and error degree of confidence for multivariate fitting. The concept of delta chi^2. | |
Mon Oct 31 |
James McBride on 'Bootstrapping'. Delta Chi-square. | |
PROBLEM |
Do this problem on chi-square fitting and uncertainties from Delta Chi-square. Due Wednesday, Nov 9. | |
Wed Nov 02 |
More on Delta Chi-square. Use of Singular Value Decomposition to handle degeneracies in least-squares fitting. Fitting with constraints. Weighted iterative fitting; a modified Chauvenet's criterion. | |
PROBLEM |
Do this problem on using SVD in least-squares fitting. Due Wednesday, Nov 16. | |
Mon Nov 07 | Weighted iterative fitting: Minimum Absolute Residual Sum (MARS) fitting. Fitting when there is no independent variable--all variables have uncertainties (Jefferys's method). | |
READING |
Read this.ps this.pdf on Bayesian model selection in preparation for the next class. | |
Wed Nov 09 |
MODEL SELECTION: Bayesian model selection. Frequentist model selection--the F test. Fitting with rational functions. Cubic splines. Least squares with cubic splines: bsplines. Least squares cubic splines using Schlegel/Burles IDL procedure "bspline_iterfit". | |
READING |
Read this.ps this.pdf on Fourier transforms and techniques. We will be referring to it during the next few classes. | |
Mon Nov 14 |
Fourier transforms: basic math aspects. A few important transform pairs. Scaling. convolution and correlation theorems with real-life astronomical examples. Aliasing in discrete sampling. | |
Wed Nov 16 |
Digital Fourier transforms as applied to CDs, movies, and optical gratings. Example of crab optical pulsar data. Wiener filtering, optimum filtering. binning. The FFT. Digital convolution and correlation Deconvolution, noise. | |
Mon Nov 21 |
Finish the example of crab optical pulsar data. Wiener filtering, optimum filtering. binning. The FFT. Digital convolution and correlation Deconvolution, noise. | |
Wed Nov 23 |
BY POPULAR DEMAND: NO CLASS because of thanksgiving. | |
Mon Nov 28 |
Irregular sampling and Fourier transforms. The window function. The Lomb periodogram. | |
PROBLEM |
Do this fascinating problem on Mike Fitzgerald/Geoff Marcy discovery data set for the planet around HD 209458. It needs this dataset, gm.sav Due Wednesday, Dec 7. | |
Wed Nov 30 |
Clean. Maximum Entropy. You might want to look at this prescription for doing clean on irregularly-sampled time series; and this "just the basics" description of how maximum entropy works for images. | |
READING |
Read this.ps this.pdf on wavelets. This was written by Eric Rosolowsky, a former grad student here, who gracioiusly covered this material for this class some yeers ago and left this wonderful writeup as a legacy. | |
Mon Dec 05 |
Wavelets I: continuous wavelets | |
Wed Dec 07 |
Wavelets II: discrete wavelets. | |
Wed Dec XX |
Wrap up wavelets. Introduction to Principal Components Analysis (PCA) | |
Sun Dec 25 |
Wrap up PCA. Brief description of what we haven't covered. | |
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PROBLEM |
Do this problem, which compares spline fitting with rational fitting. Due Friday, April 16. | |
PROBLEM |
Do this problem on our crab pulsar data from the undergraduate optical lab some years ago. Be both amused and instructed! It needs this dataset, run5.dat Due Friday, April 22. |