~ AY250 writeups

COMBINED SYLLABUS AND SCHEDULE -- for 2006. DISREGARD ANYTHING BELOW THE DASHED LINE -- IT'S FROM LAST YEAR!

DATE
Description
Wed Jan 18 Intro to IDL. Datatypes, structures. Sav files, FITS files. The GSFC website and other accessible libraries. The startup file. Paths. Managing IDL on multiple platforms.

Mon Jan 23 Making PostScript files of plots and images. Color schemes--RBG and CMYK. Visual classes: Pseudocolor, Truecolor, Directcolor. Color tables. Using color in plots.

Wed Jan 25 Basic image processing. Color images: one-dimensional, two-d, and three-d.

Mon Jan 30 Recap of eclipse problem. Annotating images. Projections.

Wed Feb 1 monovariate pdf's and their transformations.

Mon Feb 6 Random number generators. Monte Carlo basics. bivariate pdf's--basics

Wed Feb 8 bivariate pdf transformations -- three examples

Mon Feb 13 Gaussian pdf. central limit theorem. etc.

Wed Feb 15 Poisson and chi-square pdfs

Mon Feb 20 Presidents' (soon to become Emperor's) day holiday; NO CLASS.

Wed Feb 22 Homework review. Introduction to the chi square test

Mon Feb 27 CDF of chi-square pdf. KS test. Introduction to multivariate Gaussian statistics.

Wed Mar 1 Multivariate Gaussian statistics. Discrete distributions: mean, variance, variance of variance. Introduction to Error propagation including covariance.

Mon Mar 6 Error propagation including covariance. Transformation of variables, Eigenvector diagonalizing the covariance matrix.

Wed Mar 8 Maximum Likelihood (ML) for Gaussian, double-sided exponential, and binomial statistics.

Mon Mar 13 Discuss problem 4a. Critical discussion of the non-panacea character of Maximum Likelihood--e.g. for low-N Poisson and z=(x^2+y^2)^{1/2} problem

Wed Mar 15 Nonlinear ML. Least-squares fitting; illustrative example including covariance

Mon Mar 20 Chi-square fitting, confidence levels

Wed Mar 22 More on confidence levels and Chi-square fitting. Nonlinear fitting.

--------- -------------- SPRING BREAK -------------------------------------------------- ---------------------------------------------------

Mon Apr 3 Numerical derivatives; machine accuracy considerations. Least squares as a hammer for all problems.

Wed Apr 5 Polynomial fitting; rational function fitting; cubic splines; least-squares cubic splines functions.

Mon Apr 10 Weighted iterative fitting: a modified Chauvenet's criterion, Minimum Absolute Residual Sum (MARS) fitting.

Wed Apr 12 Degeneracies in least-squares; resolving them with Singular Velue Decomposition (SVD).

Mon Apr 17 Fitting when there is no independent variable--all variables have uncertainties.

Wed Apr 19 Fourier transforms. convolution and correlation theorems. Digital sampling and Fourier transforms. Aliasing, resolution, binning.

Mon Apr 24 Digital correlators in radio astronomy; gratings in optical astronomy. Digital convolution and correlation Deconvolution, noise, Wiener filtering

Wed Apr 26 Irregular sampling with Fourier: the Lomb periodogram. examples, clean.

Mon May 1 More irregular sampling: maximum entropy.

Wed May 3 Wavelets I: continuous wavelets

Mon May 8 Wavelets II: discrete wavelets.

--------- ---------------------------------------------------------------- --------------------------------------------------------------------

DATE	Description
`Wed Jan 18`	Intro to IDL. Datatypes, structures. Sav files, FITS files. The GSFC website and other accessible libraries. The startup file. Paths. Managing IDL on multiple platforms.
`Mon Jan 23`	Making PostScript files of plots and images. Color schemes--RBG and CMYK. Visual classes: Pseudocolor, Truecolor, Directcolor. Color tables. Using color in plots.
`Wed Jan 25`	Basic image processing. Color images: one-dimensional, two-d, and three-d.
`Mon Jan 30`	Recap of eclipse problem. Annotating images. Projections.
`Wed Feb 1`	monovariate pdf's and their transformations.
`Mon Feb 6`	Random number generators. Monte Carlo basics. bivariate pdf's--basics
`Wed Feb 8`	bivariate pdf transformations -- three examples
`Mon Feb 13`	Gaussian pdf. central limit theorem. etc.
`Wed Feb 15`	Poisson and chi-square pdfs
`Mon Feb 20`	Presidents' (soon to become Emperor's) day holiday; NO CLASS.
`Wed Feb 22`	Homework review. Introduction to the chi square test
`Mon Feb 27`	CDF of chi-square pdf. KS test. Introduction to multivariate Gaussian statistics.
`Wed Mar 1`	Multivariate Gaussian statistics. Discrete distributions: mean, variance, variance of variance. Introduction to Error propagation including covariance.
`Mon Mar 6`	Error propagation including covariance. Transformation of variables, Eigenvector diagonalizing the covariance matrix.
`Wed Mar 8`	Maximum Likelihood (ML) for Gaussian, double-sided exponential, and binomial statistics.
`Mon Mar 13`	Discuss problem 4a. Critical discussion of the non-panacea character of Maximum Likelihood--e.g. for low-N Poisson and z=(x^2+y^2)^{1/2} problem
`Wed Mar 15`	Nonlinear ML. Least-squares fitting; illustrative example including covariance
`Mon Mar 20`	Chi-square fitting, confidence levels
`Wed Mar 22`	More on confidence levels and Chi-square fitting. Nonlinear fitting.
`---------`	-------------- SPRING BREAK -------------------------------------------------- ---------------------------------------------------
`Mon Apr 3`	Numerical derivatives; machine accuracy considerations. Least squares as a hammer for all problems.
`Wed Apr 5`	Polynomial fitting; rational function fitting; cubic splines; least-squares cubic splines functions.
`Mon Apr 10`	Weighted iterative fitting: a modified Chauvenet's criterion, Minimum Absolute Residual Sum (MARS) fitting.
`Wed Apr 12`	Degeneracies in least-squares; resolving them with Singular Velue Decomposition (SVD).
`Mon Apr 17`	Fitting when there is no independent variable--all variables have uncertainties.
`Wed Apr 19`	Fourier transforms. convolution and correlation theorems. Digital sampling and Fourier transforms. Aliasing, resolution, binning.
`Mon Apr 24`	Digital correlators in radio astronomy; gratings in optical astronomy. Digital convolution and correlation Deconvolution, noise, Wiener filtering
`Wed Apr 26`	Irregular sampling with Fourier: the Lomb periodogram. examples, clean.
`Mon May 1`	More irregular sampling: maximum entropy.
`Wed May 3`	Wavelets I: continuous wavelets
`Mon May 8`	Wavelets II: discrete wavelets.
`---------`	---------------------------------------------------------------- --------------------------------------------------------------------

[ | UC Berkeley Astronomy ]

Being continually updated during Spring 2006.

<heiles@astron.Berkeley.EDU>