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Astro 193 Class Notes Spring 2014-2015

Last Updated: 2015may06

Astronomy 193:
Noise and Data Analysis in Astrophysics

Spring 2014-2015

isites.harvard.edu/icb/icb.do?keyword=k109189

Instructors	Dr. Aneta Siemiginowska (CfA B-425)
	Dr. Vinay Kashyap (CfA B-301)
Schedule	M/W 2PM - 3:30PM ET
Location	Observatory Classroom A-101

Schedule
26 Jan 2015	Introduction Overview of the course Course information handout [.pdf] Motivation: AS slides [.ppt] [.pdf] VK slides [.pdf] Homework 1 Find an astronomical dataset (from any telescope, ground- or space-based) and make 1-2 figures to demonstrate its content. Present the figures in the class and discuss the datasets.
28 Jan 2015	Data I Introduction to Astronomical Data: types and measurement errors AS notes [.pdf] Homework 1 HW 1 summarized: [.jpg] Homework 2 Homework 2 [.txt] Dataset for HW2 [.fits]
02 Feb 2015	Data II Measurement and Calibration Reading for Feb 2: Section 3.1.2 of Lee et al. (2011) [.pdf] VK slides [.pdf] AS Notes [.pdf]
04 Feb 2015	Data II and Basics of Model Fitting I Propagation of errors, multiple imputation, R, and Python VK slides [.pdf] AS ipython notebook [www] R demo commands [.txt] Homework 3 Homework 3 (due Feb 11) [.pdf] Tsujimoto et al. (2011) [.pdf]
09 Feb 2015	Class Canceled due to Snow storm
11 Feb 2015	Basics of Model Fitting I Best-fits, Error bars, goodness-of-fit AS slides on linear least-squares fiting [.pdf] Homework 3 Homework 3 solution [.pdf] Homework 4 Homework 4 (due Feb 18) [isites]
18 Feb 2015	Basics of Model Fitting II and Distributions Assigned Reading: Chapter 2 of Robinson or Chapter 2.4 of Wall & Jenkins linear least-squares, Random Numbers, Distributions, Probabilities VK slides on random numbers and distributions [.pdf] Homework 5 Homework 5 (due Feb 25) [.pdf]
23 Feb 2015	Parameter Estimation I Distributions, Central Limit Theorem Maximum Likelihood, non-linear least-squares fitting, confidence intervals VLK slides on Distributions (contd) [.pdf] AS slides on non-linear fitting [.pdf] Assigned reading for next class: Monograph on Bayesian inference in Astrophysics by Tom Loredo [.pdf]
25 Feb 2015	Probability Theory Parameter Estimation II Axioms, absolute and conditional, Bayes' Theorem, marginalization, intervals VLK slides on probability theory [.pdf] AS slides on parameter estimation [.pdf]
02 Mar 2015	MCMC M, MH, Gibbs, validation AS slides on MCMC Theory [.pdf] VLK slides on MCMC in practice [.pdf] Homework 6 Homework 6: MCMC (due 13 Mar) [.pdf]
04 Mar 2015	Bayesian Analysis VLK slides on the Jacobian and Bayesian Aperture Photometry (Gaussian) [.pdf] AS slides on measurement error induced bias [.pdf] Homework 7 Homework 7: Bayesian Aperture Photometry (Poisson) (due 13 Mar) [.pdf]
09 Mar 2015	Model Selection p-values, Hypothesis Tests, Type I and Type II errors VLK slides on p-values, Hypothesis Tests, Type I and Type II errors [.pdf]
11 Mar 2015	Model Selection Odds Ratios, Bayes Factors, AIC/BIC/DIC/etc AS slides [.pdf] VLK slide on XKCD frequentist rebuttal [.pdf] VLK slides on Bootstrap [.pdf]
23 Mar 2015	Survival Analysis and Upper Limits Reading: Halsey et al. 2015 (Nature Methods 12, 179) [.html] Reading: Feigelson & Nelson 1985 (ApJ 293, 192) [ADS] Reading: Schmitt 1985 (ApJ 293, 178) [ADS] Reading: Kashyap et al. 2010 (ApJ 719, 900) [.pdf] VLK slides on p-values, Source Detection, Survival Analysis, Upper Limits [.pdf]
25 Mar 2015	MCMC and Bayesian Aperture Photometry Discussion of Homework 6 and Homework 7 VLK slides on HR, priors, and solution to Homework 7 [.pdf]
30 Mar 2015	Ockham's Razor Non-parametric Tests VLK slides on Ockham's Razor, non-parametric distribution comparison tests and correlation estimators [.pdf] Reading for Fourier Transforms: Bracewell, R.N., 1989, SciAm Jun89, p86 [.pdf]
01 Apr 2015	Smoothing VLK slides on Bias-variance trade-off, kernel density estimators [.pdf] Foundations of Signal Processing I AS slides on Fourier Transforms [.pdf] Homework 8 and Homework 9 Problems 8 (bootstrapping) and 9 (Fourier Transforms) [.pdf]
06 Apr 2015	Kernel Density Estimator 1-D vs 2-D Foundations of Signal Processing II FFT, Wavelets VLK slides on histogram density, locfit, wavelets [.pdf] AS slides on Fourier Transforms [.pdf] Reading: `locfit` Tutorial [.pdf] Chapters 4 and 6 of All of Non-parametric Statistics, by Larry Wasserman Homework 10 Problem 10 (KDE) [.pdf]
08 Apr 2015	Foundations of Signal Processing II Discrete Fourier Transform, FFT, Windowing, Filtering, Denoising Haar and Daubechies wavelets AS slides on DFT [.pdf]
10 Apr 2015	Discussions individual
13 Apr 2015	Stochastic Processes and Time Series I Power Spectra, Lomb-Scargle Periodogram, BayesFT VLK slides on Projects, orthonormal wavelet basis, BayesFT [.pdf] AS slides on Time Series, power spectra, Lomb-Scargle Periodogram [.pdf] Reading: Bayesian Spectrum Analysis and Parameter Estimation, Larry Bretthorst Chapter 13 of Bayesian Logical Data Analysis for the Physical Sciences, Phil Gregory Studies in Astronomical Time Series Analysis. I. Modeling Random Processes in the Time Domain, Scargle, J., 1981, ApJS, 45, 1 (ADS) Studies in Astronomical Time Series Analysis. II. Statistical Aspects of Spectral Analysis of Unevenly Spaced Data, Scargle, J., 1981, ApJ, 263, 835 (ADS) Flicker noises in astronomy and elsewhere, Press, W.H., 1978, Comments on Modern Physics, Part C - Comments on Astrophysics, v7, p103 (ADS)
15 Apr 2015	Review Homework 10 VLK slides on Homework 10 [.pdf] Homework 11 due Apr 27 [.pdf] Homework 12 due Apr 22 29 [.pdf]
20 Apr 2015	Stochastic Processes and Time Series II 1/f noise, Correlations, Structure Functions, and CAR models AS slides on 1/f noise, Autoregressive models [.pdf] Bayesian Blocks VLK slides on Bayesian Blocks [.pdf] Homework 13 See update below. (due Apr 29) ~~For the time-tagged data of RT Cru from Homework 10, construct a Bayesian Blocks representation.~~ Reading Are the Variations in Quasar Optical Flux Driven by Thermal Fluctuations?, Kelly et al., 2009, ApJ 698, 895 Edelman et al. 2014 Studies in Astronomical Time Series Analysis. V. Bayesian Blocks, A New Method to Analyze Structure in Photon Counting Data, Scargle, J.D., 1998, ApJ 504, 405 Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations, Scargle, J.D., Norris, J.P., Jackson, B., & Chiang, J., 2013, ApJ 764, 167 Bayesian Blocks Structure in the Three-Dimensional Galaxy Distribution. I. Methods and Example Results, Way, M.J., Gazis, P.R., & Scargle, J.D., 2011, ApJ 727, 48 Structure in the 3D Galaxy Distribution. II. Voids and Watersheds of Local Maxima and Minima, Way, M.J., Gazis, P.R., & Scargle, J.D., 2015, ApJ 799, 95
22 Apr 2015	Image Processing Filtering and deconvolution Smoothing and source detection VLK slides on Upper Limits and Deconvolution (Richardson-Lucy and MaxEnt) [.pdf] animation of variation of p(nS'\|lamS,lamB) and calculation of beta [.gif] AS slides on CAR(1) likelihood and LIRA [.pdf] Updated Homework 13 Now due Apr 29 [.pdf]
27 Apr 2015	Guest Lecture by David van Dyk (Imperial College London) The Advantages of "Shrinkage Estimates" in Astronomy Abstract: Astronomical studies often involve samples or populations of sources. The parameters describing the sources can either be fit to each source in a separate analysis, or all be fit in a single unified analysis. The latter strategy allows us to incorporate the population distribution into a coherent statistical model and exhibits distinct statistical advantages. In particular, objects with smaller error bars and well-constrained parameters allow us to estimate the population distribution, which in turn can be used to better estimate the weakly-constrained parameters associated with objects with larger error bars. The fitted values of such weakly-constrained parameters will "shrink towards'' the population mean, and are thus called "shrinkage estimates''. This talk describes both frequentist and Bayesian advantages of shrinkage estimates and illustrates how they can be used in astronomy. In the first of two examples we estimate the absolute magnitudes of a SDSS sample of 288 Type Ia Supernovae using shrinkage estimates and illustrate how they differ from naive estimates. In the second example, we use photometric magnitudes of a sample of galactic halo white dwarfs to simultaneously obtain shrinkage estimates of the stellar ages and an estimate the age of the halo. Presentation slides [.pdf]
29 Apr 2015	Wrap Up Discussion of Homeworks 12 and 13, online resources for further learning, some new techniques to keep an eye on Slides [.pdf] animation of variation of p(S/N\|lamS,lamB) and calculation of beta [.gif] Projects Slides due by 1:30pm on May 4th
04 May 2015	Project Presentations 2:00pm : Christopher Merchantz : Imaging analysis of exoplanets Presentation [.key] Slides [.pdf] 2:15pm : Missy McIntosh : REXIS RMF Slides [.pdf] 2:30pm : Ben Cook : Galaxy radial profiles and metallicity uncertainties Slides [.pdf] 2:45pm : Yutong Shan : The Stats of Couples: From Pairing Algorithms to Binary Mass-Ratio Distributions Slides [.pdf] 3:00pm : Tai Ding : Hyper-velocity Stars Slides [gdocs] 3:15pm : Ashley Villar : The Transient Nature of the DIBs Slides [gdocs]
06 May 2015	Project Presentations 2:00pm : Xiawei Wang : Hunting exoplanet Slides [.pdf] 2:15pm : Peter Blanchard : The Impact of Positional Uncertainty on GRB Host Environment Studies Slides [.odp] 2:30pm : Michael Mancinelli : Exoplanet Transit Analysis Slides [.pptx] 2:45pm : Meng Gu : PCA of MaNGA spectra Slides [.pdf] 3:00pm : Jane Huang : Searching for Vibronic Progressions in the Diffuse Interstellar Bands via Agglomerative Clustering Slides [.pptx] 3:15pm : Philip Cowperthwaite : The Perils of Exoplanet Radial Velocity Fitting Slides [.pdf]

CHASC

Last Updated: 2015may06

Astronomy 193: Noise and Data Analysis in Astrophysics

Spring 2014-2015

isites.harvard.edu/icb/icb.do?keyword=k109189

Astronomy 193:
Noise and Data Analysis in Astrophysics