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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:
summary of homework 1 [.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