ASTR 600
STATISTICAL ANALYSIS IN PHYSICS AND ASTRONOMY

Spring Semester 2015 Room HBH 254; MWF 1:00-2:00

 

Instructor: Dr. Patrick Hartigan, Hermann Brown Rm. 350 , Phone: X2245

Texts:

Grading: Based on short and long class presentations, homework creation and completion, and participation

Prereqs: There are no statistical prerequisites. We will cover material as we go.

OUTLINE OF COURSE
Every discipline of science has data, and a researcher generally wants to address a scientific question with the data. The path from the data to the conclusion usually involves some sort of statistical analysis. Even if the problem is not inherently a statistical one, when writing up the results one must always address the question of how certain the conclusions are given that there are uncertainties in the measurements. Often one looks for correlations between different variables, or tries to infer what the underlying structural variables are that define the system, and how they relate to one another. The statistical literature is vast and different disciplines apply different techniques that are suitable to their data. But in most cases the techniques are quite broad, and in principle may be used in many different contexts.

In this class we will identify the statistical methods commonly used by research papers in astrophysics, and the students will chose papers to study that use these methods. By learning how statistics is used in different areas, we will broaden our toolset for use in our own studies. We will have short discussions on many such papers to get an overview of the usage, and then more in-depth discussions that will be led by students on their favorite methods. To solidify this knowledge, students will sometimes construct problems that will be distributed to the remainder of the class, and after a period of time we will discuss the solutions.

The topics will be guided by the professor, but the papers are chosen by the students. Some examples may include hypothesis testing and confidence intervals, extracting periods and signals from time-series data, using principal component analysis, maximum likelihood methods, finding groups and clusters in multidimensional data, maximum entropy reconstructions, non-parametric ranks, optimized profile extractions, Bayesian analysis with priors and so on. Most statistical methods used in astronomy will fall under one of the broad topics in this course, but if you have seen a technique and wondered how it works, we can substitute it for one of the other topics if there is interest. find a paper that uses it and we will study it.

In class we will, (*) find a broad range of papers chosen by the students that use a particular method, (*) study the mathematics of the method, (*) go in-depth into two papers chosen by the students, and (*) work through some problems to understand how the method works in practice. The students will pick the papers, and will be expected to lead the class through an overview of the science objectives. The main focus, however, will be on the method, which we will then all work together to try to understand. The problems may apply the method to some other case, perhaps with contrived data, so we are all sure we could use it if the need arose in another context. There will be a few lectures at the beginning and then interspersed as needed throughout the semester to provide some mathematical structure, and we will follow the overall format of the textbook. But the choice of specific applications is student-driven. The papers need not necessarily be astronomical, though that will likely be the focus of much of our studies.

Work Load and Grades

FALL 2013 Schedule

DATE Topic Class Type Subject
T Aug 27 Mathematical Foundation Lecture Introductory Organization; Probability Distributions Chapter 2
Th Aug 29 " Lecture Confidence Intervals Chapters 3 and 4
T Sep 3 Nonparametrics Short presentations [Everyone] Paper discussions
Th Sep 5 " Lecture Chapter 5
T Sep 10 " Papers 1 & 2 presentations [Wilson; Katya] Paper discussions + HMWK#1 handout [Sharad; Anna]
Th Sep 12 PMH on travel [NO CLASS] --- ---
T Sep 17 Regression Short presentations [Everyone] Paper discussions
Th Sep 19 " Lecture Chapter 7
T Sep 24 " Papers 1 & 2 presentations [Katya; Landon] Paper discussions + HMWK#2 handout [Sharad, Anna] Everyone do HMWK#1
Th Sep 26 Regression/Nonparametrics Discussion Wrap up Regression; Nonparametric HMWK#1 Discussion
T Oct 1 Data Smoothing Short presentations [Everyone] Paper discussions
Th Oct 3 " Lecture Chapter 6
T Oct 8 Multivariate, PCA/ICA Short presentations [Everyone] Paper discussions
Th Oct 10 " Lecture Chapter 8
T Oct 15 Midterm RECESS [NO CLASS] --- ---
Th Oct 17 " Papers 1 & 2 presentations [pmh] Paper discussions + HMWK#3 handout [Wilson]> Everyone do HMWK#2
T Oct 22 Regression/Multivariate PCA Discussion Wrap up Multivariate PCA; Regression HMWK#2 Discussion
Th Oct 24 Time Series Analysis Short presentations [Everyone] Paper discussions
T Oct 29 " Lecture Chapter 11
Th Oct 31 " Papers 1 & 2 presentations [Wilson; Anna(PCA)] Paper discussions + HMWK#4 handout [Landon; Katya] Everyone do HMWK #3
T Nov 5 Multivariate PCA/Time Series Analysis Discussion Wrap up /Time Series Analysis; Multivariate PCA HMWK#3 Discussion
Th Nov 7 Clustering Short presentations [Everyone] Paper discussions
T Nov 12 " Lecture Chapter 9
Th Nov 14 " Paper presentation [Sharad (Time-Series)] Wrap up clustering lecture
T Nov 19 Time Series Analysis/Clustering Paper presentation [Anna (Clustering)] Time Series Analysis HMWK#4 Discussion HMWK#5 handout [Landon; Katya] Everyone do HMWK#4
Th Nov 21 Truncated Data Short presentations [Everyone] Paper discussions
T Nov 26 Lecture Chapter 10
Th Nov 28 Thanksgiving RECESS [NO CLASS] --- ---
T Dec 3 Truncated Data Paper Presentations [Sharad; Landon] Paper Discussion Everyone do HMWK #5
Th Dec 5 Discussion Wrap up Truncated Data; Clustering HMWK#5 Discussion
Short summary of techniques