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:

• Modern Statistical Methods for Astronomy (with R applications) by E. Feigelson and G. Babu
This will be our main text, and students should own a copy.
• REA's Statistics Problem Solver A really nice set of worked-out examples for various statistical tests.
• All of Statistics by Larry Wasserman may turn out to be a useful general reference.

• Research Journals in Physics and Astronomy
http://adsabs.harvard.edu/abstract/_service.html is a good source for the astronomy journals

• There are many statistics reference books listed at the end of each chapter in the Feigelson and Babu book

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.