Prospectus

# Statistics for Astronomy and Physics students

Course
2012-2013

## Description

Statistics for Astronomy and Physics students

1. Basic probability

a. Essential material:

• Basic probability theory, independence, conditional probability

• Discrete probability, binominal distribution, Poisson distribution

• Continuous distributions, the normal, the gamma/exponential and log-normal.

• Probability distribution functions and cumulative distribution functions.

• The concepts of systematic and random error and the distinction between random errors and intrinsic scatter

b. Low-priority:

• The Kullback-Leibner distance between distributions.
1. Standard estimators

a. Essential material:

• Correlation estimators (Pearson’s r), rank tests

• Kolmogorov-Smirnov

• Normality tests

b. Useful but not essential:

• F-test, t-test
1. Regression and function fitting

This is something all astronomers need to know something about.
Probably best to introduce this without Bayesian arguments. Note students have already some practical familiarity with chi^2, but no detailed knowledge yet.

a. Essential material:

• Uni- and multi-variate linear regression

• Non-linear regression

• Chi^2 fitting and the relationship to Gaussian statistics/noise

b. Useful but not essential:

• Censoring & truncation in linear regression

c. Low priority:

• Mixture models/latent variables/structural equation modeling
1. Bayesian statistics

a. Essential material:

• Bayes theorem

b. Essential/useful:

• Priors, importance, how to estimate, how to use

c. Useful:

• The Bayesian-Frequentist distinction (and when you need to care)

• Bayesian inference and how you can use Bayes’ theorem to formalize linear regression fitting

d. Low priority:

• Bayesian classification.
1. Model selection

[lower priority but bias-variance trade-off is important]

a. Essential:

• Chi^2 (revisit – note students have knowledge of (weighted) LSQ)

• The bias-variance trade-off (this is quite important and could be introduced much earlier, but no need to go in details)

b. Lower priority:

• Distribution function estimation

• Complexity selection (perhaps using cross-validation)

1. Robust statistics and sampling

a. Essential:

• Robust estimators (median, median absolute deviations) and their relationship to standard (non-robust) estimators.

• Bootstrap, jack-knife and cross-validation resampling techniques and the concept of training and validation samples (some exposure)

b. Useful:

• Monte Carlo sampling

• Markov-Chain Monte-Carlo

## Programme form

Lectures and exercises.

Getting started (before the first lecture):

(1) Install R on your computer (r-project.org) and try out a tutorial or quick-start guide from internet.

(2) Get a copy of the book:

## Literature

Modern Statistical Methods for Astronomy With R Applications, Eric D. Feigelson, Pennsylvania State University, G. Jogesh Babu, Pennsylvania State University. ISBN:9780521767279, Publication date July 2012.

## Exam

(please have a look at the Exam schedule).