# About

This first IMPRS course at AEI Potsdam took place in Fall/Winter of 2019/2020.

**Synopsis:** Measurements of the properties of gravitational wave sources are imperfect due to the presence of noise in the gravitational wave interferometers used to detect them. Extracting useful scientific information from these observations therefore requires careful statistical analysis of the data in order to understand the significance of the observed events, the level of uncertainty in the parameter estimates and the implications of the observations for the population from which the sources are drawn. This lecture course will give an overview of some key statistical ideas and techniques that are essential for interpreting current and future gravitational wave observations.

The lecture dates are listed below along with the lecture titles.

The lecture recordings can be found under “course materials” on the pages of the individual lectures.

## Provisional plan for lecture topics

### Week 1 & 2: Frequentist statistics

Lecture 1: Introduction to random variables, common probability distributions (November 20th 2019)

Lecture 2: Basis statistical theory, including Cramer-Rao bound (November 22nd 2019)

Lecture 3: Hypothesis testing, Neyman-Pearson lemma, ROC curves (November 27th 2019)

Practical 1: Introduction to statistics with python (November 29th 2019)

### Week 3 & 4: Bayesian statistics

Lecture 4: Introduction to Bayesian statistics: Bayes theorem, prior choices (December 4th 2019)

Lecture 5: Introduction to Bayesian statistics: Bayesian hypothesis testing, posterior predictive checking, hierarchical models (December 6th 2019)

Lecture 6: Bayesian sampling methods (December 11th 2019)

Practical 2: Introduction to JAGS (December 13th 2019)

### Week 5 & 6: Statistics in GW astronomy

Lecture 7: Stochastic processes, optimal filtering, signal-to-noise ratio, sensitivity curves (January 15th 2020)

Lecture 8: Frequentist statistics in GW astronomy – FAR, Fisher Matrix, PSD estimation (January 17th 2020)

Lecture 9: Bayesian statistics in GW astronomy – parameter estimation, population inference (January 22nd 2020)

Practical 3: GW population analysis (January 24th 2020)

### Week 7 & 8: Advanced topics

Lecture 10: Time series analysis – auto-regressive process, moving average processes, ARMA models etc. (January 29th 2020)

Lecture 11: Nonparametric regression – kernel density estimation, smoothing splines, wavelets (January 31st 2020)

Practical 4: Nonparametric curve fitting (February 3rd 2020)

Lecture 12: Gaussian processes, Dirichlet processes (February 5th 2020)

### Lecture notes

Lecture notes for each individual lecture can be found by following the links in the drop down “Course material” menu above. A complete set of notes for the complete course is available here.