# About

This first IMPRS course at AEI Potsdam will take place in Fall/Winter 2019/2020 and will be broadcast to all IMPRS partner institutions. More courses will be offered soon.

**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.

Lectures will take place from **11:30am – 12:30pm **on the dates indicated next to the lecture titles below. The lectures will be in **seminar room 0.01** at the AEI-Potsdam and can be followed online using this Zoom link:

https://mpi-aei.zoom.us/j/867860487

Lecture recordings will be made available on the pages of the individual lectures after the fact.

## 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)

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

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

### Week 3 & 4: Bayesian statistics

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

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

Lecture 6: Bayesian sampling methods (December 11th)

Practical 2: Introduction to JAGS (December 13th)

### 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)

Lecture 9: Bayesian statistics in GW astronomy – parameter estimation, population inference (January 22nd – **time change: 10am – 11am**)

Practical 3: GW population analysis (January 24th)

### Week 7 & 8: Advanced topics

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

Lecture 11: Nonparametric regression – kernel density estimation, smoothing splines, wavelets (January 31st – **time change: 10:30am – 11:30am**)

Practical 4: Nonparametric curve fitting (February 3rd – **note change of date**; this practical **will take place in room 0.63**)

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

### 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.