# International Max Planck Research School on Gravitational-Wave Astronomy: Lectures for Graduate Students

The Astrophysical and Cosmological Relativity and Computational and Relativistic Astrophysics divisions of the AEI are part of the International Max Planck Research School (IMPRS) on Gravitational-Wave Astronomy. The divisions are organising a sequence of courses, targeted at graduate students, but open to all. The first course took place in Fall/Winter 2019/2020. The course was broadcast to all IMPRS partner institutions.

# Making sense of data: introduction to statistics for gravitational-wave astronomy

**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 gives an overview of some key statistical ideas and techniques that are essential for interpreting current and future gravitational wave observations.

**Plan for lecture topics:**

**Week 1 & 2: Frequentist statistics***Lecture 1:* Introduction to random variables, common probability distributions
*Lecture 2:* Basis statistical theory, including Cramer-Rao bound
*Lecture 3:* Hypothesis testing, Neyman-Pearson lemma, ROC curves
*Practical 1*: introduction to R**
Week 3 & 4: Bayesian statistics** *Lecture 4:* Introduction to Bayesian statistics: Bayes theorem, prior choices*
Lecture 5:* Introduction to Bayesian statistics: Bayesian hypothesis testing, posterior predictive checking, hierarchical models*
Lecture 6:* Bayesian sampling methods
*Practical 2:* Introduction to JAGS**Week 5 & 6: Statistics in GW astronomy** *Lecture 7:* Stochastic processes, optimal filtering, signal-to-noise ratio, sensitivity curves*
Lecture 8:* Frequentist statistics in GW astronomy - FAR, Fisher Matrix, PSD estimation*
Lecture 9:* Bayesian statistics in GW astronomy - PE, population inference*
Practical 3:* GW population analysis**Week 7 & 8: Advanced topics***Lecture 10:* Time series analysis - auto-regressive process, moving average processes, ARMA models etc.*
Lecture 11:* Nonparametric regression - kernel density estimation, smoothing splines, wavelets*
Lecture 12:* Gaussian processes, Dirichlet processes*
Practical 4:* Nonparametric curve fitting