## Admission requirements

None

## Description

In the era of data science the responsible, principled and accurate use of statistics is of very high importance. In this introductory course you will learn about the foundations of probability theory and statistics with a special focus on applications to astronomical research. We will start with the basic notions of probability theory and introduce the concept of statistical model. Then you will learn about estimation, uncertainty quantification and hypothesis testing techniques in various statistical models. Finally, we focus on the highly popular and frequently applied linear and logistic regression models, which we treat in more detail. You will apply the learned theory during the practical class for solving relevant exercises using both analytical computations and programming with Python.

The course covers the following themes:

Basics of probability theory

Estimation methods

Hypothesis testing methods (both parametric and non-parametric)

Uncertainty quantification (confidence intervals)

Resampling methods

Regression analysis (both linear and logistic)

## Course objectives

The main objective of this course is to give you an overview of the basic notations of statistics and probability theory. After this course, you will be able to:

Answer basic questions on the following statistical topics: estimation methods, confidence intervals, resampling schemes, hypothesis testing and regression.

Carry out a preliminary analysis of astronomical data using analytical computations and the programming language Python.

Develop critical thinking about statistical data analysis (e.g. you will be aware of possible pitfalls and be able to detect inaccurate or incomplete analysis)

## Soft skills

In this course, students will be trained in the following behaviour-oriented skills:

Problem solving (recognizing and analyzing problems, solution-oriented thinking)

Analytical skills (analytical thinking, abstraction, evidence)

Structured thinking (structure, modulated thinking, computational thinking, programming)

Complex ICT-skills (data analysis, programming, simulations, complex ICT applications)

Written communication (writing skills, reporting, summarizing)

Critical thinking (asking questions, check assumptions)

Integrity (honesty, moral, ethics, personal values)

## Timetable

See Schedules bachelor Astronomy

## Mode of instruction

Lectures

Exercise classes

## Assessment method

Homework assignments (30% of final grade)

Written exam (70% of final grade)

A minimum grade of 5.0 on homework assignments is required to take the written exam. A minimum grade of 5.0 for the exam is required to pass the course. See Examination schedules bachelor Astronomy.

## Blackboard

Blackboard will be used to communicate with students and to share lecture slides, homework assignments, and any extra materials. You must enroll on Blackboard before the first lecture. To have access, you need a student ULCN account.

## Reading list

All of Statistics. Larry Wasserman (corrected second printing, 2005), ISBN 9780387402727.

*Click title to download electronic version through Leiden University Libraries.*Practical Regression and Anova in R, Faraway.

*Click title to download electronic version.*Bayesian Methods for the Physical Sciences, Andreon & Weaver, ISBN 9783319152868.

*Click title to download electronic version through Leiden University Libraries.*Nonlinear Regression with R, Ritz & Streibig, ISBN 9780387096155.

*Click title to download electronic version through Leiden University Libraries.*Handouts

## Registration

Register via uSis. More information about signing up for classes and exams can be found here. Exchange and Study Abroad students, please see the Prospective students website for information on how to register. For a la carte and contract registration, please see the dedicated section on the Prospective students website.

## Contact information

Lecturer: Thomas Nagler