# Statistical methods in physics and engineering, 5 credits

Statistiska metoder i fysik och teknik

## COURSE INFORMATION

Language of instruction: English
Course period: HT2024
Course structure: Campus teaching and on-line teaching will be offered

## RECOMMENDED PREREQUISITES

> 60 hp in mathematically-oriented natural sciences or engineering. Basic (>5 hp) knowledge in probability theory and mathematical statistics. Basic programming in a language of choice.

## LEARNING OUTCOMES

When the course is completed, the PhD student should be able to

• account for the difference between Bayesian and frequentistic statistics
• compare different data, judge the degree of compatibility and correctly treat uncertainties
• establish confidence intervals
• estimate parameters using established methods
• perform hypothesis testing and relate the result to probability
• understand and utilize statistical data analysis methods, including Monte Carlo methods, to solve problems in modern science or engineering
• perform an unfolding of a function from data

## LEARNING OUTCOMES FOR DOCTORAL DEGREE

Goal A2: ”Demonstrate familiarity with research methodology in general and the methods of the specific field of research in particular.
Statistical methods and data analysis constitute an important part of the research methodology in many of the mathematically-oriented sciences, not only in physics but also in astronomy, engineering earth sciences and chemistry, to mention a few. In this course, the PhD students acquire a versatile toolbox that is useful in their daily life as researchers. It has also enabled the PhD student to explore his/her research problem from a new angle.

Goal B1: “Demonstrate the capacity for scholarly analysis and synthesis as well as to review and assess new and complex phenomena, issues and situations autonomously and critically”
The course provides an analytic approach to understand a research field and to draw quantitative conclusions from data. This is helpful in assessing not only the research material of one’s own, but also results from other scientists in the field.

Goal B2: “Demonstrate the ability to identify and formulate issues with scholarly precision critically, autonomously and creatively, planning and using appropriate methods to undertake research and other qualified tasks within predetermined time frames and been able to review and evaluate such work.”
The learning will be centered around three sets of hand-in exercises, that all have a research component, and a mini-project where the PhD students will connect the methods from the course to her/his own research. The hand-in exercises and the mini-projects will be carried out within well-defined time-frames and the course participants will actively review and discuss their own as well as each other’s work.

Goal B5: “Demonstrate the ability to identify the need for further knowledge.”
In the mini-project, the course participants will solve a problem that they define on their own, based on their own research. Solving this problem includes searching for suitable literature in their own field.

## COURSE CONTENTS

The course gives an understanding of statistical methods and provides training of practical skills in problem-solving using statistical methods. Though most examples come from physics and engineering, we also use problems from e.g. medicine and social sciences to illustrate concepts.

The course goes through Bayesian vs. frequentist statistics, uncertainties, probability distributions, expectation value and variance. We treat parameter estimation: The method of moments, maximum-likelihood, least squares. Hypothesis testing: chi square, Kolmogorov-Smirnov test. Signal vs. background. Systematic uncertainties. Monte Carlo generators. Data analysis in modern physics, including unfolding of functions from data. Basic orientation on common software tools, numerical minimizing procedures.
Students with less experience in programming are also offered two python-tutorials within the scope of the course.

## INSTRUCTION

Online and in-class lectures, problem solving sessions and tutorials. A lot of the learning evolves around three sets of hand-in exercises with a strong connection to real research problems. Each set of exercises has a corresponding workshop to which all students who have handed in solutions can attend. At these workshops, the students present their solutions in class and discuss them in detail. In addition, each participant will carry out a mini-project where they will define a problem related to their own research, solve using the methods taught in the course, and presented to the class in a dedicated workshop.
The students will receive individual written feedback on their solutions and their mini-project in an iterative process. In this way, the students get to work actively with the material, guided by the teacher, in a manner that is closely connected to how research is conducted within and outside academia.

## ASSESSMENT

Online-quizzes, hand-in exercises, mini-project presentation and active participation in workshops. The students should be prepared to present their solutions to the hand-in exercises to the class.

## COURSE EXAMINER

Karin Schönning, karin.schonning@physics.uu.se

## DEPARTMENT WITH MAIN RESPONSIBILITY

Department of physics and astronomy

## CONTACT PERSON/S

Karin Schönning, Karin.schonning@physics.uu.se

## APPLICATION

Submit the application for admission to: kurskansli@physics.uu.se
Submit the application not later than: October 15, 2024