Statistical methods in physics, 5 credits

Statistiska metoder i fysiken

COURSE INFORMATION

Language of instruction: English
Course period: Period 2, Winter semester 2022 (November – Mid-January)
Campus teaching or online teaching: By default, the lectures and exercise sessions are in-class which means that if the pandemic situation allows, it will be on-campus. 

RECOMMENDED PREREQUISITES

> 60 hp in either physics, astronomy, engineering or earth sciences. 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 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 in modern physics, including MC methods
  • 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 and earth sciences, 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.

COURSE CONTENTS

The course gives an understanding of statistical methods that are used in physics and related fields, such as astronomy, engineering and earth sciences. In addition, it trains practical skills in problem-solving using statistical methods. Though most examples come from physics, 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 four 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. The students also receive individual written feedback on their solutions 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 and active participation in workshops. The students should be prepared to present their solutions to the hand-in exercises to the class.

COURSE EXAMINER

Professor 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: September 15th, 2022

Last modified: 2021-11-15