Troels Christian Petersen E-mail address: petersen@nbi.ku.dk

Written language

English

Teaching language

English

Study board

Study Board of Physics, Chemistry and Nanoscience

Semester/Block

Block 2

Scheme group

B

Exam form

Continuous assessment

Exam form

Andet/Other

Exam details

Written assignment, 36 hours
The final grade is normally given based on the continuous evaluation as well as on the take-home exam with the following weight:
20% from a project, 20% from a problem set, and 60% from a 36 hours take-home exam.
It is possible to some extent to arrange a different weight in individual cases in agreement between the student and course responsible, if this can be justified.

Exam aids

All aids allowed

Grading scale

Passed / Not passed

Course workload

Course workload category

Hours

Lectures

56.00

Preparation

98.00

Theory exercises

28.00

Exam

24.00

Sum

206.00

Aim and content

The course will give the student an introduction to and a basic knowledge of statistics and data analysis. The focus will be on the application of statistics and thus proofs are omitted, while examples and use of computers take their place. For this reason, programming plays a central role and is an essential requirement (see below).

The course will cover the following subjects: â€¢Introduction to statistics. â€¢Distributions - Probability Density Functions. â€¢Error propagation. â€¢Correlations. â€¢Monte Carlo - using simulation. â€¢Statistical tests. â€¢Parameter estimation - philosophy and methods of fitting data. â€¢Chi-Square and Maximum Likelihood fits. â€¢Simulation and planning of an experiment. â€¢Multidimensional data and Fisher Discriminant. â€¢Introduction to Machine Learning. â€¢The power and limit of statistics.

Formel requirements

Programming is an essential tool and is therefore necessary for the course (we will use Python with interface to CERN’s ROOT software, both free and working on all platforms). The student should be familiar with different types of variables, loops, if-sentences, functions, and the general line of thinking in programming. Elementary mathematics (calculus, linear algebra, and combinatorics) is also needed.

Important information for students outside of Denmark: To apply for participation in this course, it is required that you send an email to the course organizer with your information and motivation for joining the course. Do not use the online application. Thank you.

Learning outcome

Skills The student should in the course obtain the following skills: â€¢ Determining mean, width, uncertainty on mean and correlations. â€¢ Understading how to use probability distribution functions. â€¢ Be able to calculate, propagate and interprete uncertainties. â€¢ Be capable of fitting data sets and obtain parameter values. â€¢ Know the use of simulation in planing experiments and data analysis.

Knowledge The student will obtain knowledge about statistical concepts and procedures, more specifically: â€¢ Binomial, Poisson and Gaussian distributions and origins. â€¢ Error propagation formula and how to apply it. â€¢ ChiSquare as a measure of Goodness-of-fit. â€¢ Calculation and interpretation of p-values. â€¢ Determination and treatment of potential outliers in data. â€¢ The applicability of Machine Learning.

Competences This course will provide the students with an understanding of statistical methods and knowledge of data analysis, which enables them to analyse data in ALL fields of science. The students should be capable of handling uncertainties, fitting data, applying hypothesis tests and extracting conclusions from data, and thus produce statistically sound scientific work.

Literature

See Absalon for final course material. The following is an example of expected course literature:

Primary literature: Statistics - A Guide to the Use of Statistical Methods in the Physical Sciences, Roger Barlow. Additional literature: Statistical Data Analysis, Glen Cowan. Data Reduction and Error Analysis, Philip R. Bevington. Statistical Methods in Experimental Physics.

Teaching and learning methods

Lectures, exercises by computers, and discussion/projects.

Lecturers

Troels Christian Petersen (petersen@nbi.ku.dk)

Content

The course will give the student an introduction to and a basic knowledge on statistics. The focus will be on application and thus proofs are omitted, while examples and use of computers take their place.

The course will cover the following subjects: â€¢Introduction to statistics. â€¢Distributions - Probability Density Functions. â€¢Error propagation. â€¢Correlations. â€¢Monte Carlo - using simulation. â€¢Statistical tests. â€¢Parameter estimation - philosophy and methods of fitting data. â€¢Chi-Square and Maximum Likelihood fits. â€¢Simulation and planning of an experiment. â€¢The power and limit of statistics. The frontier.

Remarks

It is expected that the student brings a laptop. There will be an introduction the week before the course begins. You will be informed about time and place later (on the course webpage).

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