Program Overview

Program Overview

The Advanced Methods in Applied Statistics course is designed to provide students with practical knowledge and hands-on experience in computational analysis of data in frontier physics research. The course content is based on statistical methods and does not require a specific or broad physics background, making it applicable for many non-physics disciplines in the Physical Sciences.

Course Content

The course will cover the following topics:

• Supervised machine learning algorithms and multivariate analysis techniques, such as Boosted Decision Trees
• Parameter estimation and uncertainty estimation using likelihood and Bayesian techniques
• Minimization techniques using Markov Chain Monte Carlo and numerical methods (minimizers)
• Maximum Likelihood fitting
• Construction of confidence intervals and contours
• Coding a chi-squared function in the language of the students' preference (Python, C/C++, Ruby, JAVA, R, etc.)
• Creation and usage of spline functions
• Application of Kernel Density Estimators
• Inputting and processing data from both ASCII-readable files as well as internet data scraping

Learning Outcomes

Upon completion of the course, students will be able to:

• Be familiar with supervised machine learning algorithms and multivariate analysis techniques
• Perform parameter estimation and uncertainty estimation using likelihood and Bayesian techniques
• Apply minimization techniques using Markov Chain Monte Carlo and numerical methods
• Code a chi-squared function in their preferred programming language
• Create and use spline functions
• Apply Kernel Density Estimators
• Input and process data from various sources

Teaching and Learning Methods

The course will employ the following teaching and learning methods:

• Instructor lectures
• In-class examples
• Computer-based exercises
• Discussion

Literature

There is no required literature for the course. However, for those looking for additional material, "Statistical Data Analysis" by G. Cowan is an excellent choice. Class lecture notes and links to scholarly articles will be posted online.

Recommended Prerequisites

• Extended knowledge and skill with at least one applicable computer programming language (Python, C/C++/C11, Ruby, R, Rust, JAVA, Julia, or MatLab)
• Ability and experience to install external software packages, e.g., a MultiNest Bayesian inference package or "emcee" Markov Chain Monte Carlo sampler
• Completion of "Applied Statistics: From Data to Results" or equivalent is strongly encouraged but not strictly required

Remarks

• Students are expected to bring their own laptops or have access to a computer upon which they can install software to write, compile, and execute code
• Example solution code will only be provided for a small subset of in-class exercises, and students should be prepared to develop and code their own solutions or collaborate with classmates

Assessment

• The course will be assessed through a combination of:
  • An in-class short oral presentation (10%)
  • Graded problem sets and project(s) centering around the coding, implementation, and execution of a statistical method (50%)
  • Take-home final exam (40%)
• All aids are allowed during the exam
• The marking scale is a 7-point grading scale
• There is no external censorship, and several internal examiners will be used

Re-exam

• The re-exam includes a new 28-hour take-home test which constitutes 40% of the weighted sum used to calculate the total re-exam grade
• The remaining 60% can be re-used from the continuous evaluation during the course, or the student can choose to submit 3 new projects (as defined and described during the course) 2 weeks prior to the re-exam date
• All parts are assessed together

Course Type and Workload

• The course is a single subject course (day)
• The workload is as follows:
  • Lectures: 36 hours
  • Preparation: 90 hours
  • Practical exercises: 32 hours
  • Project work: 36 hours
  • Exam: 12 hours
  • Total: 206 hours

Language and Course Number

• The course is taught in English
• The course number is NFYK15002U

ECTS and Programme Level

• The course is worth 7.5 ECTS
• The programme level is Full Degree Master

Duration and Placement

• The course duration is 1 block
• The placement is Block 3

Study Board and Contracting Department

• The study board is the Study Board of Physics, Chemistry and Nanoscience
• The contracting department is the Niels Bohr Institute
• The contracting faculty is the Faculty of Science

Course Coordinator

• The course coordinator is D. Jason Koskinen

Capacity and Schedule Group

• There is no limitation on capacity unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student
• The schedule group is A

Final Note

The Advanced Methods in Applied Statistics course is designed to provide students with practical knowledge and hands-on experience in computational analysis of data in frontier physics research. The course covers a range of topics, including supervised machine learning algorithms, parameter estimation, and minimization techniques. Students will be assessed through a combination of oral presentations, problem sets, and a take-home final exam. The course is taught in English and is worth 7.5 ECTS.