Applied Statistics (15 ECTS) (Spring 2024)

Abstract

The course gives an in-depth introduction to the fundamental principles of statistics.

Description

The course gives an in-depth introduction to the principles of statistics. It covers both statistical theory and statistical methods for practical data analysis. Further to this, the course introduces the statistical software R.

Topics include

• Descriptive statistics
• Estimation, hypothesis testing, confidence intervals
• The law of large numbers and the Central limit theorem
• Statistical inference in the binomial and multinomial distributions
• Linear regression models – theory, estimation, model selection, model diagnostics, prediction, and interpretation
• Monte Carlo methods (Simulation-based methods)
• Statistical analysis using R

Formal prerequisites

The course is mandatory for 2nd semester BSc in Data Science and relies particularly heavily on Linear Algebra and Optimization and Foundations of Probability. Some familiarity with general programming, such as has been achieved through Introduction to Data Science and Programming, will be assumed.

Intended learning outcomes

After the course, the student should be able to:

• Define key statistical concepts and principles (e.g. maximum likelihood, confidence interval, p-value).
• For simple experimental contexts: propose a statistical model, write out the likelihood function, and find the maximum likelihood estimator for the model parameter.
• Perform a statistical analysis using the models covered in the course. This process includes estimation, hypothesis testing, model assessment, relating the results to the scientific question of interest, and quantification of the uncertainty about the conclusions of the analysis.
• Use R to compute the necessary quantities for a statistical analysis and interpret standard output from linear models fitted in R.
• Discuss the choice of statistical methodology using appropriate statistical theory, such as the choice of an estimator based on its theoretical properties.
• Explain how simulation can be used to compute statistical quantities of interest and discuss the uncertainty of the associated estimate.

Learning activities

The taught part of the course comprises 14 weeks of lectures and exercises.

Exercise sessions will be a mix of practical sessions using R and classroom discussions of weekly problem sets.

Through conceptual and practical problems, the students will gain experience with statistical reasoning and oral presentation of both the scientific argumentation and the communication of analyses. Students are expected to prepare for classroom discussions by attempting to solve the problems on the associated problem sheet.

Through the mandatory assignments, students will learn to perform more comprehensive analyses and how to communicate them in writing.

Mandatory activities

There will be three mandatory group assignments during the semester. All assignments must be approved to qualify for the exam. Opportunities for re-submission of non-approved assignments will be given. 

The mandatory assignments form an integral part of the learning activities and ensure that all students get extensive feedback on written work.

The student will receive the grade NA (not approved) at the ordinary exam, if the mandatory activities are not approved and the student will use an exam attempt.

Course literature

"Introduction to Statistical Data Analysis for the Life Sciences" by Claus Thorn Ekstrøm & Helle Sørensen, 2nd edition, 2015.

Student Activity Budget

Estimated distribution of learning activities for the typical student

• Preparation for lectures and exercises: 36%
• Lectures: 14%
• Exercises: 14%
• Assignments: 13%
• Exam with preparation: 23%

Ordinary exam

Exam type:
A: Written exam on premises, External (7-point scale)
Exam variation:
A33: Written exam on premises on paper with restrictions

reexam

Exam type:
X: Experimental form, External (7-point scale)
Exam variation:
X: Experimental form

Time and date

Ordinary Exam - on premises Thu, 30 May 2024, 09:00 - 12:00
Reexam - on premises Wed, 14 Aug 2024, 09:00 - 13:00