Applied Statistics (15 ECTS) (Spring 2025)

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.

Ordinary exam