Description

The course will take the participants through the following content:

 

• Standard discrete and continuous distributions, descriptive methods, Bayes’ theorem, conditioning, independence, and selected probability results.
• Simulation.
• Mean, variance, estimators, two-sample comparisons.
• Maximum likelihood and least squares estimation.
• Standard errors and confidence intervals (e.g. via bootstrapping).
• Correlation, (generalized) linear and non-linear regression.
• The statistical programming language R and R notebooks.

Knowledge:



The basic concepts in mathematical statistics, such as:

• Probability distributions
• Standard errors and confidence intervals
• Maximum likelihood and least squares estimation
• Hypothesis testing and p-values
• (Generalized) Linear and non-linear regression

Skills:

• Master basic implementation in R and generation of analysis reports using R notebooks.
• Use computer simulations for computations with probability distributions, including bootstrapping.
• Compute uncertainty measures, such as standard errors and confidence intervals, for estimated parameters.
• Compute predictions based on regression models taking into account the uncertainty of the predictions.
• Assess a fitted distribution using descriptive methods.
• Use general purpose methods, such as the method of least squares and maximum likelihood, to fit probability distributions to empirical data.
• Summarize empirical data and compute relevant descriptive statistics for discrete and continuous probability distributions.

Competences:

• Formulate scientific questions in statistical terms.
• Interpret and report the conclusions of a practical data analysis.
• Assess the fit of a regression model based on diagnostic quantities and plots.
• Investigate scientific questions that are formulated in terms of comparisons of distributions or parameters by statistical methods.
• Investigate scientific questions regarding association in terms of (generalized) linear and non-linear regression models.

Recommended qualifications

IMPORTANT: This course requires and assumes quantitative/​mathematical prior knowledge equivalent to a MatIntro or equivalent course!



MSc students and BSc students in their 3rd year with MatIntro or an equivalent course.



Academic qualifications equivalent to a BSc degree is recommended.