Statistical Theory and Modelling, 7.5 hp

AI generated image of computer

Aim

This is a course on the Master’s Program in Data Science, Statistics and Decision Analysis at Stockholm University.

The course is specifically designed to bridge between the basic course Statistics and Data Analysis for Computer and Systems Sciences, 15 hp and the master’s level course Bayesian Learning, 7.5 hp. The objective is to provide the probability, statistical theory and modeling needed to follow the Bayesian Learning course.

Contents

  • Mathematical methods: derivatives, integrals, optimization, numerical optimization, vectors and matrices.

  • Probability theory: discrete and continuous stochastic variables, density and probability functions, distribution functions, multivariate distributions, multivariate normal distribution, marginal distributions, conditional distributions, independence, expected value, variance, and covariance, functions of stochastic variables, sampling distributions, law of large numbers, central limit theorem.

  • Modelling and prediction: linear and non-linear regression, dummy variables and interactions, model selection, cross-validation, overfitting, regularization, classification, logistic regression, multinomial logistic regression, Poisson regression.

  • Inference: point estimation, bias-variance trade-off, maximum likelihood (ML), likelihood theory, numerical optimization for ML estimation, bootstrap.

  • Time series: trend and seasonality, autocorrelation, autoregressive models.

Literature

  • Authors (2021). Book Name
  • Additional material and handouts distributed during the course.

Structure

The course consists of lectures, mathematical exercises and computer labs. See the formal course plan.

Examination

The course is examined by a

Schedule

The course schedule can be found on TimeEdit. A tip is to select Subscribe in the upper right corner of TimeEdit and then paste the link into your phone’s calendar program.

Formula cheet sheets

Interactive material

The course makes heavy use of interactive Observable notebooks in javascript that runs in your browser. The widgets will be linked below each relevant lecture. All widgets used in the course are available here.

Teachers


Mattias Villani
Course responsible and lecturer
Professor


TBD
Exercises


TBD
Computer labs