Statistical Theory and Modelling
This course is a continuation of the course "Statistics and Data Analysis for Computer and Systems Sciences". It provides advanced and expanded knowledge in probability theory, modelling, and statistical inference theory, which forms the foundation for modern machine learning and AI. Theoretical derivations are connected with practical applications in programming languages for data analysis and machine learning. Regression and classification models are a significant part of the course. Prediction-based methods such as cross-validation are used for model selection. The course offers an introduction to the mathematical methods that are essential tools for the course and ends with an introduction to time series analysis.
The following topics are covered:
- 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 estimations, bias-variance trade-off, maximum likelihood (ML), likelihood theory, numerical optimization for ML estimations, bootstrap.
- Time series: trend and seasonality, autocorrelation, autoregressive models.
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Course structure
The course is part of the Master's program "Data Science, Statistics and Decision Analysis, 120 credits", which is given by the Department of Computer and Systems Sciences.
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Schedule
The schedule will be available no later than one month before the start of the course. We do not recommend print-outs as changes can occur. At the start of the course, your department will advise where you can find your schedule during the course.