Lectures for Statistical Theory and Modelling, 7.5 hp

This page contains a short description of the contents, reading instructions and additional material for each lecture.

The reading suggestions below are section numbers from the course book Wackerley, Mendenhall and Scheaffer (2021). Mathematical Statistics with Applications, 7th edition, Cengage.

Lecture 0 - Basic maths
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Lecture 1 - Derivation. Optimization. Integration.
Read: X | Slides
Widgets: Riemann integral
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Lecture 4 - Joint and conditional distributions. Covariance and correlation. Bayes theorem.
Read: 5.1-5.8 | Slides
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Lecture 5 - Transformation of random variables. Monte Carlo simulation. Law of large numbers. Central limit theorem.
Read: 6.1-6.4, 7.3 | Slides
Widgets: Law of large numbers | central limit theorem
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Lecture 6 - Point estimation. Maximum likelihood. Sampling distributions.
Read: 9.7 | Slides
Widgets: Sampling distribution and Likelihood | ML - Bernoulli data | ML - Poisson data
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Lecture 7 - Vectors and matrices. Multivariate normal distribution.
Read: A1.1-A1.7, 5.10 | Slides
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Lecture 8 - Linear regression in vector form.
Read: X | Slides
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Lecture 9 - Observed and Fisher information. Numerical optimization.
Read: X | Slides | tutorial on numerical ML
Widgets: Second derivative as function curvature
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Lecture 10 - Logistic regression.
Read: X | Slides
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Lecture 11 - Nonlinear regression. Interactions. Overfitting. Regularization. Cross-validation. Bias-variance trade-off
Read: X | Slides
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Lecture 12 - Time series. Autocorrelation function. Autoregressive models.
Read: X | Slides
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Lecture 13 - Course summary and example exam.
Read: X | Slides
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