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.

Schedule

The course schedule can be found on TimeEdit.

Literature

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

Lecture contents

Preparatory - Basic maths (math check/self-study)
This is not a lecture, but check that you remember this prerequisite high school maths, or otherwise freshen it up at the start of the course.
Read: basic math notes with check-up exercises

Lecture 1 - Derivation. Optimization. Integration.
Read: Derivative notebook | Integral notebook | Slides
Widgets: Derivative | Riemann integral
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Lecture 4 - Joint and conditional distributions. Covariance and correlation. Bayes theorem.
Read: MSA 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: MSA 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: MSA 9.1-9.4, 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. Linear regression in vector form.
Read: MSA A1.1-A1.7, 5.10, 11.10-11.11 | Slides
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Lecture 8 - Observed and Fisher information. Numerical optimization.
Read: X | Slides | tutorial on numerical ML
Widgets: Second derivative as function curvature
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Lecture 9 - Logistic and Poisson regression.
Read: X | Slides
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Lecture 10 - Poisson regression and beyond
Read: X | Slides
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Lecture 11 - Nonlinear regression. Regularization.
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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