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

The BLprequel listed below are section numbers from a book Bayesian Learning - the prequel that I have started writing for this course.

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: BLprequel 1.1-1.7.

Lecture 1 - Differentiation
Read: BLprequel 1.8-1.14 | Slides
Notebooks and widgets: Exponential function | Logarithms | Derivatives

Lecture 2 - Optimization. Integration.
Read: BLprequel 1.16 | Notebook on function optimization | Slides
Widgets: Integrals | Common functions and their derivatives

Lecture 3 - Discrete random variables.
Read: If needed, refresh basic probability in Ch. 12-13 in the SDA1 course book MSA 3.1-3.6, 3.8, 3.11 | Slides
Widgets: Bernoulli | Binomial | Geometric | Poisson | Negative binomial | Chebychev’s inequality
Extras: List with 50+ statistical distribution widgets

Lecture 5 - Joint and conditional distributions. Covariance and correlation. Bayes theorem.
Read: MSA 5.1-5.8, 5.11 | BLprequel 1.16 (double integrals) | Slides

Lecture 6 - Transformation of random variables. Monte Carlo simulation. Law of large numbers. Central limit theorem.
Read: MSA 6.1-6.4, 7.3 | Law of large numbers notebook | central limit theorem notebook | Slides
Widgets: Law of large numbers | central limit theorem

Lecture 7 - Point estimation. Maximum likelihood. Sampling distributions.
Read: MSA 9.1-9.2, 9.3 (pages 448-451), 9.4, 9.7 | Sections 1-4 of tutorial on maximum likelihood | Slides
Widgets: Sampling distribution and Likelihood | ML - Bernoulli data | ML - Poisson data

Lecture 8 - Vectors and matrices. Linear Regression. Multivariate normal distribution.
Read: MSA A1.1-A1.7, 5.10, 11.10-11.11 | Slides
Widgets: Bivariate normal distribution

Lecture 9 - Observed and Fisher information. Numerical optimization.
Read: Sections 5-7 of tutorial on maximum likelihood | Slides |
Widgets: Second derivative as function curvature | Likelihood and Information
Code: Optim for Poisson model | Optim for Gamma model

Lecture 10 - Logistic, Poisson regression and beyond.
Read: Sections 5-7 of tutorial on maximum likelihood | Slides
Widgets: Poisson regression

Lecture 11 - Nonlinear regression. Regularization.
Read: X | Slides
Code:
Data:

Lecture 12 - Time series. Autocorrelation function. Autoregressive models.
Read: X | Slides
Code:
Data:

Lecture 13 - Course summary and example exam.
Read: X | Slides
Code:
Data: