MRC LMS - Introduction to computational statistics

Jesús Urtasun Elizari, MRC LMS & RCDS ICL

LMS email address Jesus.Urtasun@lms.mrc.ac.uk

ICL email address jurtasun@ic.ac.uk

Find the content of the course in GitHub:

LMS Introduction to computational statistics

This course provides an introduction to computational statistics. The aim of the course is to build simple and accessible yet strong mathematical foundations in probability theory, descriptive statistics, and hypothesis testing, while learning how to interpret and analyze data with clarity and confidence.

In each chapter, we will navigate together through practical exercises that connect theory to real-world applications, using Python and R with real datasets.

No prior mathematical or programming experience is required to attend this course. The course is organized in four chapters, covering the topics listed below.

Roadmap of the course

Chapter 1. Prediction and inference.

• General frameworks for statistics and probability.
• Introduction to descriptive statistics, population and sampling.
• Statistical estimators for central tendency and variation.
• Data visualization: histogram, box, violin, dispersion.

Chapter 2. Foundations of probability.

• Introduction to probability and random events.
• Discrete events: Bernoulli, Binomial, Poisson, and discrete Uniform distributions.
• Continuous events: Gaussian, Exponential, and continuous Uniform distributions.
• Mean and variance as expected values.

Chapter 3. Hypothesis testing (I): Parameter estimation.

• Prediction vs inference revisited. Variables, parameters and estimators.
• The Law of Large Numbers (LLN).
• The Central Limit Theorem (CLT).
• Confidence intervals and critical regions.

Chapter 4. Hypothesis testing (II): Some examples.

• The modern Pearson-Neyman approach to hypothesis testing.
• Common examples of statistical tests (t-test, Fisher's exact, ANOVA, χ²).
• Parametric vs non-parametric tests.
• Revisiting P-values: errors, power, and Bayesian probability.

Chapter 5. Introduction to Bayesian probability.

• Error types in hypothesis testing. The Fisher and the Pearson-Neyman approach.
• Independent and conditional events.
• Conditional probability: The Bayes' rule.

Setting up your codespace

Log-in with user account, then navigate to the green code tab:

Once logged-in, you shall find the local tab. Move to the codespaces tab in the upper-right corner:

Once logged-in, inside the codespaces tab, you shall find the create a codespace on main option:

Remote access to JEX

To access JEX, the LMS HPC cluster, open a terminal and type

ssh user@jex.lms.mrc.ac.uk

where user should be your username as set up with corresponding IT service.

You will be asked to input your passsword to access, also set up with IT.

Remote access to Krypton

To access Krypton, the former LMS HPC cluster, open a terminal and type

ssh user@krypton

where user should be your username as set up with corresponding IT service.

You will be asked to input your passsword to access, also set up with IT.

Remote access to CX2

To access CX2, the Imperial College HPC cluster, open a terminal and type

ssh user@login.hpc.ic.ac.uk

where user should be your username as set up with corresponding IT service.

You will be asked to input your passsword to access, also set up with IT.

Setting up Python and R on your own machine

Setting up Python and R on your own machine

Instructions for Mac and Linux

Instructions for Mac and Linux (...)

Instructions for Windows

Instructions for Windows (...)

Licence

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International Licence.