Introduction & prerequisites

Introduction & prerequisites#

These are short exercises (with worked solutions) to refresh the core mathematics and statistics ideas that show up repeatedly in:

Ecological & Evolutionary Modelling (building and analysing mechanistic models)
Advanced Data Analyses and Statistics (fitting models to data and doing inference)

There are no formal prerequisites. However, what you should prioritise depends on which MQB section you are preparing for.

This section uses mathematical models as the main language. You will get most value if you can:

Manipulate algebraic expressions (rearrange equations; logs/exponentials)
Interpret derivatives/integrals as rates and accumulation
Multiply a small matrix by a vector; read a matrix model; basic eigenvalue intuition

These skills are used heavily in:

This section is about fitting models and quantifying uncertainty. You will get most value if you can:

Work comfortably with exponentials/logs and simple calculus (for optimisation and likelihoods)
Understand probability basics (expectation/variance; common distributions)
Read and manipulate a log-likelihood (dropping constants; interpreting parameters)

These skills are used heavily in:

Bayesian chapters are not yet deployed, but if/when you take them you will get most value if you can:

Manipulate probabilities and densities (including conditional probability)
Understand what a prior, likelihood, and posterior represent
Interpret uncertainty summaries (credible intervals) and posterior predictive thinking
Recognise that computation (e.g. sampling) is often required when posteriors are not available in closed form

The closest prerequisites in the current MQB material are:

Machine-learning chapters are not yet deployed, but if/when you take them you will get most value if you can:

Think in terms of prediction vs explanation (and when each is appropriate)
Understand train/test splits, cross-validation, overfitting, and why leakage matters
Be comfortable with feature/response notation and basic matrix/vector operations
Interpret performance metrics (e.g. accuracy/AUC for classification; RMSE/\(R^2\) for regression)

The closest prerequisites in the current MQB material are:

If you want a quick refresher on the “basic stats” pipeline first (design → tests → regression), see:

Do the Exercises first, then use the Solutions to check your reasoning.
If you are about to start E&E Modelling, prioritise sections 2–4 (calculus, linear algebra, differential equations) in the exercises.
If you are about to start Advanced Data Analyses and Statistics, prioritise sections 2, 5, and 6 (calculus, probability, optimisation/likelihood).
If you are preparing for Bayesian modelling, prioritise sections 5 and 6 (probability + likelihood/optimisation), then skim 2 (calculus) as needed.
If you are preparing for Machine Learning, prioritise sections 5 and 6 (probability + optimisation/likelihood), and make sure you can follow the optional Python checks.