Background knowledge in the following areas is essential or helpful for some courses as listed in the introductory section on Statistics in the Guide to Courses.

## Basic Statistics

You will need this for the following Part III courses:

• Modern Statistical Methods
• Statistical Learning in Practice
• Statistics in Medicine
• Causal Inference
• Robust Statistics
• Topics in Statistical Theory
• Bayesian Modelling and Computation.

First level prerequisites

• Basic probability theory, including common distributions such as Binomial, Normal, Poisson, Chi-squared, etc. See e.g. Basic Probability and official prerequisites page mentioned above.
• Basic Linear Algebra. You can check if you are at the required level by doing the following exercises: Statistical Modelling Example Sheet 1 (2014/15) Q 1, 2a, 5, Example Sheet 2 (2014/15) Q8a
• Basic Real Analysis. You can check if you are at the required level by doing the following exercises: Past Exam Question Part IA 2016 Paper 1 Q3, Part IA 2012 Paper 1 Q3

Second level prerequisites

• Maximum Likelihood Estimation. Common examples, consistency and asymptotic normality.
• Hypothesis Tests and Confidence Intervals. Likelihood ratio statistics, Wilks' theorem, t-tests and F-tests.
• The Linear Model. MLEs, hypothesis tests, confidence intervals and extensions.
• Bayesian Statistics. Definitions, examples and comparisons with MLEs.

You can use the following exercises to check your present level and to guide your study.

Useful books and resources

IB Statistics course page by Sergio Bacallado with notes and relevant information.

## Basic Probability

The relevant Cambridge undergraduate course is IA Probability.

Useful books and resources

## Markov Chains

Relevant Cambridge undergraduate courses are IB Markov Chains.