# Faculty of Mathematics

Please read in particular Introduction and prerequisites given 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

• Bayesian Modelling and Computation

• Topics in Statistical Theory

• Astrostatistics

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 Prof. Spiegelhalter with notes and relevant information.

## Basic Probability

The relevant Cambridge undergraduate course is Ia Probability.

Useful books and resources

• Prof. Weber's lecture notes from 2015.

• More very good resources on Prof Weber's page.

## Markov Chains

Relevant Cambridge undergraduate courses are IB Markov Chains.

Useful books and resources

• Parts of a book by Prof. Norris.