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# Faculty of Mathematics

Please take this page in conjunction with the Part III Guide to Courses Statistics section.

Background knowledge in the following areas is essential, helpful 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
• Bayesian Modelling and Computation
• Topics in Statistical Theory
• Astrostatistics

Relevant undergraduate courses are:

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

Undergraduate statistics, including:

• 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.