Statistics

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

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 (below)
• Basic Probability
• Markov Chains
• (Part II Probability and Measure: see Measure Theory)

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.

Relevant undergraduate courses are:

• Part IB Statistics
• Part II Mathematics of Machine Learning
• Part II Principles of Statistics
• Part II Statistical modelling

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.

• Part IB Statistics Example Sheet 1 (2014/15) Q3, 8, 9, 10
• Part IB Statistics Example Sheet 2 (2014/15)  Q1, 2
• Part IB Statistics Example Sheet 3 (2014/15) Q1, 4, 5, 9

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

• Perla Sousi's lecture notes.
• More very good resources on Prof. Weber's page.

Markov Chains

Relevant Cambridge undergraduate courses are IB Markov Chains.