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Durham University

Department of Mathematical Sciences

MATH1617 Statistics

Statistics teaches us how to make rational inferences from data, and how to describe our uncertainty about those inferences. It is the foundation of everything from the work of the National Audit Office to the latest developments in artificial intelligence. This module lays the foundations for all subsequent study of statistics by introducing and illustrating the fundamental principles and methods of the two main statistical paradigms: frequentist and Bayesian.

Outline of Course

Aim: To introduce the principles and procedures of frequentist and Bayesian statistics, and illustrate them with canonical examples; to present frequentist and Bayesian principles as alternative approaches to doing statistics, and to compare frequentist and Bayesian procedures and results; to demonstrate the relevance of these principles and procedures to real problems.

  • Two schools of thought: frequentist and Bayesian.
  • Statistics and sampling distributions: Random sampling (Bernoulli). Sample mean and its distribution (binomial). Normal approximation to binomial. Statistics, estimators, and sampling distributions (general case). Sample mean of Normally distributed population.
  • Confidence intervals and hypothesis testing: Generating confidence intervals. Basic ideas about hypothesis testing, type I and type II errors. Significance tests. P values. Running Normal example (known variance).
  • Inference for continuous data: Single samples (large n, CLT, unknown variance, t tests).
  • Principles of Bayesian statistics: Bayes theorem and partition. Disease test example.
  • Binomial / Beta: Posterior, normalizations, credible intervals, comparison to frequentist.
  • Normal / Normal: Posterior, normalizations, credible intervals, comparison to frequentist.

Prerequisites

For details of prerequisites, corequisites, excluded combinations, teaching methods, and assessment details, please see the Faculty Handbook.

Reading List

Please see the Library Catalogue for the MATH1617 reading list.

Examination Information

For information about use of calculators and dictionaries in exams please see the Examination Information page in the Degree Programme Handbook.