This module aims to (i) introduce students to the basic concepts of probability and statistics and (ii) illustrate their relevance to practical problem-solving.
A part of this module's aim is to enable students to become aware of and develop their academic, professional, and personal skills through Personal Best, a development programme available to all students at Loughborough University.Â
Content
Basic set theory and counting problems: direct product of finite sets, multiplication rule, counting rules of subsets of finite sets;
Introductory probability theory: sample space, basic theorems of probability, conditional probability, independence, Bayes' formula;
Discrete and continuous random variables: probability density and distribution functions, expectation, variance, specific classes of random variables;
Introductory statistics: sample statistics, unbiased estimators, Central Limit Theorem and its uses, confidence intervals on the mean with standard deviation known/unknown.
The aims of this module are:
- to introduce rigorous mathematical tools which are useful in economics analysis;
- to give students a solid mathematical background in game theoretic models.
Contents
Elements of a game, strategic games, extensive games, Nash equilibrium, subgame-perfect equiliibrium, backward induction, Bayesian Nash equilibrium, auctions, signalling games.
The aims of this module are:
- to introduce Bayesian statistics;
- to study posterior distributions and their properties;
- to discuss applications of Bayesian statistics to a range of data sets.
Contents:
Frequentist and subjective probabilities. Prior, likelihood and posterior. Conjugate priors. The Monte Carlo method. Markov chain Monte Carlo methods. Applications.