# Probability and Stochastic Modelling

## Overview

• Credit value: 30 credits at Level 7
• Tutors: Anthony Brooms, Richard Pymar
• Assessment: a three-hour written examination plus coursework amounting to 20% of the final mark

## Module description

This module provides a solid grounding in the fundamentals of random variables and their distributions, together with an introduction to axiomatic probability theory and the convergence of sequences and sums of random variables. These form the foundations of statistics. We will then discuss the theory underlying modern statistics as well as (mathematical) statistics and the principles of statistical inference. Emphasis is placed on demonstrating the applicability of the theory and techniques in practical applications.

Lectures on time series and forecasting and Markov chains aim to extend the static ideas of the probability lectures to a dynamic framework in which randomness unfolds over time. They will introduce you to the properties of ARMA models and the principles of ARIMA modelling, including model identification, estimation and forecasting. A variety of models are discussed together with examples of their application, and you will use advanced statistical software to analyse time series data.

### Indicative module syllabus

• Probability and Distribution Theory
• Statistical Inference
• Time Series and Forecasting
• Discrete Time Markov Chains

## Learning objectives

By the end of this module, you should be able to demonstrate:

• knowledge and understanding of the theory of random variables and their distributions, together with knowledge of a wide range of standard distributions
• knowledge and understanding of the axiomatic approach to probability
• the ability to recognise the appropriate distributions to use when modelling data that arise in different contexts and applications
• knowledge and understanding of the principles and theory of statistical inference and the ability to use the theory and available data to estimate model parameters and formulate and test statistical hypotheses
• knowledge and understanding of the theory and properties of ARMA and ARIMA models, and the ability to apply the theory to the analysis of times series data, to model fitting, model choice, interpretation and forecasting
• the ability to use advanced statistical software for the analysis of time series data
• knowledge and understanding of the theory of homogeneous discrete time Markov Chains.