ST2PST: Probability and Statistical Theory

Module code: ST2PST

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: Level 2 (Intermediate)

When you'll be taught: Semester 2

Module convenor: Dr Jeroen Wouters, email: j.wouters@reading.ac.uk

Pre-requisite module(s): BEFORE TAKING THIS MODULE YOU MUST ( TAKE ST1PS AND TAKE MA1FM ) OR ( TAKE ST1PSNU AND TAKE MA0FMNU ) (Compulsory)

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded:

Placement information: NA

Academic year: 2024/5

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 21 May 2024

Overview

Module aims and purpose

This module rigorously introduces basic concepts of probability from a mathematical perspective and develops the theoretical foundations of methods used in statistical practice and data science applications. 

It aims to equip the students with a basic knowledge in probability which will reveal the interplay between probability theory and fundamental areas of mathematics, will allow students to formulate general real or abstract problems in a probabilistic model and will unravel the fundamentals which statistical methods are built on. 

The module covers random variables together with probability distributions as the fundamental objects of probability theory, limit laws, as well as a first introduction of stochastic processes such as Markov chains. The method of moments and the method of maximum likelihood are considered for point estimation of parameters, and properties of estimators, such as bias and mean square error, are described. Interval estimation and hypothesis testing are also developed. 

Module learning outcomes

By the end of the module, it is expected that students will be able to: 

1. Identify and demonstrate understanding of the main concepts and definitions in probability theory 
2. Identify and formulate problems in terms of probability and solve them by constructing simple stochastic model 
3. Justify the use of, and apply, methods of estimation and state and derive the properties of estimators; 
4. Describe, justify and make use of the concepts of hypothesis testing and confidence intervals. 

Module content

Random variables with continuous, discrete and mixed distributions, expectation of random variables, independence, sums of independent random variables, generating functions, concepts of convergence of random variables, dependent random variables, conditional distributions, and Markov chains. 

Point estimators: Introduction to inference. Bias, mean square error, sufficiency, minimum variance unbiased estimators. Estimation methods: method of moments, maximum likelihood. 

Confidence intervals, likelihood technique, central limit theorem. Principles of hypothesis testing and likelihood ratio test. Introduction to Bayesian statistics. 

Structure

Teaching and learning methods

Lectures, supported by non-assessed problem sheets, weekly tutorials, and exercises. 

Study hours

At least 54 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 40% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

The Support Centres will apply the following penalties for work submitted late:

Assessments with numerical marks

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: https://www.reading.ac.uk/cqsd/-/media/project/functions/cqsd/documents/qap/penaltiesforlatesubmission.pdf

You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

Reassessment

Additional costs