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Study information

Bayesian statistics, Philosophy and Practice - 2023 entry

MODULE TITLEBayesian statistics, Philosophy and Practice CREDIT VALUE15
MODULE CODEMTH3041 MODULE CONVENERProf Daniel Williamson (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 0 0
Number of Students Taking Module (anticipated) 25
DESCRIPTION - summary of the module content

Since the 1980s, computational advances and novel algorithms have seen Bayesian methods explode in popularity, today underpinning modern techniques in data analytics, pattern recognition and machine learning as well as numerous inferential procedures used across science, social science and the humanities.

This module will introduce Bayesian statistical inference, describing the differences between it and classical approaches to statistics. It will develop the ideas of subjective probability theory for decision-making and explore the place subjectivity has in scientific reasoning. It will develop Bayesian methods for data analysis and introduce modern Bayesian simulation based techniques for inference. As well as underpinning a philosophical understanding of Bayesian reasoning with theory, we will use software currently used for Bayesian inference in the lab, allowing you to apply techniques discussed in the course to real data.

Pre-requisite: MTH2006 Statistical Modelling and Inference or equivalent

AIMS - intentions of the module

This module will cover the Bayesian approach to modelling, data analysis and statistical inference. The module describes the underpinning philosophies behind the Bayesian approach, looking at subjective probability theory, subjectivity in science as well as the notion and handling of prior knowledge, and the theory of decision making under uncertainty. We then move to Bayesian modelling and inference looking at parameter estimation in simple models and then hierarchical models. Finally, we explore simulation-based inference in Bayesian analyses and develop important algorithms for Bayesian simulation by Markov Chain Monte Carlo (MCMC) such the Gibbs sampler and the Metropolis-Hastings algorithm.This module is an excellent precursor to MTH3012. 

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module you should be able to:


Module Specific Skills and Knowledge

1. Show understanding of the subjective approach to probabilistic reasoning;

2. Demonstrate an awareness of Bayesian approaches to statistical modelling and inference and an ability to apply them in practice;

3. Demonstrate understanding of the value of simulation-based inference and knowledge of techniques such as MCMC and the theories underpinning them;

4. Demonstrate the ability to apply statistical inference in decision-making;

5. Utilise appropriate software and a suitable computer language for Bayesian modelling and inference from data.

Discipline Specific Skills and Knowledge

6. Demonstrate understanding, appreciation of and aptitude in the quantification of uncertainty using advanced mathematical modelling;

Personal and Key Transferable / Employment Skills and Knowledge

7. Show advanced Bayesian data analysis skills and be able to communicate associated reasoning and interpretations effectively in writing;

8. Apply relevant computer software competently;

9. Use learning resources appropriately;

10. Exemplify self-management and time-management skills.

SYLLABUS PLAN - summary of the structure and academic content of the module

Introduction: Bayesian vs Classical statistics, Nature of probability and uncertainty, Subjectivism.

Decision Theory: Bayes’ rule, Bayes’ risk, Decision trees, Sequential Decision making, Utility.

Bayesian inference: Conjugate models, Prior and Posterior predictive distributions, Posterior summaries and simulation, Objective and subjective priors, Nuisance parameters, Hierarchical models, Bayesian regression.

Bayesian Computation: Monte Carlo, Inverse CDF, Rejection Sampling, Markov Chain Monte Carlo (MCMC), The Gibbs sampler, Metropolis Hastings, Diagnostics.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 33 Guided Independent Study 117 Placement / Study Abroad 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities 33 Lectures/practical classes
Guided independent study 33 Post-lecture study and reading
Guided independent study 40 Formative and summative coursework preparation and attempting un-assessed problems
Guided independent study 44 Exam revision/preparation

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework - practical and theoretical exercises 15 hours All

Verbal in class, written feedback on script and oral feedback in office hour

       
       
       
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 20 Written Exams 80 Practical Exams
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – Restricted Note. 1 Sheet of A4 (two sides) handwritten or typed notes 80 2 hours (Summer) 1-8, 9, 10 Written/verbal on request
Coursework - practical and theoretical exercises 20 15 hours All Written feedback on script and oral feedback in office hour
         
         
         

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
Written exam * Written Exam (2 hours) 1-7, 9, 10 August Ref/Def Period
Coursework * Coursework All August Ref/Def Period
       

*Please refer to reassessment notes for details on deferral vs. Referral reassessment

RE-ASSESSMENT NOTES

Deferrals: Reassessment will be by coursework and/or written exam in the deferred element only. For deferred candidates, the module mark will be uncapped. 

Referrals: Reassessment will be by a single written exam worth 100% of the module only. As it is a referral, the mark will be capped at 40%. 

 

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Basic reading:

 

ELE: http://vle.exeter.ac.uk/

 

Web based and Electronic Resources:

 

Other Resources:

Lindley, D. V. “Making Decisions”

De Groot, M. H. “Optimal Statistical Decisions”.

Sivia, D. S. “Data Analysis, A Bayesian Tutorial”.

Reading list for this module:

Type Author Title Edition Publisher Year ISBN
Set A Gelman Bayesian Data Analysis 3rd CRC Press 2013 9781439840955
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES MTH2006
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 6 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Tuesday 10th July 2018 LAST REVISION DATE Wednesday 15th February 2023
KEY WORDS SEARCH Bayesian; Bayes; Statistics; Data, Big Data; Analysis; Decision Theory; Inference; Mathematics; Probability.

Please note that all modules are subject to change, please get in touch if you have any questions about this module.