# STAT40850 Bayesian Analysis (online)

Bayesian Analysis models all unknown quantities in a coherent probabilistic framework. Full probability distributions for model parameters conditional on observed data are derived. This module explores how this can be done, both algebraically and computationally. Understanding the Bayesian approach to inference is central and manipulation of conditional distributions is key. The free software package JAGS will be used to perform analysis on a range of statistical models, from simple to complex hierarchical models. Topics covered include: conditional probability, Bayes' Theorem, prior distributions, conjugacy, the likelihood principle, multi-parameter problems, Bayesian hypothesis testing and model checking, methods for finding the posterior mode, Markov Chain Monte Carlo, advanced Bayesian modelling. Illustrative examples from the scientific literature will be used.

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Curricular information is subject to change

Learning Outcomes:

By the end of the course the students should be able to propose and fit a fully Bayesian statistical model to a wide variety of data sets. They should be able to check the model and give a critique of the Bayesian process as opposed to its Frequentist counterpart.

Student Effort Hours:
Student Effort Type Hours
Specified Learning Activities

24

Autonomous Student Learning

72

Online Learning

24

Total

120

Approaches to Teaching and Learning:
Video lectures posted each week that walk through module content, blending theory with example exercises.
Practice problem sheets posted each week to enable self-assessment of learning outcomes. Sample solutions for these will be posted approximately one week after each problem set. Coding based problem sets posted with solutions again following.
All content delivered using the VLE which includes a monitored discussion forum with topics created for each weeks lecture material and each problem set.
Requirements, Exclusions and Recommendations
Learning Recommendations:

You should have completed a basic course in statistics including probability, inference, hypothesis testing, estimation and regression.

Module Requisites and Incompatibles
Incompatibles:
STAT40380 - Bayesian Analysis, STAT40390 - Bayesian Analysis

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Examination: 2 hour end of trimester examination. 2 hour End of Trimester Exam No Graded No

60

Continuous Assessment: Assignments will be a mix of theory and computer based problem sheets. Throughout the Trimester n/a Graded No

40

Carry forward of passed components
No

Resit In Terminal Exam
Summer Yes - 2 Hour
Feedback Strategy/Strategies

• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Bayesian Statistics: An Introduction by Lee
Bayesian Data Analysis by Gelman, Carlin, Stern, and Rubin.
Name Role
Dr Riccardo Rastelli Lecturer / Co-Lecturer
Mr John O'Sullivan Tutor
Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.

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