STAT314-24S2 (C) Semester Two 2024

Bayesian Inference

15 points

Details:
Start Date: Monday, 15 July 2024
End Date: Sunday, 10 November 2024
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 28 July 2024
  • Without academic penalty (including no fee refund): Sunday, 29 September 2024

Description

This course explores the Bayesian approach to statistics by considering the theory, methods for computing Bayesian solutions, and examples of applications.

STAT314 and STAT461 introduce theory and application of Bayesian Inference. Due to recent advances in computing and to the existence of some relatively user-friendly software Bayesian methods are becoming more and more popular in many applied fields of study, including epidemiology, bioinformatics, ecology and archaeology. This course will cover the basics of Bayesian theory as well as introduce computing methods necessary for implementation of this theory in practice. In addition to generalised linear regression models, analysis of variance and basic tests, for which the results of Bayesian inference will be compared with those for the classical frequentist results, the course will demonstrate the attractive flexibility and multifacetedness of Bayesian methods considering such problems as threshold analysis, and Poisson change-point problems among others.

Topics that are usually covered include:
• Bayes’ Inverse Probability Formula and Bayes’ Theorem. The concepts of prior and posterior distributions. Posterior predictive distribution. Various types of prior distributions.
• Bayesian model comparison and Bayesian model averaging.
• Numerical tools for Bayesian estimation: Markov Chain Monte Carlo (MCMC) methods, Gibbs sampler and Metropolis-Hasting sampler.
• Bayesian inference on linear regression models, generalised linear models, and mixed-effects models.
• Treatment of missing data and latent parameters

The statistical computations will be performed using a combination of WinBUGS (a software for Bayesian inference) and R (a statistical software package). Prior knowledge of WinBUGS is not required. Prior knowledge of R is highly recommended.

Learning Outcomes

 introduce the foundations of Bayesian inference
 introduce the use of statistical software WinBUGS and R.
 introduce numerical algorithms required for practical Bayesian inference.
 demonstrate application of Bayesian inference to a wide range of common problems
 provide some comparison of Bayesian inference to the classical frequentist methods

You will be able to:

 choose appropriate method for analysis of your dataset
 use WinBUGS or R to perform your analysis
 be able to interpret the analysis results in such a way that a non-user of statistics can
understand

University Graduate Attributes

This course will provide students with an opportunity to develop the Graduate Attributes specified below:

Critically competent in a core academic discipline of their award

Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.

Employable, innovative and enterprising

Students will develop key skills and attributes sought by employers that can be used in a range of applications.

Biculturally competent and confident

Students will be aware of and understand the nature of biculturalism in Aotearoa New Zealand, and its relevance to their area of study and/or their degree.

Globally aware

Students will comprehend the influence of global conditions on their discipline and will be competent in engaging with global and multi-cultural contexts.

Prerequisites

30 points from 200 level MATH, EMTH, STAT202-299, DATA203 and PHYS285

Timetable 2024

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Wednesday 10:00 - 11:00 Jack Erskine 315
15 Jul - 25 Aug
9 Sep - 20 Oct
Lecture B
Activity Day Time Location Weeks
01 Monday 11:00 - 12:00 Rehua 529
15 Jul - 25 Aug
9 Sep - 20 Oct
Computer Lab A
Activity Day Time Location Weeks
01 Thursday 15:00 - 16:00 Jack Erskine 442 Computer Lab
15 Jul - 25 Aug
9 Sep - 20 Oct

Course Coordinator

Elena Moltchanova

Lecturer

John Holmes

Assessment

Assessment Due Date Percentage  Description
4 Assignments 40% Assignments are graded as best 4 out of five.
Written Examination 60% Written Final Examination


4 Assignments 40%
Written Examination (3hrs) 60%

Textbooks / Resources

Recommended Reading

Gelman, Andrew et al; Bayesian data analysis ; Third edition; CRC Press, 2014.

Indicative Fees

Domestic fee $847.00

International fee $4,988.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All STAT314 Occurrences

  • STAT314-24S2 (C) Semester Two 2024