## 15 Points

Division of Health Engineering Computing & Science
School of Computing and Mathematical Sciences
Department of Mathematics and Statistics

### Staff

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#### Lecturer(s)

: rachael.foote@waikato.ac.nz

#### Librarian(s)

You can contact staff by:

• Calling +64 7 838 4466 select option 1, then enter the extension.
• Extensions starting with 4, 5, 9 or 3 can also be direct dialled:
• For extensions starting with 4: dial +64 7 838 extension.
• For extensions starting with 5: dial +64 7 858 extension.
• For extensions starting with 9: dial +64 7 837 extension.
• For extensions starting with 3: dial +64 7 2620 + the last 3 digits of the extension e.g. 3123 = +64 7 262 0123.
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### Paper Description

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In theory, Bayesian statistics is simple. However, implementing it requires solving multivariate integrals which might be too difficult to
solve. So in practice, Bayesian statistics is more difficult, and requires the use of computational methods to approximate these
integrals. There are several important computational methods used these days. These algorithms are particularly well suited for
complicated models with many parameters. This has revolutionised applied statistics in the past two decades.

This course will introduce some of those methods. We'll motivate the basic ideas by using simple algorithms such as importance
sampling and rejection sampling and then move onto the cutting edge 'Approximate Bayesian Computation' (ABC). We'll devote most
of our time learning about the most widely used class of computational methods of all namely, the Markov Chain Monte Carlo (MCMC)
methods. These computer intensive methods enable Bayesian inference by drawing a large number of samples from the posterior
distribution.

The course will start by reviewing the basic theoretical aspects of probability and statistical inference. Then highlight the contrast
between the two approaches to statistical inference frequentist vs. the Bayesian. Then we will review the theoretical study of Bayesian
inference before moving on the computational methods.

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### Paper Structure

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Contact hours: Three lecture hours per week.
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### Learning Outcomes

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Students who successfully complete the course should be able to:

• Understand the theory behing Bayesian inference.
• Understand the basics of frequentist inference and appreciate the contrast between the frequentist and the Bayesian approaches
• Understand the theory behind the computational methods discussed in the course.
• Be able to write pseudocode to implement the computational methods discussed in the course.
• Be able to write a corrrectly working R code to implement these computational methods on the statistical models discussed in the course
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### Assessment

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#### Assessment Components

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The internal assessment/exam ratio (as stated in the University Calendar) is 50:50. There is no final exam. The final exam makes up 50% of the overall mark.

The internal assessment/exam ratio (as stated in the University Calendar) is 50:50 or 0:0, whichever is more favourable for the student. The final exam makes up either 50% or 0% of the overall mark.

Component DescriptionDue Date TimePercentage of overall markSubmission MethodCompulsory
1. Assignment 1
7.5
• Hand-in: In Lecture
2. Test 1
12.5
3. Assignment 2
7.5
• Hand-in: In Lecture
4. Project
10
5. Test 2
12.5
6. Exam
50
 Assessment Total: 100
Failing to complete a compulsory assessment component of a paper will result in an IC grade
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The recommended text for this course is Understanding Computation Bayesian Statistics by Bill Bolstad. A copy of this textbook is available in the library.

#### Other Resources

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Other texts you may find helpful include:
Bayesian Essentials with R by JM. Marin and C.P. Robert
Introduction to Bayesian Statistics (2nd edition) by Bill Bolstad (the textbook for STAT226)
Bayesian Statistics: An Introduction by Peter Lee
Markov Chain Monte Carlo by Dani Gamerman
Bayesian Data Analysis by A. Gelman, J. Carlin, H. Stern and D.B. Rubin
Markov Chain Monte Carlo in Practice by W. Gilks, S. Richardson and D. Spiegelhalter
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### Online Support

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Copies of slides will be available on the Moodle website for most of the topics of this course. You can print any notes you require from
the computer laboratory. Lecturers will use their discretion to decide whether to record lectures with the Panopto system. Lecture
recordings should be considered a useful revision aid, or opportunity to catch-up on irregularly missed lectures, and are not to be
regarded as a substitute for attending lectures in person.
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Students should expect to spend a minimum of 10-12 hours per week on this paper. This includes the four lecture hours, the suggested four hours of self-study in the computer lab, and reading time.

In special cases, STAT226 / STAT221 may be taken concurrently with STAT326, but the student must take full responsibility for this decision.

Mathematical background: Please note that STATS326 is a high-level theoretical paper in mathematical statistics. We strongly recommend students to have successfully completed at least a Stage 1 mathematics paper, and ideally a Stage 2 mathematics papers in calculus and / or algebra before attempting this course.

Computational background: Prior experience using the statistical software R is strongly recommended. Also any prior computer coding
experience will be highly beneficial.

#### Prerequisite(s)

Prerequisite papers: STAT221 or STATS221 or STAT226 or STATS226 or at the discretion of the Paper Convenor.

#### Restriction(s)

Restricted papers: STAT326