KC7014 - Bayesian Statistics

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What will I learn on this module?

You will gain an understanding of Bayesian statistics. The module introduces Bayes’ Theorem and its application to both simple and complex problems. It examines the algebraic and numerical techniques used to handle different problems and the important concept of combining prior information with data to form a posterior distribution. A wide range of real-life problems will be used to motivate the subject matter. Both conjugate and non-conjugate problems will be considered.

The module will be delivered using a combination of lecture and computer laboratory sessions. Assessment will be via a formal examination.

OUTLINE SYLLABUS

Bayes’ Theorem and its application. Bayesian inference.
Prior distributions, maximum likelihood estimation, posterior distributions.
Single-parameter models, multi-parameter models. Vague and informative priors.
Large-sample inference. Normal approximation to the posterior distribution.
Monte Carlo method and simulation of data. Markov Chain Monte Carlo (MCMC) methods for non-conjugate problems, including the Gibbs sampler and Metropolis-Hastings.
Introduction to Bayesian regression modelling.

How will I learn on this module?

You will learn through a series of formal sessions including both lectures and computer laboratory sessions. During lectures, you will learn main concepts with suitable applications/examples. You will gain experience in applying concepts introduced in lectures and deepen your understanding of the material through working on practical questions during regular practical sessions, which are scheduled in our modern computer laboratories. Through practise, you will develop your confidence to explore the subject area further as an independent learner outside the classroom.

You will receive formative feedback weekly in the classes as you get to grips with new techniques and solve problems. In addition, we operate an open door policy where you can meet with your module tutor to seek further advice or help if required.

Your ability to select, perform and critique techniques to solve practical problems is assessed in via a formal examination.

You will be given general feedback on assessments in class as well as written individual feedback. When you receive your marked work, you will also have an opportunity to discuss work further on an individual basis as well as through the open door policy.

How will I be supported academically on this module?

Direct contact with the teaching team during the formal sessions will involve participation in both general class discussions as well as one to one discussions during the hands-on part of the formal sessions. This gives you a chance to get immediate feedback pertinent to your particular needs in this session. Further feedback and discussion with the teaching team are also available at any time through our open door policy. In addition, all teaching materials and supplementary material (such as relevant journal articles and news) are available through the e-learning portal.

What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk
(Reading List service online guide for academic staff this containing contact details for the Reading List team – http://library.northumbria.ac.uk/readinglists)

What will I be expected to achieve?

Knowledge & Understanding:
1. Combine prior information with sampled/observed data in order to carry out a Bayesian analysis and draw valid conclusions.

Intellectual / Professional skills & abilities:
2. Apply Bayesian methods to data arising from physical phenomena, medical studies and sports;
3. Tackle non-standard problems using numerical methods.

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
4. Communicate uncertainty involved in a scientific investigation effectively and appropriately.

How will I be assessed?

SUMMATIVE
Examination (100%) – 1, 2, 3, 4

FORMATIVE – 1, 2, 3, 4
Formative assessment will be available on a weekly basis in the formal sessions through normal lecturer-student interactions, allowing them to extend, consolidate and evaluate their knowledge.

Formative feedback will be provided on student work and errors in understanding will be addressed reactively using individual discussion. Solutions for laboratory tasks will be provided after the students have attempted the questions, allowing students to receive feedback on the correctness of their solutions and to seek help if matters are still not clear.

Pre-requisite(s)

None

Co-requisite(s)

None

Module abstract

‘Bayesian Statistics’ will equip you with a solid understanding of Bayesian statistics and will enable you to tackle real-life problems using appropriate Bayesian techniques. You will learn the important concept of combining prior information with data to form a posterior distribution and various methods to make summary based on this posterior distribution. You will gain an in-depth understanding of different sources of uncertainty involved in a scientific investigation. Based on this understanding, you will be able to quantify and communicate uncertainty appropriately.

This module comprises of both lectures, where main concepts with suitable applications are introduced, and seminars, which allow you to gain experience in applying various concepts through working on practical questions. You will be assessed by a final examination (100%).

‘Bayesian statistics’ will enhance your employability, providing you with a sound foundation in Bayesian statistics, which is high-valued by industry sectors and beneficial for your future study.

Course info

UCAS Code G101

Credits 20

Level of Study Undergraduate

Mode of Study 4 years full-time or 5 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2020

Fee Information

Module Information

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