The Bayesian approach to statistics assigns probability distributions to both the data and unknown parameters in the problem. This way, we can incorporate prior knowledge on the unknown parameters before observing any data. Statistical inference is summarised by the posterior distribution of the parameters after data collection, and posterior predictions for new observations. The Bayesian approach to statistics is very flexible because we can describe the probability distribution of any function of the unknown parameters in the model. Modern advances in computing have allowed many complicated models, which are difficult to analyse using ‘classical’ (frequentist) methods, to be readily analysed using Bayesian methodology.
The aim of this course is to equip students with the skills to perform and interpret Bayesian statistical analyses. The first part of the course is devoted to describing the fundamentals of Bayesian inference by examining some simple Bayesian models. More complicated models will then be explored, including linear regression and hierarchical models in a Bayesian framework. Bayesian computational methods, especially Markov Chain Monte Carlo methods will progressively be introduced as motivated by the models discussed. Emphasis will also be placed on model checking and evaluation.
Upon successful completion, students will have the knowledge and skills to:
- Explain in detail the Bayesian framework for data analysis and when it can be beneficial, including its flexibility in contrast to the frequentist approach.
- Develop, analytically describe, and implement both single and multiparameter probability models in the Bayesian framework.
- Demonstrate the role of the prior distribution in Bayesian inference and be able to articulate the usage of non-informative priors and conjugate priors.
- Show high level Interpretation of Bayesian Analysis Results and perform Bayesian model evaluation and assessment.
- Fit hierarchical models and provide thorough technical specifications for these models.
- Perform Bayesian computation using Markov chain Monte Carlo methods using R.
- Demonstrate how Bayesian Methods can be used to solve real world problems, including forming a hypothesis, collecting and analysing data, and reaching appropriate conclusions.
- Typical assessment may include, but is not restricted to: exams, assignments, quizzes, presentations and other assessment as appropriate (100) [LO 1,2,3,4,5,6,7]
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Students are expected to commit 130 hours of work in completing this course. This includes time spent in scheduled classes and self-directed study time.
Requisite and Incompatibility
Information about the prescribed textbook will be available via the Class Summary.
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