Bayesian Inference in Finance provides a detailed overview of the theory of Bayesian methods and explains their real-world applications to portfolio management and market risk management. Bayesian inference is a probabilistic framework that allows to uncover uncertainty about parameters and general statistical inference in a natural way. Computation is a crucial part of this course, and students will be taught advanced Markov chain Monte Carlo algorithms for inference in demanding statistical problems that require them to learn about thousands or even millions of parameters. For that reason, while the focus is on how Bayesian inference can be applied to standard problems in macroeconomics and finance, this course teaches a broader set of tools that are used extensively in other disciplines related to machine learning and computing science (e.g. Bayesian networks, signal processing, compressive sensing). 

One two-hour lecture per week for 10 weeks.

One two-hour revision lecture.

One two-hour computer lab per week for 10 weeks.

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Assessment

The main aim of this course is to cover a new statistical methodology that will equip the students with new data analytic skills. While these skills are applied to finance, they are more general skills that are used in several other disciplines related to machine learning and computing science. The lectures teach the basic theory behind the Bayesian approach to statistical inference. The computer labs focus on teaching computational techniques that are used in Bayesian inference, and that are not immediately related to previous computational techniques students have acquired in previous econometrics classes. At the same time the computer labs will allow students to apply theory and computation to numerous financial datasets, with a focus on demanding high-dimensional ones.

By the end of this course students will be able to:

1. Evaluate the fundamental philosophical differences between the Bayesian approach to probability and traditional frequentist approaches.

2. Build flexible Bayesian models by means of a likelihood and prior functions.

3. Program advanced Markov chain Monte Carlo algorithms in MATLAB for inference in small and medium-sized problems.

4. Demonstrate ability in developing Bayesian machine learning algorithms for inference in problems of high and ultra-high dimensions.

5. Adapt Bayesian inference principles in order to achieve new solutions to empirical problems in finance and macroeconomics.

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.