Advanced Stochastic Modelling and Monte Carlo Methods
In Semester 1 this year, I will again be teaching an honours course which I have roughly titled: Advanced Stochastic Modelling and Monte Carlo Methods. For those of you considering it, this post gives an outline of the topics I intend to cover this year. Due to the restrictions on in-person teaching and workload constraints, all honours courses will be run as reading courses this year. This means there will be no lectures and instead a single weekly workshop. The picture above is created using a technique called path tracing that we will cover and code in week 3.
Obviously, this is a course with a large coding component. I will teach and provide examples using the Julia language. The syntax is similar to MATLAB, but it’s much faster and perfect for this type of numerical work. I don’t mind if you have another favourite you want to use (R or Python) but you will have to translate the answers yourself. Currently I’m planning on the assessment comprising 4 assignments and 2 mini-projects with no exam. If you want more information please come and see me or send me an email.
- Monte Carlo methods and random number generation.
- Importance sampling and variance reduction techniques.
- Path tracing, aka solving the light transport equation.
- SDE models and option pricing.
- Multi-level Monte Carlo
- Continuos-time Markov chain models, reaction network specification.
- Markov chain Monte Carlo: Metropolis-Hastings, Gibbs etc….
- Inference for state-space models, Kalman filter
- Sequential Monte Carlo, particle filters
- Pseudo-marginal methods (PMMH).