Coursework

Coursework option 1: particle methods

1- Pick a SSM of your choice so that it is possible the state and observation to be multidimensional with dimensions \(d_x\) and \(d_y\) respectively.

2- Using some known values for the static parameters implement the bootstrap particle filter

3- generate plots and tables for varying \(N\), \(d_x\) and \(d_y\).

4- assess BPF based on accuracy (wrt true states) & variance of normalising constant and integrals like posterior (filter) mean.

5- Consider a parameter estimation method of your choice (particle MCMC, gradients, nested PF…)

6- implement it and describe results for varying \(N\) (and \(M\) in the nested PF case), \(d_x\) and \(d_y\) using plots and tables.

7- In your answers provide also short comments

Coursework option 2:

If your research is related to computational statistics, or uses MCMC:

1- present your model of interest and problem at hand

2- the inferential method for problem (e.g. Bayesian inference, optimisation etc.) and the challenges involved,

3- simulation method (e.g. MCMC, IS, SMC),

4- numerical results

5- a discussion on how material in this course can be used for extensions

Submission

Page limit: 10 pages, recommended length around 6-8 pages, use appendices if you need to go beyond page limits

Submit by email to name.surname at imperial.ac.uk

Here name = deniz and surname = akyildiz

Coursework submission deadline: 16 January 2024