MFC CDT Course on Probability and Statistics#
This is a companion webpage to Probability and Statistics course delivered by Alessandra Luati (Weeks 1-5) and O. Deniz Akyildiz (Weeks 6-10) jointly at Imperial College London, University of Reading, and University of Southampton as a part of the EPSRC Centre for Doctoral Training in the Mathematics for our Future Climate: Theory, Data and Simulation (MFC CDT).
Main resources for this year will be the slides and notebooks that I will upload here.
For the second part of the course, see this page for the resources of an undergraduate course on Stochastic Simulation, which is largely relevant. See Bayesian filtering summer course for some extra material on Bayesian filtering.
Slides#
Slides can be found below. I will try to upload them before the lecture.
Please download the slides and open it with Adobe Acrobat if you want to see the animations (activates when you click). They won’t run on your browser.
Week 1 (07/10/2024): Basic measure theory and probability theory (Alessandra Luati)
Week 2 (14/10/2024): Conditional expectations (Alessandra Luati)
Week 3 (21/10/2024): Martingales, Markov processes (Alessandra Luati)
Week 4 (28/10/2024): Time series: linear processes (Alessandra Luati)
Week 5 (04/11/2024): Time series: nonlinear processes (Alessandra Luati)
Week 6 (11/11/2024): Introduction to Monte Carlo, direct sampling, rejection sampling [PDF], [notes].
Week 7 (18/11/2024): Importance sampling, introduction to Markov chain Monte Carlo [PDF], [notes].
Week 8 (25/11/2024): Unadjusted Langevin algorithm, introduction to generative models [PDF].
Week 9 (02/12/2024): The stochastic filtering problem, Kalman filters, particle filters [PDF].
Week 10 (09/12/2024): Parameter estimation in state-space models, maximum-likelihood and Bayesian estimation [PDF].