Instructor: Terry Soo

email: t.soo@ucl.ac.uk

My homepage

Original posting

- 10.30-12.30; Mondays, starting November 8

- UCL Cruciform B304 (weeks 1-4)
- UCL Physics A1/3 (week 5)
- Zoom link (when available)
- Office hours, by request, most likely will be Zoom

Related materials from UCL Stat 9 2021

Related materials from UCL Stat 9 2020

Extra reading and references

- Week1: Introductions; Review of probability theory
- Recording; you may need to manually download to see the entire video.

- Week2: Weierstrass approximation, the strong law, coupling and total variational distance.
- Recording
- I believe that I technically only proved the Bernstein polynomials converged pointwise, and did not argue enough that the convergence is uniform; for this, you really need to use Markov’s inequality and notice that the variance is maximized at \(p=\tfrac{1}{2}\); see the notes for details.

- I believe that I technically only proved the Bernstein polynomials converged pointwise, and did not argue enough that the convergence is uniform; for this, you really need to use Markov’s inequality and notice that the variance is maximized at \(p=\tfrac{1}{2}\); see the notes for details.

- Recording
- Week3: Markov chains and Doeblin’s coupling.
- Week4: Law of large numbers for Markov chains
- Week5: Poisson processes

- Re-introduction to probability theory (mostly review)
- Probability and R
- Weierstrass approximation
- The strong law of large numbers
- Coupling and total variational distance
- Review of Markov chains
- Coupling and the long term behaviour of Markov chains
- Poisson processes
- Continuous-time Markov chains
- Renewal processes

Version: 06 March 2022