ST553 Half Unit
Probability and Mathematical Statistics II
This information is for the 2019/20 session.
Prof Konstantinos Kardaras
This course is available on the MPhil/PhD in Statistics. This course is available with permission as an outside option to students on other programmes where regulations permit.
Probability and Mathematical Statistics I is a pre-requisite.
This course provides instruction in advanced topics in probability and mathematical statistics, mainly based on
martingale theory. It is a continuation of Probability and Mathematical Statistics I. The following topics will in particular be covered:
- Conditional expectation revisited; linear regression; martingales and first examples.
- Concentration inequalities; dimension reduction; log-Sobolev inequalities.
- Martingale transforms; optional sampling theorem; convergence theorems.
- Sequential testing; backwards martingales; law of large numbers; de Finetti’s theorem.
- Markov chains; recurrence; reversibility; foundations of MCMC.
- Ergodic theory.
- Brownian motion; quadratic variation; stochastic integration.
- Stochastic differential equations; diffusions; filtering.
- Bayesian updating; Ergodic diffusions; Langevin samplers.
- Brownian bridge; empirical processes; Kolmogorov-Smirnov statistic.
20 hours of lectures and 10 hours of seminars in the LT.
Week 6 is Reading Week.
Students will be expected to produce 9 problem sets in the LT.
Weekly problem sets that are discussed in subsequent seminars. The coursework that will be used for summative assessment will be chosen from a subset of these problems.
- Williams, D. (1991). Probability with Martingales. Cambridge University Press.
- Durrett, R. (2019). Probability: Theory and Examples. Cambridge Series in Statistical and Probabilistic Mathematics.
- Karatzas, I, Shreve S. (1991). Brownian motion and Stochastic Calculus. Springer GTM.
- Shao, J. (2007). Mathematical Statistics. Springer Texts in Statistics.
- Keener, R. (2010). Theoretical Statistics. Springer Texts in Statistics.
Exam (70%, duration: 3 hours, reading time: 10 minutes) in the summer exam period.
Three of the homework problem sets will be submitted and marked as assessed coursework.
Total students 2018/19: Unavailable
Average class size 2018/19: Unavailable
Value: Half Unit
Personal development skills
- Problem solving
- Application of numeracy skills
- Specialist skills