Syllabus of taught modules
(back to
Teaching
🔗)Bayesian
statistics III/IV/V (MATH3341/MATH4031/MATH43220)
Michaelmas
Syllabus:
Multivariate. distributions and
calculus ● Exchangeable model ● Specification of priors (conjugate,
Jeffreys, Max. entropy, etc...) ● elements of decision theory (Bayes
risk, admissibility, etc...) ● point estimators ● credible sets ●
hypothesis tests ● model comparison ● model averaging ● Lindley's
paradox ● Bayesian hierarchical modeling ● empirical Bayes ●
asymptotic behavior of the posterior ● intro to JAGS ● examples in
Bayesian linear regression ● logistic regression and Normal mixture
model
Variational Bayesian inference (as
self study material)
Bayesian statistics III/IV/V
(MATH3341/MATH4031/MATH43220)
Epiphany
Syllabus:
- Graphical models: Graph theory ● Conditional
independence ● Bayesian networks
- Stochastic simulation: Inverse sampling method ●
Rejection sampler ● Importance sampling ● Markov chain Monte
Carlo (Gibbs alg, Metropolis-Hastings alg, central limit
theorem, law of large numbers, convergence, implementation,
diagnostics, and output use)
Topics in
Statistics III/IV (MATH3361/MATH4071)
Michaelmas
- Contingency tables: graphical
investigation ● 3 way tables ● multi-way tables ● models of
conditional independencies ● Goodness-of-fit tests ●
residuals/diagnostics ● odds ratios ● Mantel-Haenszel test ●
Simpson's paradox ● estimation ● log-linear models ● model
comparison (profile likelihood ; AIC/BIC ; forward selection ;
backward elimination ; stepwise selection) ● parameter
estimation (Newton algorithm ; iterative proportions fitting)
- Likelihood methods: modes of
convergence of sequences of random variables ● Taylor expansion
with remainder (multivariate) ● characteristic functions ●
consistency ● laws of large numbers ● central limit theorems ●
Mann-Wald notation (big/little Oh pee) ● Cramer's theorem and
Delta method ● Asymptotic efficiency ● variance stabilization ●
MLE (and properties) ● method of moments (and properties) ●
one-step-estimators (and properties) ● symptotic confidence
regions and hypothesis tests (with: ML ; Wald ; Score
statistics) ● inference with nuisance parameters (profile
likelihood ; Wald ; Score statistic) ● Expectation-Maximization
- Bootstrap methods as self
study material
Spatio-Temporal Statistics IV
(MATH4341)
Michaelmas
Syllabus:
Machine
learning and neural networks III (MATH3431)
Epiphany
Syllabus:
- Foundations: Convex learning problems and related theory
- Stochastic learning: stochastic gradient decent, stochastic
gradient Langevin dynamics, and variations
- Support vector machines: geometry, hard SVM, soft SVM,
- Kernel methods: projections in feature spaces, the kernel trick,
kernelised SVM, Gaussian process regression
- Neural networks: single/multi-layer perception, error
back-propagation, Bayesian/classical framework, relation to other
models
- Optional (if time allows): Latent variable models, mixture
models, expectation maximization alg. variational inference
- Software implementation of the above
Statistical
methods III (MATH3051)
Epiphany
Syllabus:
Linear regression ● Regression
diagnostics (assumptions ; influential points ; outliers) ● model
selection (profile likelihood ; AIC/BIC ; forward selection ;
backward elimination ; stepwise selection) ● ANOVA ● principal
component analysis ● dimension reduction ● mixture models of
distributions ● Expectation Maximisation
Statistics
(MATH1541)
Epiphany
Syllabus:
Introduction to: Random variables ●
distributions ● expectations ● Central Limit Theorem ● Law of Large
Numbers ● parametric tests for 1 and 2 populations (mean, variance,
proportions) ● non parametric tests for 1 and 2 populations (median)
● 1 way ANOVA