Teaching


This term...


MSc Project (COMP52060) --topic:
  • (Easter) 2022
    Statistical and Machine Learning methods for classification and clustering πŸ”—


Β  Next terms...


Machine learning and neural networks III (MATH3431)
Epiphany
  • Teaching material ... soon ...
    Β  2023

Dept. handbook πŸ”— ; Faculty handbook πŸ”—
Topics: (provisional)
  • Mixture models, latent variable models, and EM algorithms
  • Kernel methods (the kernel trick, support vector machine, Gaussian process regression)
  • Neural networks (the model, back-propagation, stochastic gradient decent, stochastic gradient Langevin dynamics)
  • Software implementation

Internship Project III (MATH3452)Β  --study topics:
  • Β (Epiphany) 2023
    Analysis of data from a clinical studyΒ 
    • (with Prof J. Eibeck)
  • Β (Epiphany) 2023
    Radiological protectionsΒ 
    • (with Prof J. Eibeck)


Previous terms (by programme) ...


MMath Master of Mathematics (G103) ; Mathematics and Statistics (G114)
BSc in Mathematical Sciences (G100) ; Mathematics and Statistics (G111)
Department of Mathematical sciences, Durham University, UK

***

Undergraduate levels III, IV & postgraduate

Bayesian statistics III/IV (MATH3341/MATH4031)
Michaelmas
Description πŸ”—Β  ;Β  Handouts πŸ”— ;Β  Exercise sheet πŸ”— ;Β  Computer practicals πŸ”—
Topics:Β 
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 (MATH3341/MATH4031)
Epiphany
  • Teaching material available from Blackboard ULTRA
    2022
Topics:
    • 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)
    • Laplace approximation

Topics in Statistics III/IV (MATH3361/MATH4071)
Michaelmas
Contingency tables: Β Β  Handouts πŸ”— ;Β  Exercise sheet πŸ”— ;Β  Computer practicals πŸ”—
Likelihood methods:Β  Handouts πŸ”— ;Β  Exercise sheet πŸ”—
Topics:
    • 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


Undergraduate level III

Machine learning and neural networks III (MATH3431)
Epiphany
  • Teaching material ... soon ...
    2023

Dept. handbook πŸ”— ; Faculty handbook πŸ”—
Topics: (provisional)
  • Mixture models, latent variable models, and EM algorithms
  • Kernel methods (the kernel trick, support vector machine, Gaussian process regression)
  • Neural networks (the model, back-propagation, stochastic gradient decent, stochastic gradient Langevin dynamics)
  • Software implementation

Statistical methods III (MATH3051)
Epiphany
  • Teaching material available from DUO
    2021
Handout for Mixtures & EM πŸ”— ; Code for PCA on images πŸ”—
Topics:Β  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

Undergraduate level III

Statistics (MATH1541)
Epiphany

Topics: 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

Final year projects @ undergraduate levels III & IV

Project IV (MATH4072) --study topics
  • 2020-2021
    Bayesian hierarchical modeling and analysis of spatial-temporal data πŸ”—

Project III (MATH3382) --study topics
  • Β 2021-2022
    Statistical techniques and models for the analysis of functional dataΒ  πŸ”—
  • 2020-2021
    Bayesian hierarchical modeling and analysis of spatial data πŸ”—
  • (Michaelmas) 2019
    Bayesian computational methodsΒ  πŸ”—
  • 2018-2019
    Bayesian statistics under model uncertainty and computations πŸ”—
  • 2017-2018
    Bayesian global optimisation πŸ”—

Internship Project III (MATH3452) --research topics
  • Β (Epiphany) 2023
    Analysis of data from CAP-MEM clinical studyΒ 
    • (with Prof J. Eibeck)
  • Β (Epiphany) 2023
    Radiological protectionsΒ 
    • (with Prof J. Eibeck)



MSc Scientific Computing and Data Analysis (G5K609)
Department of Mathematical sciences, Durham University, UK
***

Final year projects @ postgraduate levels

MSc Project (COMP52060) --Dissertation topics
  • 2022
    Statistical and Machine Learning methods for classification and clustering πŸ”—
  • 2021
    Bayesian hierarchical modeling and analysis of spatial and spatio-temporal dataΒ  πŸ”—
  • 2020
    Calibration of computer models with Bayesian global optimizationΒ  πŸ”—



MDS Master of Data Science (G5K823)
Department of Mathematical sciences, Durham University, UK
***

Final year projects @ postgraduate levels

Data Science Research Project (DATA40160) --Dissertation topics
  • 2021
    Geostatistical methods for the analysis of spatial data πŸ”—



Internships / Summer research projects
***

London Mathematical Society undergrad research project
2020
  • Bayesian computational methods for big data
  • @ Department of Mathematical sciences, Durham University, UK
  • in July & August, 2020

London Mathematical Society undergrad research project,
2017
  • Gaussian processes emulation in big data
  • @ Department of Mathematical sciences, Durham University, UK
  • in July & August, 2017

International Association for the Exchange of Students for Technical Experience, research project
2017
  • Monte Carlo methods for big data
  • @ Department of Mathematical sciences, Durham University, UK
  • in July & August, 2017



Other programs
***

Introduction to Bayesian Statistics (UTOPIAE)
Β  Summer, 2018
  • @Durham Training School, Department of Mathematical sciences, Durham University, UK
  • Learning material in GitHub πŸ”— ; Handouts πŸ”— ; Slides πŸ”—
  • Karagiannis G.P. (2022) Introduction to Bayesian Statistical Inference. In: Aslett L.J.M., Coolen F.P.A., De Bock J. (eds) Uncertainty in Engineering. SpringerBriefs in Statistics. Springer, Cham.


Introduction to Gaussian process regression (SURF)

August, 2016


Markov chain Monte Carlo (in course: Introduction to Uncertainty Quantification)

March, 2016




Web applets for the courses
***

Web applets are available from : GitHubΒ  πŸ”—



Useful links
***