Statistical Data Science - MSc

The curriculum introduces (and revises for some students) the essentials of probability and classical (frequentist) statistical inference.

Probability: review of elementary probability, concept of random variable, discrete and continuous probability distributions, cumulative distribution function, expectation and variance, joint distributions, marginal and conditional distributions, generating functions and transformation of random variables.

Statistics: sampling distributions, point estimation, method of moment and maximum likelihood estimation, confidence intervals, hypothesis testing, association between variables and linear regression.

Linear model. Least squares. General linear model; simple and multiple regression, polynomial regression. Model selection, residuals, outliers, diagnostics. Analysis of variance. Generalised linear model.

Discrete data analysis. Review of Binomial, Poisson, negative binomial and multinomial distributions. Properties, estimation, hypothesis tests.

Contingency tables. Tests for independence. Measures of association. Logistic models.

Multidimensional tables. Log–linear models; fitting and model selection.

Bayes Theorem for density functions; Conjugate models; Predictive distribution; Bayes estimates; Sampling density functions; Gibbs and Metropolis-Hastings samplers; Winbugs/OpenBUGS; Bayesian hierarchical models; Bayesian model choice; Objective priors; Exchangeability; Choice of priors; Applications of hierarchical models.

Introduction: Machine learning and data visualisation with R.

Classification and prediction: Generalised linear model (GLM), linear discrimination analysis (LDA), k-nearest neighbors (KNN). R-based worked examples.

Resampling methods: Cross-validation (CV) and bootstrap. R-based worked examples.

Regression tree-based methods: Classification and regression trees (CART), bagging, random forests and boosting. R-based worked examples.

Support vector machines (SVM): Support vector classifier, regression SVM. R-based worked examples.

Machine Learning in Action:

(a) Biomedical and health data analysis;

(b) Bond default data analysis;

(c) Insurance data analysis;

(d) Financial data analysis;

(e) Other big data analysis.

Multivariate normal distribution, Inference from multivariate normal samples, principal component analysis, mixture models, factor analysis, clustering methods, discrimination and classification, graphical models, the use of appropriate software.

Statistics methods contribute significantly to areas such as biology, ecology, sociology and economics. The real data collected does not always follow standard statistical models. This module looks at modern statistical models and methods that can be utilised for such data, making use of R programs to execute these methods.

Indicative module content: Motivating examples; model fitting through maximum likelihood for specific examples; function optimization methods; profile likelihood; score tests; Wald tests; confidence interval construction; latent variable models; EM algorithm; mixture models; simulation methods; importance sampling; kernel density estimation; Monte Carlo inference; bootstrap; permutation tests; R programs.

In addition, for level 7 students: advanced EM algorithm methods, advanced simulation methods, writing R programs for advanced methods and applications.

This is a practical module to develop the skills required by a professional statistician (report writing, consultancy, presentation, wider appreciation of assumptions underlying methods, selection and application of analysis method, researching methods).

Software: R, SPSS and Excel (where appropriate/possible). Report writing in Word. PowerPoint for presentations.

• Presentation of data
• Report writing and presentation skills
• Hypothesis testing: formulating questions, converting to hypotheses, parametric and non-parametric methods and their assumptions, selection of appropriate method, application and reporting. Use of resources to explore and apply additional tests. Parametric and non-parametric tests include, but are not limited to, t-tests, likelihood ratio tests, chi-squared tests, Mann Whitney U-test, Wilcoxon signed rank test, McNemar's test.
• Linear and Generalised Linear Models: simple linear and multiple regression, ANOVA and ANCOVA, understanding the limitations of linear regression, generalised linear models, selecting the appropriate distribution for the data set, understanding the difference between fixed and random effects, fitting models with random effects, model selection.
• Consultancy skills: group work exercise(s)

In addition, for level 7 students:

• Advanced presentation of data, such as visualisation of data points on a map
• Further extensions to Linear and Generalised Linear Models, such as hierarchical generalised linear models.

The module enables students to undertake an independent piece of work in a particular area of statistics, or statistical finance/financial econometrics and to write a coherent account of the material.

There is no specific syllabus for this module.

Introduction Deeplearning with python.

Backgrounds of python software: Basic knowledge of python, as wellas python deep learning library, for example Keras, Tensorflow.

Fundamentals of deep learning: What is deep learning? Concept ofneural network.

Neural network: Feed Forward Neural Networks (FFNN), ConvolutionalNeural Networks (CNN), Recurrent Neural Networks (RNN), Deep SequenceModelling, Deep Generative Models.

Algorithms: Backpropagation, Stochastic Gradient Descent (SGD).

Applications: Image Recognition, Mortality Forecasting, Insuranceand Finance.

This module is designed to cover: Ethics and compliance of data science. Impact of international regulations. Appropriate handling of data. Simple random sampling. Sampling for proportions and percentages. Estimation of sample size. Stratified sampling. Systematic sampling. Cluster sampling. Data streams. Finding frequentist items. Estimating the number of distinct elements. Sparse recovery. Weight-based sampling. Real time analytics. Network data: Density, clustering coefficient, centrality and degree distribution.