# Core05: Mathematical Analytics - Archived material for the year 2019-2020

This course addresses short- and long-term challenges arising in customer-facing industries and will exploit data available from shopping baskets, twitter, mobile telecoms and energy demands. The course will start with probability, covers graphs and their application to social networks, looks at dynamically evolving networks, clustering and classification, hypothesis testing and forecasting.

Odds, likelihoods and evidence; Common pitfalls; Bayes' theorem, updating, probability distributions, Laplace's law of succession, Monte Hall problem, conjugate priors, transposed conditionals.

Self-adjoint matrices, non-negative matrices, Perron-Frobenius theory, Singular value decomposition, graph theory, similarity matrices, random matrices, clustering, range dependent networks, small world networks, scale-free networks., inverse problems for networks.

Katz centrality, matrix valued functions, corporate email networks, mobile phone call networks, fragility of networks, discrete time evolving networks, and continuous time evolving networks.

Twitter networks, diffusion on networks, fully coupled networks, activator-inhibitor systems, homophily, Turing instabilities, transient influencers, Event driven activity spikes, justifying investments in digital advertising, Bootstrap sampling, embedding, Bayes Factors

K-means clustering, the EM algorithm, finite mixture modelling, behavioural segmentations, energy demand, mobile phone usage, supermarket customer shopping missions.

Multiple hypotheses, Bayesian updating, Beatles versus Stones, Mobile phone networks, logistic regression.

Bayesian updating, product launches, linear models, domestic energy demand, smart meter data, discrete and continuous optimization.

Customer behaviour and customer value, Markov chains, genetic algorithms, behavioural dynamics, seasonality, case studies.

• P. Grindrod, The Mathematical Underpinnings of Analytics, OUP, 2014

• E.T. Jaynes and G.L. Bretthorst, Probability Theory: The Logic of Science, CUP, 2003

*Please note that e-book versions of many books in the reading lists can be found on SOLO and ORLO.*