Introductory description

N/A.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Basic probability: distributions characteristic functions.

Basic statistics: sample mean and variance, law of large numbers and central-limit theorem

Frequentist statistics: point estimation, confidence integrals, type-I and II errors, hypothesis tests

Bayesian statistics: likelihood, maximum likelihood, Bayes theorem, conjugate priors, credible intervals

Spectral methods for time-series analysis Ornstein-Uhlenbeck process, autocovariance, power spectrum, Weiner-Khinchin theorem

Machine-learning approaches to data analysis: gradient descent, logistic regression, linear classifier, neural networks, backpropogation and networks with hidden layers.

Learning outcomes

By the end of the module, students should be able to:

• By the end of this module, the students will be able to quantitatively summarise and critically assess data from real-world systems.
• By the end of this module, the students will be able to use modern methods of parameter estimation to model and forecast time-series data.
• By the end of this module, the students will be able to compute and interpret spectral representations of time-series data and incorporate observations into mathematical models to reduce the uncertainty in predictions made using these models.

Indicative reading list

C.M. Bishop, Pattern Recognition and Machine Learning, Springer 2006

J.D. Hamilton, Time Series Analysis, Princeton University Press 1994

G.E.P. Box, G.M. Jenkins and G.C. Reisel, Time Series Analysis: Forecasting and Control, Prentice Hall 1994

Notes and scientific literature provided during lectures

Subject specific skills

See learning outcomes.

Transferable skills

Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.