Lecturer: Magnus Richardson (Mathematics Institute and Zeeman Institute)
This is a core module for the MSc in Mathematics of Systems. The main aims are to provide the students with a broad knowledge of modern techniques of exploratory data analysis, time series modelling and forecasting, spectral analysis, data assimilation and machine learning. By the end of this module, the students will be able to quantitatively summarise and critically assess data from real-world systems, use modern methods of parameter estimation to model and forecast time-series data, 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.
- 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.
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
See main calendar for timetable
- Per week: 2 x 2 hours of lectures, 2 x 2 hours of classwork
- Duration: 5 weeks (second half of term 1)
For deadlines see Module Resources page
- Written homework assignments (20%)
- Written class test (40%) and
- Oral examination (40%)