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CO902 Probabilistic and statistical inference

This programme is no longer running.

Module Syllabus and Resources 2016

Taken by students from:

Code Degree Title Year of study core or option credits
P-F3P4 Complexity Science MSc




P-F3P5 Complexity Science MSc+PhD




P-F3P6/7 Erasmus Mundus Masters in Complex Systems




Context: This is the second opening module of the Complexity DTC taught programme.

Module Aims:

The problem of searching for regularities in data and using such regularities to better understand the properties of the system from which the data were obtained has a long history in science. In recent years, there has been a massive increase in our ability to collect data from complex systems of all kinds, from living cells to the Internet. The field of machine learning is concerned with computational methods for analyzing such data. This course introduces key concepts in machine learning, with a particular emphasis on approaches relevant to “reverse-engineering” complex systems with multiple interacting components.

link to Learning Outcomes

Syllabus 2013:

1. Probability and statistical inference

  • Probability: including Bayes' rule, Markov chains and Monte Carlo integration.
  • Parametric statistical models: including likelihood functions, estimators, and an introduction to Bayesian inference.

2. Supervised learning: classification and regression

  • Introduction: training versus test data, notions of overfitting and cross-validation.
  • Regression: including least squares, ridge regression and Bayesian approaches.
  • Classification, including multivariate class-conditional distributions and generalised linear models.

3. Unsupervised learning: dimensionality reduction and clustering

  • Dimensionality reduction, including principal components analysis
  • Clustering, including k-means, mixture models and the expectation-maximisation algorithm


Main textbook: Pattern Recognition and Machine Learning, C. M. Bishop (Springer-Verlag Series in Information Science & Statistics, 2006)

Recommended texts:

Probability and statistics 

  • Probability and statistics, M. H. De Groot & M. J. Schervish (Addison-Wesley, 2002)
  • Statistical Inference (2nd Ed), Casella & Berger (Duxbury Press, 2001)
  • Bayesian Data Analysis, A. Gelman et al. (Chapman & Hall, 2004)

Machine learning

  • The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd Ed. (Springer, 2009)
  • Pattern Classification , R. O. Duda et al. (Wiley, 2000)


  • Getting Started with MATLAB: A Quick Introduction for Scientists and Engineers (OUP, 2009)
  • Mastering MATLAB 7, D. Hanselman & B. Littlefield (Pearson, 2012)

Teaching 2016:

Lectures per week

2 x 2 hours

Classwork sessions per week

Lecture: Mondays 14:00-16:00
Fridays 14:00-16:00

D1.07 Complexity

Module duration

10 weeks

Total contact hours


Private study and group working


Assessment information:


Week  Assessment  Issued  Deadline  %credit


Written assignment 5 Feb 19 Feb


4-8 Written assignment 26 Feb 11 Mar


10 Oral Examination

14 Mar