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Department of Computer Science and Technology



Course pages 2023–24

Data Science

Principal lecturer: Dr Damon Wischik
Taken by: Part IB CST
Term: Michaelmas
Hours: 16 (16 lectures)
Format: In-person lectures
Suggested hours of supervisions: 4
Prerequisites: Mathematics for Natural Sciences
This course is a prerequisite for: Advanced Data Science, Computer Systems Modelling, Machine Learning and Bayesian Inference, Natural Language Processing, Quantum Computing
Exam: Paper 6 Question 5, 6
Past exam questions, Moodle, timetable


This course introduces fundamental tools for describing and reasoning about data. There are two themes: designing probability models to describe systems; and drawing conclusions based on data generated by such systems.


  • Specifying and fitting probability models. Random variables. Maximum likelihood estimation. Generative and supervised models. Goodness of fit.
  • Feature spaces. Vector spaces, bases, inner products, projection. Linear models. Model fitting as projection. Design of features.
  • Handling probability models. Handling pdf and cdf. Bayes’s rule. Monte Carlo estimation. Empirical distribution.
  • Inference. Bayesianism. Frequentist confidence intervals, hypothesis testing. Bootstrap resampling.
  • Random processes. Markov chains. Stationarity, and drift analysis. Processes with memory. Learning a random process.


At the end of the course students should

  • be able to formulate basic probabilistic models, including discrete time Markov chains and linear models
  • be familiar with common random variables and their uses, and with the use of empirical distributions rather than formulae
  • understand different types of inference about noisy data, including model fitting, hypothesis testing, and making predictions
  • understand the fundamental properties of inner product spaces and orthonormal systems, and their application to modelling

Recommended reading

* F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester (2005). A modern introduction to probability and statistics: understanding why and how. Springer.

S.M. Ross (2002). Probability models for computer science. Harcourt / Academic Press.

M. Mitzenmacher and E. Upfal (2005). Probability and computing: randomized algorithms and probabilistic analysis. Cambridge University Press.