Statistical Data Analysis (SDA | SPA6328)

Year: 3 | Semester: A | Level: 6 | Credits: 15

Course organiser: Dr Adrian Bevan | Course deputy: Dr Marcella Bona

Synopsis:

This course will review basic metrics and techniques used to describe ensembles of data such as averages, variances, standard deviation, errors and error propagation. These will be extended to treat multi-dimensional problems and circumstances where observables are correlated with one another. The Binomial, Poisson, and Gaussian distributions will be discussed, with emphasis on physical interpretation in terms of events. Concepts of probability, confidence intervals, limits, hypothesis testing will be developed. Optimization techniques will be introduced including chi^2 minimisation and maximum-likelihood techniques. A number of multivariate analysers (sample discriminants) will be discussed in the context of data mining. These will include Fisher discriminants, multi-layer perceptron based artificial neural networks, decision trees and genetic algorithms.

Aims:

The aim is to demonstrate the use of statistics in making measurements that underpin the whole of the physical sciences. Students will see and understand the fundamental concepts of statistics developed through to a treatment of Baysean and Frequentist interpretations of probability, errors, error propagation, hypotheses, confidence intervals and limits, optimisation using chi^2 and maximum likelihood techniques, set theory sufficient to describe sub-samples of data, data mining techniques used to separate samples from more than one population in a data set.

Outcomes:

A student passing this course should be suitably equipped to appreciate the meaning of the word measurement in a scientific context, and understand how to translate raw data into a robust measurement, or to otherwise interpret the data with reference to a given hypothesis. They will be prepared to use data analysis techniques in future research, either in a project assignment, industry or future graduate studies. The material learned through this module could also benefit in a non-physics environment that used similar techniques such as financial modelling or industrial research.

Recommended books:

Statistical data analysis for the physical sciences (Cambridge University Press) by A. Bevan. ISBN-10 1107670349

Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences (Manchester Physics Series)
by Prof. R. Barlow. ISBN-10: 0471922951

Statistical Data Analysis (Oxford science publications) 
by G. Cowan. ISBN-10: 0198501552

Statistical Methods in Experimental Physics (World Scientific) 
by F. James. ISBN-10: 9812705279