PX4128: Data Analysis
| School | Cardiff School of Physics & Astronomy |
| Department Code | PHYSX |
| Module Code | PX4128 |
| External Subject Code | 100425 |
| Number of Credits | 10 |
| Level | L7 |
| Language of Delivery | English |
| Module Leader | Dr Paul Clark |
| Semester | Autumn Semester |
| Academic Year | 2015/6 |
Outline Description of Module
To introduce students to the mathematical and statistical techniques used to analyse physics data. Similar techniques are also employed in a non-physics environment such as financial modeling, industry or other sciences.
To develop research skills, computing skills and the ability to work independently.
To translate raw data into a robust measurement and to interpret data given a hypothesis.
To be familiar with approaches and methods in interpreting data, particularly with large data sets.
To be familiar with using statistical techniques and methods of quantitative analysis of data.
To develop sound judgment in interpreting experimental results and uncertainties.
To gain experience with analyzing and interpreting real data sets from physics and astronomy.
On completion of the module a student should be able to
Calculate the uncertainty in quantities derived from experimental results of specified precision.
Use the method of least squares-fitting and interpret chi-squared.
Articulate the differences between, and strengths and limitations of Bayesian and Frequentist approaches.
Apply a simple MCMC program to physical data.
Demonstrate by application to real data, an understanding of probability, priors, parameter estimation and sampling.
How the module will be delivered
Lectures 22 x 1 hr, Exercises, group work and computing 11 x 1 hr.
Skills that will be practised and developed
Problem solving. Analytical skills. Investigative skills. Computational skills. Mathematics. Communication Skills.
How the module will be assessed
Continuous Assessment 100%.
Assessment Breakdown
| Type | % | Title | Duration(hrs) |
|---|---|---|---|
| Written Assessment | 100 | Data Analysis | N/A |
Syllabus content
The basics: Displaying and interpreting data. Data mining, causes of uncertainty. Linear error propagation.
Introduction to Bayesian Foundations: What is probability, distributions, hypothesis testing (t-tests, Mann Whitney, Kilmogorov-Smirnov test), confidence intervals; Bayes theory, priors.
Parameter Estimation and sampling: Relationships between quantities, correlation; minimizing and maximizing functions, global and local minima, least squares, maximum likelihood, singular-value decomposition, Principle component analysis.
Sampling: Bias, Monte Carlo sampling, pseudo random distributions, MCMC method, bootstrapping and Jack-knife samples, multivariate analysis techniques.
Time-frequency analysis and Image/Signal Processing: Fourier techniques including convolution, deconvolution, filtering techniques, wavelets, Floquet modes, modulation.
Background Reading and Resource List
Python for Data Analysis
Bayesian Reasoning in Data Analysis: A Critical Introduction
Principles of data analysis, P Saha,
Handbook of Astronomical Data Analysis