PXT125: Data Analysis
School | Cardiff School of Physics & Astronomy |
Department Code | PHYSX |
Module Code | PXT125 |
External Subject Code | 100425 |
Number of Credits | 10 |
Level | L7 |
Language of Delivery | English |
Module Leader | PROFESSOR Haley Gomez |
Semester | Autumn Semester |
Academic Year | 2023/4 |
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
Test (Quizzes) 15%. Coursework 35%. Project 50%.
Assessment Breakdown
Type | % | Title | Duration(hrs) |
---|---|---|---|
Class Test | 15 | Quizzes | N/A |
Written Assessment | 35 | Continuous Assessment | N/A |
Project | 50 | Project | N/A |
Syllabus content
The basics: Displaying and interpreting data. Data mining, causes of uncertainty. Error propagation and transformation bias.
Introduction to Bayesian Foundations: What is probability, distributions, hypothesis testing (t-tests, Mann Whitney, Kolmogorov-Smirnov test), confidence intervals; Bayes theory, priors. Techniques for estimating the evidence term.
Parameter Estimation and sampling: Relationships between quantities, correlation; minimizing and maximizing functions, global and local minima, least squares, maximum likelihood, Principle component analysis, Differences between linear and non-linear function fitting. Techniques for non-linear function fitting.
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, filtering techniques, cross-correlation.