Introductory course in data analysis
Bayesian metaphysics for experimental data

Author Ksenia N. Kyzyurova

Description

This course is an introductory course to data analysis. The course examines foundations for statistical model building and Bayesian statistical inference from such a model. The course focuses on applications of this methodology to analysis and inference from physical experiments. The ultimate goal of the course is to develop a student's intuition towards construction of such an experiment whose result is feasible for subsequent analysis within a simple statistical framework.

Prerequisites

MAS111 (Mathematics Core II)

Aims

• To introduce basic ideas and concepts of statistical modeling and Bayesian inference to general audience. (Mathematical aspects which necessitate the knowledge of probability theory and/or measure theory are omitted.)
• To attract students from other disciplines, e.g. physics, chemistry, engineering, biology, who work with experimental data, to stimulate interdisciplinary research efforts, with the goal of improving the practice of data analysis in these (or other) domain knowledge areas.
• To construct this course as a prerequisite for a special topic course "Bayesian analysis of scientific computer simulator data".
• To find students interested in performing a philosophy doctor (PhD) thesis with me.

Outline syllabus

• Experimental data, Statistical model, Bayesian inference.
• Foundations for data analysis of experimental data.
• Bayesian inverse problem.
• Implementation of analysis in R.

Teaching methods

• Lectures, tutorials, including problem-solving and computer simulations.

Assessment

Assignments

Full syllabus

1. Random variable; Distribution.
2. Statistical model: likelihood function; parametric specification of a model.
3. Bayesian inference: prior distribution, posterior distribution, marginal distribution, predictive distribution, posterior predictive distribution.
4. Implementation of the normal statistical model: proper and improper priors; discrete and continuous distributions; subjective inference and objective inference.
5. Inference from a statistical model: closed-form inference; conjugate analysis of a statistical model.
6. Numerical inference from a statistical model: Gibbs sampling.
7. Bayesian inverse problem: numerical sampling.
8. Computational implementation of data analysis in R: basic functions, distribution functions, elements of code testing, visualization of data analysis.

Reading list

• None.