87947 - Statistical Data Analysis for Applied Physics

Learning outcomes

At the end of the course the student will be acquainted with the main statistical concepts used in Physics. After a review of the fundamentals of probability theory, parametric inferential statistics will be introduced, from point estimates and confidence intervals to hypothesis testing and goodness-of-fit. Each item will be addressed both in the Bayesian and frequentist approaches. Dedicated practical sessions will allow the student to become familiar with these conceptual tools by studying applications in Applied Physics.

Course contents

Module 1 – Foundations of probability theory and statistics; introduction to using R for statistical analysis (taught by E. Giampieri)
Module 2 – Hypothesis testing; linear models (basic, generalized, additive, penalized) (taught by C. Sala)

Syllabus – Module 1

• Introduction to R

• Managing tabular data; basic operations

• Concept of probability: axiomatic, combinatorial, frequentist, and subjectivist definitions. Conditional probability. Statistical independence. Bayes’ theorem. Principle of indifference and Bertrand’s paradox.

• Random variables and probability density functions. Multivariate distributions. Marginal and conditional densities. Functions of random variables.

• Descriptive statistics: expectation, variance, covariance, median, quantiles, mode.

• Examples of distributions: binomial, multinomial, Poisson, exponential, normal, multivariate normal, chi-squared, Breit-Wigner, Landau.

• Central limit theorem, law of large numbers.

• Monte Carlo methods: convergence criteria, integral estimation and uncertainties, variance reduction.

• Error propagation – theoretical concepts and simulations; synthetic data.

• Parameter estimation: fundamental concepts, Bayesian and frequentist approaches.

• Statistical tests: introduction; false positives and negatives; various fallacies; Bayesian and frequentist perspectives. Concept of prior, Jeffreys priors, utility theory.

Syllabus – Module 2

• Hypothesis testing. Student’s t-test. Fisher’s F-test.

• P-value. Statistical significance and power.

• Correlation. Linear regression. Ordinary Least Squares (OLS). Maximum Likelihood Estimation (MLE).

• Analysis of variance (ANOVA).

• Generalized linear models. Logistic regression.

• Multivariate linear regression. Multicollinearity. Lasso, Ridge, and Elastic-net regularization.

• Survival analysis. Log-rank test. Kaplan–Meier curve. Cox model.

• Generalized additive models (GAMs).

Readings/Bibliography

Module 1

• Glen Cowan, Statistical Data Analysis, Oxford University Press, 1998

• (Optional, for deeper statistical insights) Trevor Hastie et al., The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Vol. 2, Springer, 2009

Module 2

• John Maindonald and W. John Braun, Data Analysis and Graphics Using R – An Example-Based Approach, Cambridge University Press, 2003

• Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, An Introduction to Statistical Learning with Applications in R, Springer, 2013

• Simon N. Wood, Generalized Additive Models – An Introduction with R, Chapman and Hall/CRC, 2017

Teaching methods

Lectures will cover theoretical elements and include peer-learning group exercises to support comprehension and engagement.

Assessment methods

The final examination will be conducted jointly with the instructors of both modules and can be completed in one of two ways:

1. Oral exam: theoretical comprehension questions and critical discussion of statistical analyses from the literature.

2. Project: agreed upon with the instructors, involving the analysis of a dataset to answer specific research questions, and the production of a written report detailing the methodology and results (accompanied by the analysis code).

Students with learning disabilities (DSA) or temporary/permanent disabilities: are encouraged to contact the university’s support office in advance https://site.unibo.it/studenti-con-disabilita-e-dsa/it . The office will propose any necessary accommodations, which must be submitted to the instructors at least 15 days in advance for approval, based on the course’s learning objectives.

Teaching tools

Lecture slides are available on the course’s GitHub page.

Office hours

See the website of Enrico Giampieri

See the website of Claudia Sala