Physics Data Analysis Course

Lesson 1 • Measurement and Physical Quantities

Covers SI units, dimensional analysis, and scalar vs. vector quantities. Establishes the language needed for all subsequent data interpretation.

Lesson 2 • Descriptive Statistics for Physics

Applies mean, median, variance, and standard deviation to physical datasets. Connects statistical summaries to physical interpretation of repeated measurements.

Lesson 3 • Experimental Uncertainty Basics

Introduces systematic and random errors and their sources. Provides the framework for quantifying measurement reliability throughout the course.

Lesson 4 • Data Representation and Visualization

Teaches correct graph construction, axis labeling, and error bar placement. Proper visualization is essential for communicating experimental results accurately.

Lesson 1 • Other Distributions in Physics

Introduces chi-squared, Student's t, and Breit-Wigner distributions. Each is linked to specific physics analysis contexts such as goodness-of-fit and resonance peaks.

Lesson 2 • Poisson and Binomial Distributions

Presents counting-event statistics relevant to particle and nuclear physics. Students apply these distributions to detector count data.

Lesson 3 • The Gaussian Distribution

Derives the normal distribution and its parameters from first principles. The Gaussian is the most common model for measurement noise in physics.

Lesson 4 • Core Probability Concepts

Covers sample spaces, events, and conditional probability. These concepts underpin all statistical inference applied to experimental data.

Lesson 1 • Systematic Uncertainty Estimation

Identifies and quantifies systematic effects such as calibration drift and environmental factors. Distinguishes systematic from statistical contributions in a budget.

Lesson 2 • Numerical Uncertainty Propagation

Uses Monte Carlo methods to propagate uncertainties when analytical formulas are intractable. Complements the analytical approach for complex functions.

Lesson 3 • Uncertainty in Derived Physical Constants

Applies propagation techniques to compute uncertainties in derived quantities like density and refractive index. Reinforces skills with realistic physics examples.

Lesson 4 • Uncertainty Budgets and Reporting

Structures contributions from multiple error sources into a formal uncertainty budget. Teaches standard reporting formats aligned with metrology best practices.

Lesson 1 • Linear Least-Squares Fitting

Derives the ordinary least-squares estimator for linear models. Provides the analytical foundation for all regression techniques in the chapter.

Lesson 2 • Nonlinear Curve Fitting

Extends fitting to arbitrary model functions using iterative numerical optimization. Students fit exponential, power-law, and oscillatory models to data.

Lesson 3 • Polynomial and Multivariate Regression

Extends regression to polynomial models and multiple predictor variables. Addresses overfitting risks and model selection criteria.

Lesson 4 • Maximum Likelihood Estimation

Introduces MLE as a general parameter estimation framework beyond least squares. Connects likelihood functions to Gaussian and Poisson data models.

Lesson 1 • Multiple Testing and Look-Elsewhere Effect

Addresses inflated false-positive rates when many tests are performed simultaneously. Teaches Bonferroni correction and the look-elsewhere effect in searches.

Lesson 2 • Foundations of Hypothesis Testing

Defines null and alternative hypotheses, test statistics, and significance levels. Establishes the decision framework used throughout experimental physics.

Lesson 3 • Confidence Intervals and Limits

Constructs confidence intervals for measured parameters and upper limits for undetected signals. Connects interval estimation to hypothesis test inversion.

Lesson 4 • Common Statistical Tests in Physics

Applies t-tests, z-tests, and F-tests to physics measurement comparisons. Students select the appropriate test based on sample size and variance knowledge.

Lesson 1 • Fourier Analysis Fundamentals

Introduces the Fourier series and transform as tools for decomposing signals into frequency components. Builds the mathematical basis for all spectral methods.

Lesson 2 • Autocorrelation and Cross-Correlation

Uses correlation functions to detect periodicity and measure time delays between signals. Applied to gravitational wave and optical physics datasets.

Lesson 3 • Power Spectral Density and Noise

Computes power spectral density to characterize noise floors and signal strength. Distinguishes white, pink, and shot noise in physics measurements.

Lesson 4 • Filtering and Signal Processing

Designs low-pass, high-pass, and band-pass filters to isolate physics signals. Applies digital filtering using SciPy to experimental time-series data.

Lesson 1 • Bayesian Model Comparison

Uses Bayes factors and evidence integrals to compare competing physics models. Applies nested sampling to compute model evidence efficiently.

Lesson 2 • Prior Selection and Sensitivity

Guides selection of informative and non-informative priors for physics parameters. Analyzes how prior choice affects posterior conclusions.

Lesson 3 • Markov Chain Monte Carlo Sampling

Implements MCMC to sample high-dimensional posterior distributions intractable analytically. Covers Metropolis-Hastings and Gibbs sampling algorithms.

Lesson 4 • Bayesian Inference Framework

Formalizes Bayes' theorem as a parameter estimation tool and contrasts it with frequentist methods. Establishes prior, likelihood, and posterior concepts.

Lesson 1 • Multivariate Analysis and Dimensionality Reduction

Applies PCA and linear discriminant analysis to high-dimensional physics datasets. Reduces feature space while preserving physically meaningful variance.

Lesson 2 • Reproducible Analysis and Publication Standards

Structures analysis code for reproducibility, version control, and peer review. Aligns output formats with standards expected in physics journals.

Lesson 3 • Machine Learning for Signal Classification

Trains decision trees, random forests, and neural networks to classify physics events. Evaluates classifiers using ROC curves and area under the curve.

Lesson 4 • Particle Physics Data Analysis Pipeline

Constructs a full analysis chain from raw detector hits to invariant mass spectra. Applies fitting, background subtraction, and significance estimation.