Statistical Methods in Experimental Particle Physics

The course is based on a series of guided exercises in computational statistics of progressively increasing complexity, ranging from simple simulations to realistic case studies inspired by modern experimental particle physics. Lectures will be held once or twice per week and will introduce the statistical concepts and computational techniques required to solve the proposed exercises. Students will be expected to submit their solutions regularly and discuss them during class. Short written reports will accompany some of the exercises. The final case studies will reproduce, in simplified form, selected research problems encountered in contemporary particle-physics experiments. The corresponding written reports will constitute part of the final assessment.

The course covers the main concepts of statistical inference, including point estimation, interval estimation, hypothesis testing, and goodness-of-fit techniques, together with practical examples based on the ROOT data-analysis framework and the C++ programming language. Students may use their preferred software environment to complete the exercises. However, ROOT is strongly recommended and fully supported by the instructor. A prerequisite for the course is the ability to use a programming environment capable of performing numerical calculations, generating random numbers, producing histograms, and visualizing data.

The main topics covered in the course include:

- Foundations of probability theory: frequentist and Bayesian interpretations, conditional probability, independence, and Bayes’ theorem.

- Random variables, probability density functions, moments, characteristic functions, and generating functions.

- Law of Large Numbers and Central Limit Theorem.

- Common probability distributions in particle physics: binomial, Poisson, Gaussian, and exponential distributions.

- Likelihood function and principles of statistical inference.

- Bayesian inference and the role of prior information.

- Sufficient statistics, Fisher information, and information-preserving data reduction.

- Point estimation: bias, consistency, efficiency, method of moments, and maximum likelihood estimation.

- Least-squares methods, chi-square minimization, and likelihood fitting of binned and unbinned data.

- Interval estimation: confidence intervals, coverage, Bayesian credible intervals, and the Feldman–Cousins approach.

- Likelihood-ratio methods, Wilks’ theorem, profile likelihoods, and treatment of nuisance parameters.

- Statistical hypothesis testing: significance, power, Neyman–Pearson lemma, likelihood-ratio tests, and optimal tests.

- Goodness-of-fit tests, p-values, and model validation.

- Multiple testing, the Look-Elsewhere Effect, local and global significance, and statistical methods for searches for rare signals in high-energy physics.

Below is a non-exhaustive list of examples of guided exercises:

- Branching-fraction measurement of a decay process (multidimensional unbinned likelihood fit);

- Particle identification using Cherenkov-radiation detectors (hypothesis testing, likelihood ratios);

- Lifetime measurement of an unstable particle (resolution modelling and background subtraction);

- Search for a rare decay process in the presence of background (significance estimation, confidence intervals, Look-Elsewhere Effect);

- Vertex reconstruction in a silicon tracking detector (least-squares fit with constraints);

- Measurement of the detection asymmetry of neutral kaons propagating through matter (profile likelihood methods with nuisance parameters);

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