Advanced Statistics For Physics Analysis

Period: Second semester

Course unit contents: 

Review of basic concepts: probability, odds and rules, updating probabilites, uncertain numbers (probability functions)
- from Bernoulli trials to Poisson processes and related distributions
- Bernoulli theorem and Central Limit Theorem
- Inference of the Bernoulli p; inference of lambda of the Poisson distribution. Inference of the Gaussian mu. Simultaneous inference of mu and sigma from a sample: general ideas and asymptotic results (large sample size).
- fits as special case of parametric inference
- Monte Carlo methods: rejecion sampling, inversion of cumulative distributions, importance sampling. Metropolis algorithm as example of Markov Chain Monte Carlo. Simulated annealing
- the R framework and language for applied statistics.

Planned learning activities and teaching methods: Lectures complemented by practical examples with laboratory exercises to be solved with the R analysis framework.

In addition to contacting the course instructor, students with disabilities, Specific Learning Disorders (SLD), Special Educational Needs (SEN), and other health conditions can reach out to the Student Services Office - Inclusion Unit to receive more information about opportunities to access teaching with specific support and tools.

The use of generative-AI tools (e.g. ChatGPT) is permitted only for group projects. Any use must be clearly declared and must comply with University of Padova and with the Physics of Data policies on academic integrity.