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.