Syllabus

The first module of the course is dedicated to the review of the concepts and operations at the basis of a measurement. A measurement starts by reviewing the properties of the quantity of interest, of the method of measurement, and of the instrument chosen to perform the measurement. Such information is distilled by means of probability theory into mathematical functions to express the observer's degree of belief the true value of the quantity of interest lies within a certain range.

This module is structured in the following 3 submodules:

1. The concepts at the basis of a measurement and the meaning of the result of a measurements.

2. Review of the basic concepts of probability theory, of the interpretation of probability statements, and of the laws of probabilistic theory. Probability calculus, random variables, and functions of random variables. Graphical representation of probability by means of the bayesian networks. Connection between probability theory and measurement's uncertainty.

3. Introduction to probabilistic inference and usage of the Bayes theorem. Inversion of probability. Assignment of prior probability. Parametric inference and model inference. Model comparison, odds ratio, Bayes factor, and Ockham Razor.

The second module is devoted to a thorough discussion of the concepts presented in the first module. Several examples inspired by real situations occurring in the scientific research are proposed. Many examples will be provided in R and python. The topics discussed include:

• Main probability functions and their typical usage.

• Inference with binomial, poissonian, and normal likelihood. Multivariate inference.

• Systematic errors, uncertainty propagation and combination of measurements.

• Model fitting and parameter estimations.

• Model comparison.

• Markov Chain Monte Carlo and numerical approach to probabilistic inference.

• Unfolding the detector response from a measurement.