# Friday 15 Dec 2017: Bayesian data analysis tools for physics

### Martino Trassinelli - Institut des NanoSciences de Paris

**Newman Red** 12:30-13:30

Classical statistical methods as the maximum likelihood and minimum chi-square methods, are widely and successfully implemented for data analysis of many and different experiments. However, they have some limitations due their basic assumptions. These methods are based on the probability maximization to obtain certain data values for a given set of model parameters. But what commonly is required is just the opposite; for given experimental data, one would like to obtain the probability for having certain parameter values. In general this does not cause major problems except in cases where prior information of the analysis parameter is important. For example, if the studied parameter is a mass, it has to be strictly positive, which cannot be correctly taken into account in the maximum likelihood method. Another problematic case occurs when we want to test different models for describing a same set of data. Classical approaches provide criterion methods to determine the more likely model but they cannot assign probabilities for each hypothesis. To overcome these and other difficulties, a different approach has to be implemented with a new and more general definition of probability. This approach is the result of the work of Th. Bayes (1783), P.-S. Laplace (19^{th} century), H. Jeffreys and of many others (20^{th} century) and is commonly called Bayesian statistics. Bayesian methods are routinely used in many fields: cosmology, particle physics, nuclear physics, etc. They are in fact particularly useful for rare phenomena where the use of standard probability, based on the principle of infinite experiment repeatability, is not justified. We present here an introduction to the concepts of Bayesian statistics with the application to simple examples.