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In the past years, many advanced techniques in statistical data analysis have been used in High Energy Physics (such as maximum likelihood fits, Neural Networks, and Decision Trees). In the past, the most common technique was the simple cut and count analysis. This technique consists in the following steps: several cuts are applied on well studied discriminating variables, background estimation is performed using Monte Carlo simulation samples or events outside the signal region, and then the final measurement is done counting the events after cuts minus the estimated background events.

This simple technique is hampered by its  low efficiency (defined as ratio between the number events after and before the cuts) and does not provide a good discrimination between signal and background events. For this reason it was replaced by more sophisticated techniques, such as the multivariate maximum likelihood for the measurements done at the BaBar experiment, running at Stanford Linear Accelerator Center (SLAC) in California.

The maximum likelihood (ML) technique permits to achieve higher efficiency, the possibility to take in account errors with a better precisions, and consider correlations between the discriminating variables used in the analysis. Anyway, in future experiments, like LHC experiments at CERN, it may be crucial to have better discrimination between signal and background events to discover new phenomenas, which suffer higher background. Neural Networks and Decision Trees are good techniques to reach this goal. Another important issue to take into account lies in the fact  that these techniques are in most cases very CPU-time consuming. It is possible to speed them up using concepts of High Performance Computing (HPC).

In this lecture we will give an overview of the advanced data analysis techniques mentioned above, introducing some software packages commonly used in HEP. This will be preceded by a short session at the end of the previous theme,  giving briefly examples of possible HPC optimizations.