646
L. Lyons
Summer Schools for graduate students regularly have a series of lectures on statistics
for Particle Physics[21].
This article is a slightly updated version of the one that appeared in ref. [22] in
2012.
15.1.1 Types of Statistical Analysis
There are several different types of statistical procedures employed by Particle
Physicists:
• Separating signal from background: Almost every Particle Physics analysis
uses some method to enhance the possible signal with respect to uninteresting
background.
• Parameter determination: Many analyses make use of some theoretical or
empirical model, and use the data to determine values of parameters, and their
uncertainties and possible correlations.
• Goodness of fit: Here the data are compared with a particular hypothesis, often
involving free parameters, to check their degree of consistency.
• Comparing hypotheses: The data are used to see which of two hypotheses is
favoured. These could be the Standard Model (SM), and some specific version of
new physics such as the existence of SUperSYmmetry (SUSY), or the discovery
of the Higgs boson[23].
• Decision making: Based on one’s belief about the current state of physics, the
value of possible discoveries and estimates of the difficulty of future experiments,
a decision is made on what should be thrust of future research. This subject is
beyond the scope of this article.
15.1.2 Statistical and Systematic Uncertainties
In general any attempt to measure a physics parameter will be affected by statistical
and by systematic uncertainties. The former are such that, if the experiment were
to be repeated, random effects would result in a distribution of results being
obtained. These can include effects due to the limited accuracy of the measurement
devices and/or the experimentalist; and also from the inherent Poisson variability
of observing a number of counts n. On the other hand, there can be effects that
shift the measurements from their true values, and which need to be corrected for;
uncertainties in these corrections contribute to the systematics. Another systematic
effect could arise from uncertainties in theoretical models which are used to interpret
the data. Scientists’ systematics are often ‘nuisance parameters’ for statisticians.
Consider an experiment designed to measure the temperature at the centre of
the sun by measuring the flux of solar neutrinos on earth. The main statistical
L. Lyons
Summer Schools for graduate students regularly have a series of lectures on statistics
for Particle Physics[21].
This article is a slightly updated version of the one that appeared in ref. [22] in
2012.
15.1.1 Types of Statistical Analysis
There are several different types of statistical procedures employed by Particle
Physicists:
• Separating signal from background: Almost every Particle Physics analysis
uses some method to enhance the possible signal with respect to uninteresting
background.
• Parameter determination: Many analyses make use of some theoretical or
empirical model, and use the data to determine values of parameters, and their
uncertainties and possible correlations.
• Goodness of fit: Here the data are compared with a particular hypothesis, often
involving free parameters, to check their degree of consistency.
• Comparing hypotheses: The data are used to see which of two hypotheses is
favoured. These could be the Standard Model (SM), and some specific version of
new physics such as the existence of SUperSYmmetry (SUSY), or the discovery
of the Higgs boson[23].
• Decision making: Based on one’s belief about the current state of physics, the
value of possible discoveries and estimates of the difficulty of future experiments,
a decision is made on what should be thrust of future research. This subject is
beyond the scope of this article.
15.1.2 Statistical and Systematic Uncertainties
In general any attempt to measure a physics parameter will be affected by statistical
and by systematic uncertainties. The former are such that, if the experiment were
to be repeated, random effects would result in a distribution of results being
obtained. These can include effects due to the limited accuracy of the measurement
devices and/or the experimentalist; and also from the inherent Poisson variability
of observing a number of counts n. On the other hand, there can be effects that
shift the measurements from their true values, and which need to be corrected for;
uncertainties in these corrections contribute to the systematics. Another systematic
effect could arise from uncertainties in theoretical models which are used to interpret
the data. Scientists’ systematics are often ‘nuisance parameters’ for statisticians.
Consider an experiment designed to measure the temperature at the centre of
the sun by measuring the flux of solar neutrinos on earth. The main statistical