## Computing Likelihood Functions for High-Energy Physics Experiments
when Distributions are Defined by Simulators with Nuisance Parameters

**Radford M. Neal,
Dept. of Statistics and Dept. of Computer Science, University of Toronto**

When searching for new phenomena in high-energy
physics, statistical analysis is complicated by the presence of
nuisance parameters, representing uncertainty in the physics of
interactions or in detector properties. Another complication, even
with no nuisance parameters, is that the probability distributions of
the models are specified only by simulation programs, with no way of
evaluating their probability density functions. I advocate expressing
the result of an experiment by means of the likelihood function,
rather than by frequentist confidence intervals or *p*-values. A
likelihood function for this problem is difficult to obtain, however,
for both of the reasons given above. I discuss ways of circumventing
these problems by reducing dimensionality using a classifier and
employing simulations with multiple values for the nuisance
parameters.

In the proceedings of the PHYSTAT-LHC Workshop on Statistical
Issues for LHC Physics, June 2007, CERN 2008-001, pp. 119-126:
Postscript, PDF.

Full proceedings available
here.