209 research outputs found
Statistical Models with Uncertain Error Parameters
In a statistical analysis in Particle Physics, nuisance parameters can be
introduced to take into account various types of systematic uncertainties. The
best estimate of such a parameter is often modeled as a Gaussian distributed
variable with a given standard deviation (the corresponding "systematic
error"). Although the assigned systematic errors are usually treated as
constants, in general they are themselves uncertain. A type of model is
presented where the uncertainty in the assigned systematic errors is taken into
account. Estimates of the systematic variances are modeled as gamma distributed
random variables. The resulting confidence intervals show interesting and
useful properties. For example, when averaging measurements to estimate their
mean, the size of the confidence interval increases for decreasing
goodness-of-fit, and averages have reduced sensitivity to outliers. The basic
properties of the model are presented and several examples relevant for
Particle Physics are explored.Comment: 26 pages, 27 figure
Effect of Systematic Uncertainty Estimation on the Muon Anomaly
The statistical significance that characterizes a discrepancy between a
measurement and theoretical prediction is usually calculated assuming that the
statistical and systematic uncertainties are known. Many types of systematic
uncertainties are, however, estimated on the basis of approximate procedures
and thus the values of the assigned errors are themselves uncertain. Here the
impact of the uncertainty {\it on the assigned uncertainty} is investigated in
the context of the muon anomaly. The significance of the observed
discrepancy between the Standard Model prediction of the muon's anomalous
magnetic moment and measured values are shown to decrease substantially if the
relative uncertainty in the uncertainty assigned to the Standard Model
prediction exceeds around 30\%. The reduction in sensitivity increases for
higher significance, so that establishing a effect will require not
only small uncertainties but the uncertainties themselves must be estimated
accurately to correspond to one standard deviation.Comment: 6 pages, 2 figure
Asymptotic formulae for likelihood-based tests of new physics
We describe likelihood-based statistical tests for use in high energy physics
for the discovery of new phenomena and for construction of confidence intervals
on model parameters. We focus on the properties of the test procedures that
allow one to account for systematic uncertainties. Explicit formulae for the
asymptotic distributions of test statistics are derived using results of Wilks
and Wald. We motivate and justify the use of a representative data set, called
the "Asimov data set", which provides a simple method to obtain the median
experimental sensitivity of a search or measurement as well as fluctuations
about this expectation.Comment: fixed typo in equations 75 & 7
Higher-order asymptotic corrections and their application to the Gamma Variance Model
We present improved methods for calculating confidence intervals and
-values in a specific class of statistical model that can incorporate
uncertainties in parameters that themselves represent uncertainties
(informally, ``errors on errors'') called the Gamma Variance Model (GVM). This
model contains fixed parameters, generically called , that
represent the relative uncertainties in estimates of standard deviations of
Gaussian distributed measurements. If the parameters are small,
one can construct confidence intervals and -values using standard asymptotic
methods. This is formally similar to the familiar situation of a large data
sample, in which estimators for all adjustable parameters have Gaussian
distributions. Here we address the important case where the
parameters are not small and as a consequence the asymptotic distributions do
not represent a good approximation. We investigate improved test statistics
based on the technology of higher-order asymptotics ( approximation and
Bartlett correction).Comment: 22 pages, 8 figure
Comparison of unfolding methods using RooFitUnfold
In this paper we describe RooFitUnfold, an extension of the RooFit
statistical software package to treat unfolding problems, and which includes
most of the unfolding methods that commonly used in particle physics. The
package provides a common interface to these algorithms as well as common
uniform methods to evaluate their performance in terms of bias, variance and
coverage. In this paper we exploit this common interface of RooFitUnfold to
compare the performance of unfolding with the Richardson-Lucy, Iterative
Dynamically Stabilized, Tikhonov, Gaussian Process, Bin-by-bin and inversion
methods on several example problems
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