  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.
