In statistics, a confidence region is a multi-dimensional
generalization of a confidence interval. It is a set of points
in an n-dimensional space, often represented as an ellipsoid
around a point which is an estimated solution to a problem,
although other shapes can occur. The confidence region is
calculated in such a way that if a set of measurements were
repeated many times and a confidence region calculated in the
same way on each set of measurements, then a certain percentage
of the time, on average, (e.g. 95%) the confidence region would
include the point representing the "true" values of the set of
variables being estimated. However, unless certain assumptions
about prior probabilities are made, it does not mean, when one
confidence region has been calculated, that there is a 95%
probability that the "true" values lie inside the region, since
we do not assume any particular probability distribution of the
"true" values and we may or may not have other information about
where they are likely to lie. The