This Demonstration shows the effect of transforming a uniformly distributed variable. Naively we may choose to use the uniform distribution to represent a state of no information, perhaps as an uninformative prior for Bayesian inference. However, if
is uniformly distributed, even simple transformations of
may not be—in this example the phenomenon is illustrated with powers of
. To give a concrete example, suppose
represents the radius of a circle. Then if
is uniformly distributed (we might say we were completely "uninformed" about
) then we know something about the area of the circle (the distribution of
squared is not uniform)! This suggests that the concept of an "uninformative" distribution is not as simple or clearly defined as it first appears.