  Vesicoureteral Reflux (VUR) is a pediatric disorder in which urine flows
backwards from the bladder to the upper urinary tract. Its detection is of
great importance as it increases the risk of a Urinary Tract Infection, which
can then lead to a kidney infection since bacteria may have direct access to
the kidneys. Unfortunately the detection of VUR requires a rather painful
medical examination, called voiding cysteourethrogram (VCUG), that exposes the
child to radiation. In an effort to avoid the exposure to radiation required by
VCUG some recent studies examined the use of machine learning techniques for
the detection of VUR based on data that can be obtained without exposing the
child to radiation. This work takes one step further by proposing an approach
that provides lower and upper bounds for the conditional probability of a given
child having VUR. The important property of these bounds is that they are
guaranteed (up to statistical fluctuations) to contain well-calibrated
probabilities with the only requirement that observations are independent and
identically distributed (i.i.d.). Therefore they are much more informative and
reliable than the plain yes/no answers provided by other techniques.
