  Change points in time series are perceived as isolated singularities where
two regular trends of a given signal do not match. The detection of such
transitions is of fundamental interest for the understanding of the system's
internal dynamics. In practice observational noise makes it difficult to detect
such change points in time series. In this work we elaborate a Bayesian method
to estimate the location of the singularities and to produce some confidence
intervals. We validate the ability and sensitivity of our inference method by
estimating change points of synthetic data sets. As an application we use our
algorithm to analyze the annual flow volume of the Nile River at Aswan from
1871 to 1970, where we confirm a well-established significant transition point
within the time series.
