Abstract

We are interested in the evaluation of uncertainty in the location of change points. Because of the discrete nature of change points, standard statistical theory does not apply easily and only few asymptotic results are available to evaluate quantity of interest such as confidence intervals for change point locations. In a Bayesian framework, such quantities are often obtained via computationally demanding Monte-Carlo techniques. We will present a general Bayesian methodology to compute such quantities in an exact manner, with quadratic complexity. A parallel can be made between this approach and dynamic programming algorithms. This methodology allows to compute a series of posterior distributions, such as this of the total number of breakpoints or this of any change point location. Based on these results we will consider a Bayesian method to compare the location of change points in independent sequences. Eventually, this method will be used to compare the location of transcript boundaries in yeast under different growth condition.