  This paper employs Bayesian probability theory for analyzing data generated
in femtosecond pump-probe photoelectron-photoion coincidence (PEPICO)
experiments. These experiments allow investigating ultrafast dynamical
processes in photoexcited molecules. Bayesian probability theory is
consistently applied to data analysis problems occurring in these types of
experiments such as background subtraction and false coincidences. We
previously demonstrated that the Bayesian formalism has many advantages,
amongst which are compensation of false coincidences, no overestimation of
pump-only contributions, significantly increased signal-to-noise ratio, and
applicability to any experimental situation and noise statistics. Most
importantly, by accounting for false coincidences, our approach allows running
experiments at higher ionization rates, resulting in an appreciable reduction
of data acquisition times. In addition to our previous paper, we include
fluctuating laser intensities, of which the straightforward implementation
highlights yet another advantage of the Bayesian formalism. Our method is
thoroughly scrutinized by challenging mock data, where we find a minor impact
of laser fluctuations on false coincidences, yet a noteworthy influence on
background subtraction. We apply our algorithm to data obtained in experiments
and discuss the impact of laser fluctuations on the data analysis.
