Fissile matter detection and characterization are crucial issues, especially in nuclear safety, safeguards, matter compatibility, and reactivity measurements. In this context, we want to identify a source of fissile matter knowing external measures such as instants of detection of neutrons during an interval of measure. Thus, we observe the neutron detection times emitted by the fissile matter and going through the detector, and then, we compute the moments of the empirical distribution of the number of neutrons detected during a time gate . In order to identify the source, we have to get the following parameters: multiplication factor of the system, intensity of the source , and fission efficiency .

Given the parameters of the source, there are some models that allow us to predict the moments of the counted number of neutrons during a time gate . We consider a point model stating that monokinetic neutrons are moving in an infinite, isotropic, and homogeneous medium.

The method makes it possible to compute the first moments of the neutron counting distribution. Then, given the moments of the counted number of neutrons during a time gate we want to get the parameters of the fissile source. In order to achieve this goal, we will use the following method: a Bayesian approach to get the distribution of parameters, where the a posteriori distribution is nontrivial and samples can be achieved with Markov Chain Monte Carlo methods with Covariance Matrix Adaptation.

Finally, we will consider two time gates and in two complementary regimes of the first moments. For a time of measurements of 3600 s, it is already settled that the use of and provides a better sampling of the a posteriori distribution of the parameters knowing the measurements than with just or . We also compare the sampling for the use of for a time of measurements of 7200 s and and for a time of measurements of 3600 s. We conclude that using this larger time of measurements and provides a better sampling of the a posteriori distribution of interest than the use of the smaller time of measurements or Comparisons are done to provide the order of magnitude for the experimenters.