On the detection probability of neutron star glitches

Neutron stars are observed to undergo small, abrupt rotational speed-up. This phenomenon is known as glitch. In pulsar timing observations, detection of a neutron star glitch is constrained by the time of occurrence of the event relative to entire observing span and observing cadences, time of occurrence of preceding/subsequent glitches relative to observing cadences and the strength of timing noise. Using the Yu et al. (2013) data sets, in this paper, we analyse the observational selection in terms of detection probability. We define partial probabilities for the constraints and use Monte Carlo method with assuming glitches distribute uniformly to solve the complete probability formula for both group case involving 157 pulsars and individual cases for each of the seven pulsars with glitch numbers $\geqslant 5$. In the simulations, numerical Bayesian inference is used for glitch identification. With the derived detection probability density and observed results, we uncover glitch size probability distribution embedded in the data for both the group and individual cases. We find the most prominent correction occurred for PSR~J1341$-$6220, in which exponent of the power-law model varies from the observed $+0.7^{+1.4}_{-0.7}$ to $-0.4^{+1.0}_{-0.4}$. We suggest observers determine the detection probability for glitch theories, e.g. the self-organised criticality.