A Probabilistic Method for Estimating VLBI Jet-Component Ejection Epochs. Application to MOJAVE 15 GHz VLBA Kinematics
Ejection epochs of parsec-scale jet components in active galactic nuclei (AGN), tracked with Very Long Baseline Interferometry (VLBI), are commonly estimated by extrapolating fitted trajectories back to the VLBI core. However, trajectory uncertainties, non-radial motion, acceleration, and the finite size and position variability of the core can make such estimates uncertain and restrict usable samples. We develop a probabilistic framework for estimating VLBI-component ejection epochs, including accelerated features, and for quantifying how consistently each backward-extrapolated trajectory is associated with an effective VLBI core region. We apply the framework to 1923 jet-component trajectories from the 15 GHz MOJAVE kinematic sample. Ejection epochs are defined as the times of closest approach of the extrapolated trajectories to the core, with trajectory uncertainties propagated through Monte Carlo sampling. The effective core radius is treated as a random variable, whose population-level scale is calibrated from the distribution of closest-approach positions. Each component is then assigned a model-dependent probability that its closest approach lies within this effective core region. The method yields 1589 ejection epochs. The fitted effective core-region scale is $σ_{\rm c}=0.16\pm0.02$ mas, corresponding to an average core radius of $0.20\pm0.03$ mas, and gives a population-level upper limit of $\lesssim0.16$ mas on the characteristic 15 GHz core wander perpendicular to the jet. Using the same probability weighting, the full probabilistic sample has $N_{\rm eff}=624$, 2.8 times the legacy MOJAVE value of 222, while the overlapping ejection epochs remain consistent with previous estimates. The framework provides a flexible basis for population studies and cross-correlation analyses of jet structural evolution and AGN variability.