Trending in Probability of Collision Measurements via a Bayesian Zero-Inflated Beta Mixed Model

transformation of these probabilities and argue that this transformation yields values that canbe considered bounded in practice. Additionally, this bounded random variable, after scaling, iszero-inflated. Consequently, we model these values using the zero-inflated Beta distribution, andutilize the Bayesian paradigm and the mixed model framework to borrow information from past andcurrent events. This provides a natural way to model the data and provides a basis for answeringquestions of interest, such as what is the likelihood of observing a probability of collision equal tothe effective value of zero on a subsequent observation.Keywords: Conjunction Analysis, Probability of Collision, Trending, Bayesian, Prediction1. IntroductionThe problem of deciding whether to maneuver a satellite that is in conjunction with another spaceobject is often not straightforward, and a serious threat involves the deliberation and cooperationof various parties[1]. Quantifying the risk for any such conjunction is generally accomplishedthrough the use of the predicted miss distance at time of closest approach (TCA) and the calculatedprobability of collision (P