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

We investigate the performance of a generalized linear mixed model in predicting the Probabilities of Collision (Pc) for conjunction events. Specifically, we apply this model to the log(sub 10) transformation of these probabilities and argue that this transformation yields values that can be considered bounded in practice. Additionally, this bounded random variable, after scaling, is zero-inflated. Consequently, we model these values using the zero-inflated Beta distribution, and utilize the Bayesian paradigm and the mixed model framework to borrow information from past and current events. This provides a natural way to model the data and provides a basis for answering questions of interest, such as what is the likelihood of observing a probability of collision equal to the effective value of zero on a subsequent observation.

Conjuction Assessment↗

Trending in Pc Measurements via a Bayesian Zero-Inflated Mixed Model

Two satellites predicted to come within close proximity of one another, usually a high-value satellite and a piece of space debris moving the active satellite is a means of reducing collision risk but reduces satellite lifetime, perturbs satellite mission, and introduces its own risks. So important to get a good statement of the risk of collision in order to determine whether a maneuver is truly necessary. Two aspects of this Calculation of the Probability of Collision (Pc) based on the most recent set of position velocity and uncertainty data for both satellites. Examination of the changes in the Pc value as the event develops. Events should follow a canonical development (Pc vs time to closest approach (TCA)). Helpful to be able to guess where the present data point fits in the canonical development in order to guide operational response.

Conjuction Assessment↗

Territory and Population Attributes Affect Florida Scrub-Jay Fecundity in Fire Adapted Ecosystems

Fecundity, the number of young produced by a breeding pair during a breeding season, is a primary component in evolutionary and ecological theory and applications. Fecundity can be influenced by many environmental factors and requires long-term study due to the range of variation in ecosystem dynamics. Fecundity data often include a large proportion of zeros when many pairs fail to produce any young during a breeding season due to nest failure or when all young die independently after fledging. We conducted color banding and monthly censuses of Florida scrub-jays (Aphelocoma coerulescens) across 31 years, 15 populations, and 761 territories along central Florida’s Atlantic coast. We quantified how fecundity (juveniles/pair-year) was influenced by habitat quality, presence/absence of nonbreeders, population density, breeder experience, and rainfall, with a zero-inflated Bayesian hierarchical model including both a Bernoulli (e.g., brood success) and a Poisson (counts of young) submodel, and random effects for year, population, and territory. The results identified the importance of increasing “strong” quality habitat, which was a mid-successional state related to fire frequency and extent, because strong territories, and the proportion of strong territories in the overall population, influenced fecundity of breeding pairs. Populations subject to supplementary feeding also had greater fecundity. Territory size, population density, breeder experience, and rainfall surprisingly had no or small effects. Different mechanisms appeared to cause annual variation in fecundity, as estimates of random effects were not correlated between the success and count submodels. The increased fecundity for pairs with nonbreeders, compared to pairs without, identified empirical research needed to understand how the proportion of low-quality habitats influences population recovery and sustainability, because dispersal into low-quality habitats can drain nonbreeders from strong territories and decrease overall fecundity. We also describe how long term study resulted in reversals in our understanding because of complications involving habitat quality, sociobiology, and population density.

Long-term studies↗