Office of the Secretary of Defense: 25_Sky_View_Final_Draft

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Military installations – Military installation data are sourced to U.S. Census TIGER/Line
shapefiles and downloaded from data.gov (data.gov, 2022). The U.S. Census created this dataset
in collaboration with the U.S. Department of Defense and the U.S. Department of Homeland
Security. The data represent the boundaries of military installations. For this research, those
boundaries were overlaid onto U.S. counties, where the area of each county that is military
installation is calculated.
Models
The NUFORC dataset is first explored alone to identify general spatial patterns of
reported sightings using hotspot analysis. This exploratory analysis is based on the Getis-Ord
(Gi*) index. This index identifies significant clusters of low values (cold spots) and high values
(hot spots), by comparing the aggregate number of population standardized sightings in a set of
neighboring counties to the full distribution of counts (Getis and Ord, 1992; Ord and Getis,
1995). Different from a heat map, the resulting map shows statistically significant regions of
high and low occurrences.
To model potential for seeing UAPs we use Bayesian small area estimation, based on the
relative rate of sightings in the population of an area. Small area models are commonly used in
epidemiology to study the spatial pattern of diseases. These incorporate a spatial autoregressive
term to limit the influence of extreme values, which are often linked to small population sizes.
For this model, the count of reported sightings for county i is assumed to follow a Poisson
distribution as follows:
𝑦𝑖 ∼ 𝑃𝑜𝑖𝑠(𝜃𝑖𝐸𝑖 )
Where 𝐸𝑖is the expected number of sightings for county i and 𝜃𝑖 is the relative rate. To get the
expected value, first we estimate the per capita rate of sightings for the entire study region as the
total number of sightings divided by the total population. The expected value for any county is
obtained by multiplying this value by the population of that county. Where 𝜃𝑖 > 1, the number of
sightings is greater than would be expected based on population alone. Finally, the set of relative
rates are modeled as follows:
log(𝜃𝑖) = 𝛽𝑋𝑖 + 𝜖
Where 𝛽𝑋𝑖 is the set of z-score transformed covariates representing visibility and air traffic
described above with associated coefficients. Finally, the model error (𝜖) is decomposed into a
spatial autoregressive effect and non-spatial random noise. Model parameters and coefficients
are estimated using Integrated Nested Laplacian Approximation (Rue et al., 2017). Model results
are reported as the mean of the posterior probability distribution for each coefficient (Table 1)
and spatially as the probability of a counties relative rate being over twice the national average
(Figure 4). Variance Inflation Factors (VIFs), which signal potential multicollinearity within aPage determined to be Unclassified
Reviewed by Chief of Staff, AARO
IAW FY24 NDAA, Section 1841 (a)(1)(C)
Date: 02/06/2025