Office of the Secretary of Defense: 25_Sky_View_Final_Draft

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rates, the posterior estimates have been exponentiated to help in interpretation. With the
exception of the intercept, all model coefficients describe the rate of change of the relative rate of
sightings for a one standard deviation increase in that coefficient (Table 1). Values above 1
indicate a positive relationship (i.e. increasing sightings); values below 1 indicate a negative
relationship (decreasing sightings). For example, the coefficient for Mean Light Pollution is
0.923, indicating that a one standard deviation increase in light pollution will result in a 7.7%
decrease in sightings. Coefficients are reported as the mean of the posterior distribution plus the
95% credibility interval.
In contrast to classical frequentist analysis, Bayesian posterior estimates can be used to
test specific hypotheses (McElreath, 2018). Here, we test the hypotheses that the relationship
between each covariate and the rate of sightings is positive (i.e. >1) or negative (<1). Support for
a given hypothesis is based on the posterior probability distribution of model coefficients, and is
described as the credibility of that hypothesis. For example, if 95% of the posterior distribution
of a coefficient is above one, this indicates a positive relationship between that covariate and the
rate of sightings, and would be assigned a credibility of 95% of a positive relationship. If the
posterior distribution is equally split into negative and positive estimates, this would be assigned
a credibility of approximately 50% for either hypothesis. Credibility estimates are provided in
Table 1. With the exception of cloud cover, all results support our initial hypothesis – that people
will see things when they have the opportunity to. The exception is cloud cover, which has a
non-credible relationship with sightings, with no support of either a negative or positive
relationship.
Variables Exponentiated
Results
Positive
coefficient
credibility
Negative
coefficient
credibility
Relationship
(Intercept) 0.862 (0.848, 0.877)
Mean Canopy 0.961 (0.915, 1.01) 6% 94% More Canopy = Fewer Sightings
Mean Cloud Cover 0.998 (0.929, 1.072) 48% 52% No Relationship
Mean Light Pollution 0.923 (0.899, 0.947) 0% 100% More Light = Fewer Sightings
Percent Military Area 1.013 (0.994, 1.033) 92% 8% More Military = More Sightings
Air Traffic / Sq. Km 1.099 (1.068, 1.131) 100% 0% More Air Traffic = More Sightings
Table 1 Results from Bayesian small area model. From left to right: variable name; mean
posterior distribution (95% credible range); credibility of positive relationship with sightings;
credibility of negative relationship with sightings; brief description of result
As a further hypothesis, we use the model results to estimate the probability that the
sightings in any county are more than twice the national average (the exceedance probability;
Figure 4). The results confirm the hotspot analysis, with higher probabilities in western U.S.
However, the area with the highest probability (80-100%) is restricted to a smaller area running
from New Mexico and Nevada in the south to Washington in the north. Another smaller areaPage determined to be Unclassified
Reviewed by Chief of Staff, AARO
IAW FY24 NDAA, Section 1841 (a)(1)(C)
Date: 02/06/2025