  Neural networks (NN) have become almost ubiquitous with image classification,
but in their standard form produce point estimates, with no measure of
confidence. Bayesian neural networks (BNN) provide uncertainty quantification
(UQ) for NN predictions and estimates through the posterior distribution. As NN
are applied in more high-consequence applications, UQ is becoming a
requirement. BNN provide a solution to this problem by not only giving accurate
predictions and estimates, but also an interval that includes reasonable values
within a desired probability. Despite their positive attributes, BNN are
notoriously difficult and time consuming to train. Traditional Bayesian methods
use Markov Chain Monte Carlo (MCMC), but this is often brushed aside as being
too slow. The most common method is variational inference (VI) due to its fast
computation, but there are multiple concerns with its efficacy. We apply and
compare MCMC- and VI-trained BNN in the context of target detection in
hyperspectral imagery (HSI), where materials of interest can be identified by
their unique spectral signature. This is a challenging field, due to the
numerous permuting effects practical collection of HSI has on measured spectra.
Both models are trained using out-of-the-box tools on a high fidelity HSI
target detection scene. Both MCMC- and VI-trained BNN perform well overall at
target detection on a simulated HSI scene. This paper provides an example of
how to utilize the benefits of UQ, but also to increase awareness that
different training methods can give different results for the same model. If
sufficient computational resources are available, the best approach rather than
the fastest or most efficient should be used, especially for high consequence
problems.
