  Data analysis and individual policy-level modeling for insurance involves
handling large data sets with strong spatiotemporal correlations, non-Gaussian
distributions, and complex hierarchical structures. In this research, we
demonstrate that by utilizing gradient-based Markov chain Monte Carlo (MCMC)
techniques accelerated by graphics processing units, the trade-off between
complex model structures and scalability for inference is overcome at the
million-record size. By implementing our model in NumPyro, we leverage its
built-in MCMC capabilities to fit a model with multiple sophisticated
components such as latent conditional autoregression and spline-based exposure
adjustment, achieving an 8.8x speedup compared to CPU-based implementations. We
apply this model to a case study of 2.6 million individual policy-level claim
count records for automobile insurance from Brazil in 2011. We illustrate how
this modeling approach significantly advances current risk assessment processes
for numerous, closely related outcomes. The code and data are available at
https://github.com/ckrapu/bayes-at-scale.
