  Dynamic linear models with Gaussian observations and Gaussian states lead to
closed-form formulas for posterior simulation. However, these closed-form
formulas break down when the response or state evolution ceases to be Gaussian.
Dynamic, generalized linear models exemplify a class of models for which this
is the case, and include, amongst other models, dynamic binomial logistic
regression and dynamic negative binomial regression. Finding and appraising
posterior simulation techniques for these models is important since modeling
temporally correlated categories or counts is useful in a variety of
disciplines, including ecology, economics, epidemiology, medicine, and
neuroscience. In this paper, we present one such technique, P\'olya-Gamma data
augmentation, and compare it against two competing methods. We find that the
P\'olya-Gamma approach works well for dynamic logistic regression and for
dynamic negative binomial regression when the count sizes are small.
Supplementary files are provided for replicating the benchmarks.
