  We provide a method for approximating Bayesian inference using rejection
sampling. We not only make the process efficient, but also dramatically reduce
the memory required relative to conventional methods by combining rejection
sampling with particle filtering. We also provide an approximate form of
rejection sampling that makes rejection filtering tractable in cases where
exact rejection sampling is not efficient. Finally, we present several
numerical examples of rejection filtering that show its ability to track time
dependent parameters in online settings and also benchmark its performance on
MNIST classification problems.
