Advancements in autonomous robotic systems have been impeded by the lack of a specialized computational hardware that makes real-time decisions based on sensory inputs. We have developed a novel circuit structure that efficiently approximates naïve Bayesian inference with simple Muller C-elements. Using a stochastic computing paradigm, this system enables real-time approximate decision-making with an area-energy-delay product nearly one billion times smaller than a conventional general-purpose computer. In this paper, we propose several techniques to improve the approximation of Bayesian inference by reducing stochastic bitstream autocorrelation. We also evaluate the effectiveness of these techniques for various naïve inference tasks and discuss hardware considerations, concluding that these circuits enable approximate Bayesian inferences while retaining orders-of-magnitude hardware advantages compared to conventional general-purpose computers.