Although Bayesian inference enhances intelligent probabilistic computing systems, it is computationally expensive and not efficient to implement on traditional von Neumann architectures. In this paper we propose a simple and novel way to implement approximate Bayesian inference that relies on the Naive Bayes Nearest Neighbour (NBNN) algorithm using memristors. We also show that incorporating variable prior probabilities helps the inference process and helps in saving ≈ 300× the power because we can lower the input voltage without having to sacrifice significant performance. We tested our system with the MNIST dataset and showed that it can perform up to ≈ 2 − 4% better by including variable priors. Index Terms—Memristor, Crossbar Architecture, Bayesian Inference, Probabilistic Inference, Associative Memory.