Bayesian reasoning is a machine learning approach that provides explainable outputs and excels in small-data situations with high uncertainty. However, it requires intensive memory access and computation and is, therefore, too energy-intensive for extreme edge contexts. Near-memory computation with memristors (or RRAM) can greatly improve the energy efficiency of its computations. Here, we report two fabricated integrated circuits in a hybrid CMOS-memristor process, featuring each sixteen tiny memristor arrays and the associated near-memory logic for Bayesian inference. One circuit performs Bayesian inference using stochastic computing, and the other uses logarithmic computation; these two paradigms fit the area constraints of near-memory computing well. On-chip measurements show the viability of both approaches with respect to memristor imperfections. The two Bayesian machines also operated well at low supply voltages. We also designed scaled-up versions of the machines. Both scaled-up designs can perform a gesture recognition task using orders of magnitude less energy than a microcontroller unit. We also see that if an accuracy lower than 86.9% is sufficient for this sample task, stochastic computing consumes less energy than logarithmic computing; for higher accuracies, logarithmic computation is more energy-efficient. These results highlight the potential of memristor-based near-memory Bayesian computing, providing both accuracy and energy efficiency.