Methods, apparatus, systems, and articles of manufacture providing an improved Bayesian neural network and methods and apparatus to operate the same are disclosed. An example apparatus includes an oscillator to generate a first clock signal; a resistive element to adjust a slope of a rising edge of a second clock signal; a voltage sampler to generate a sample based on at least one of (a) a first voltage of the first clock signal when a second voltage of the second clock signal satisfies a threshold or (b) a third voltage of the second clock signal when a fourth voltage of the first clock signal satisfies the threshold; and a charge pump to adjust a weight based on the sample, the weight to adjust data in a model.