Build your own probability monads

Probability is often counter-intuitive, and it always involves a great deal of math. This is unfortunate, because many applications in robotics and AI increasingly rely on probability theory. We introduce a modular toolkit for constructing probability monads, and show that it can be used for everything from discrete distributions to weighted particle filtering. This modular approach allows us to present a single, easy-to-use API for working with many kinds of probability distributions. Our toolkit combines several existing components (the list monad, the Rand monad, and the MaybeT monad transformer), with a stripped down version ofWriterT Prob, and a new monad for sequential Monte Carlo sampling. Using these components, we show that MaybeT can be used to implement Bayes’ theorem. We also show how to implement a monad for weighted particle filtering.