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Probabilistic Modeling

For my induction into Scala, I wanted to translate the probabilistic monad of Chapter 9 of Expert F# (Introducing Language-Oriented Programming). The idea, based on the paper Stochastic Lambda Calculus and Monads of Probability Distributions, is to define a probability monad to compute over distributions of a domain instead of the domain itself. We limit ourselves to distributions over discrete domains characterized by three functions:

  1. sampling
  2. support (i.e. a set of values where all elements outside the set have zero chance of being sampled)
  3. expectation of a function over the distribution (e.g. the probability of selecting element A by evaluating the function f(x) = 1 if x equals A and 0 otherwise)