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module System.Random.MWC.
Probability A probability monad based on sampling functions, implemented as a thin wrapper over the mwc-random library. Probability distributions are abstract constructs that can be represented in a variety of ways. The sampling function representation is particularly useful -- it's computationally efficient, and collections of samples are amenable to much practical work. Probability monads propagate uncertainty under the hood. An expression like beta 1 8 >>= binomial 10 corresponds to a beta-binomial distribution in which the uncertainty captured by beta 1 8 has been marginalized out. The distribution resulting from a series of effects is called the predictive distribution of the model described by the corresponding expression. The monadic structure lets one piece together a hierarchical structure from simpler, local conditionals:
hierarchicalModel = do [c, d, e, f] <- replicateM 4 $ uniformR (1, 10) a <- gamma c d b <- gamma e f p <- beta a b n <- uniformR (5, 10) binomial n p
The functor instance allows one to transforms the support of a distribution while leaving its density structure invariant. For example, uniform is a distribution over the 0-1 interval, but fmap (+ 1) uniform is the translated distribution over the 1-2 interval:>>> create >>= sample (fmap (+ 1) uniform) 1.5480073474340754
The applicative instance guarantees that the generated samples are generated independently:>>> create >>= sample ((,) <$> uniform <*> uniform)
newtype
Prob (m :: Type -> Type) amwc-probability System.Random.MWC.Probability A probability distribution characterized by a sampling function.
>>> gen <- createSystemRandom >>> sample uniform gen 0.4208881170464097
Prob :: (Gen (PrimState m) -> m a) -> Prob (m :: Type -> Type) amwc-probability System.Random.MWC.Probability No documentation available.