Control.Monad.MC.Class

The abstract MonadMC interface and utility functions for Monte Carlo computations.

The Monte Carlo monad type class

class HasRNG m

Associated Types

type RNG m

The random number generator type for the monad.

Instances

HasRNG MC

Monad m => HasRNG (MCT m)

class (Monad m, HasRNG m) => MonadMC m where

Methods

getRNG :: m (RNG m)

Get the current random number generator.

setRNG :: RNG m -> m ()

Set the current random number generator.

uniform :: Double -> Double -> m Double

uniform a b generates a value uniformly distributed in [a,b).

uniformInt :: Int -> m Int

uniformInt n generates an integer uniformly in the range [0,n-1]. It is an error to call this function with a non-positive value.

normal :: Double -> Double -> m Double

normal mu sigma generates a Normal random variable with mean mu and standard deviation sigma.

exponential :: Double -> m Double

exponential mu generates an Exponential variate with mean mu.

levy :: Double -> Double -> m Double

levy c alpha gets a Levy alpha-stable variate with scale c and exponent alpha. The algorithm only works for 0 < alpha <= 2.

levySkew :: Double -> Double -> Double -> m Double

levySkew c alpha beta gets a skew Levy alpha-stable variate with scale c, exponent alpha, and skewness beta. The skew parameter must lie in the range [-1,1]. The algorithm only works for 0 < alpha <= 2.

poisson :: Double -> m Int

poisson mu generates a Poisson random variable with mean mu.

cauchy :: Double -> m Double

cauchy a generates a Cauchy random variable with scale parameter a.

beta :: Double -> Double -> m Double

beta a b generates a beta random variable with parameters a and b.

logistic :: Double -> m Double

logistic a generates a logistic random variable with parameter a.

pareto :: Double -> Double -> m Double

pareto a b generates a Pareto random variable with exponent a and scale b.

weibull :: Double -> Double -> m Double

weibull a b generates a Weibull random variable with scale a and exponent b.

gamma :: Double -> Double -> m Double

gamma a b generates a gamma random variable with parameters a and b.

multinomial :: Int -> Vector Double -> m (Vector Int)

multinomial n ps generates a multinomial random variable with parameters ps formed by n trials.

dirichlet :: Vector Double -> m (Vector Double)

dirichlet alphas generates a Dirichlet random variable with parameters alphas.

unsafeInterleaveMC :: m a -> m a

Get the baton from the Monte Carlo monad without performing any computations. Useful but dangerous.

Instances

MonadMC MC

Monad m => MonadMC (MCT m)

Random distributions

bernoulli :: MonadMC m => Double -> m Bool

Generate True events with the given probability

Sampling from lists

sample :: MonadMC m => [a] -> m a

sample xs samples a value uniformly from the elements of xs. The results are undefined if length xs is zero.

sampleWithWeights :: MonadMC m => [(Double, a)] -> m a

sampleWithWeights wxs samples a value from the list with the given weight.

sampleSubset :: MonadMC m => [a] -> Int -> m [a]

sampleSubset xs k samples a subset of size k from xs by sampling without replacement. The return value is a list of length k with the elements in the subset in the order that they were sampled. Note also that the elements are lazily generated.

sampleSubset' :: MonadMC m => [a] -> Int -> m [a]

Strict version of sampleSubset.

sampleSubsetWithWeights :: MonadMC m => [(Double, a)] -> Int -> m [a]

Sample a subset of the elements with the given weights. Return the elements of the subset lazily in the order they were sampled.

sampleSubsetWithWeights' :: MonadMC m => [(Double, a)] -> Int -> m [a]

Strict version of sampleSubsetWithWeights.

Sampling Ints

sampleInt :: MonadMC m => Int -> m Int

sampleInt n samples integers uniformly from [ 0..n-1 ]. It is an error to call this function with a non-positive n.

sampleIntWithWeights :: MonadMC m => [Double] -> Int -> m Int

sampleIntWithWeights ws n samples integers from [ 0..n-1 ] with the probability of choosing i proportional to ws !! i. The list ws must have length equal to n. Also, the elements of ws must be non-negative with at least one nonzero entry.

sampleIntSubset :: MonadMC m => Int -> Int -> m [Int]

sampleIntSubset n k samples a subset of size k by sampling without replacement from the integers { 0, ..., n-1 }. The return value is a list of length k with the elements in the subset in the order that they were sampled. Note also that the elements are lazily generated.

sampleIntSubset' :: MonadMC m => Int -> Int -> m [Int]

Strict version of sampleIntSubset.

sampleIntSubsetWithWeights :: MonadMC m => [Double] -> Int -> Int -> m [Int]

sampleIntSubsetWithWeights ws n k samplea size k subset of { 0, ..., n-1 } with the given weights by sampling elements without replacement. It returns the elements of the subset lazily in the order they were sampled.

sampleIntSubsetWithWeights' :: MonadMC m => [Double] -> Int -> Int -> m [Int]

Strict version of sampleIntSubsetWithWeights.

Shuffling

shuffle :: MonadMC m => [a] -> m [a]

shuffle xs randomly permutes the list xs and returns the result. All permutations of the elements of xs are equally likely.

shuffleInt :: MonadMC m => Int -> m [(Int, Int)]

shuffleInt n generates a sequence of swaps equivalent to a uniformly-chosen random permutatation of the integers {0, ..., n-1}. For an input of n, there are n-1 swaps, which are lazily generated.

shuffleInt' :: MonadMC m => Int -> m [(Int, Int)]

Strict version of shuffleInt.

Repeating computations

repeatMC :: MonadMC m => m a -> m [a]

Produce a lazy infinite list of values from the given Monte Carlo generator.

replicateMC :: MonadMC m => Int -> m a -> m [a]

Produce a lazy list of the given length using the specified generator.