cdsmith / monoidal-stats

monoidal-stats: Statistics that accumulate as a monoid

Calculate populations, means, variances, and covariances in an arbitrary vector space in a single pass, in parallel, or incrementally. Generalizing Welford's algorithm, this library provides a monoidal interface for calculating statistics that accumulate.

Example

import Data.MonoidalStats

dataSet :: [Vector Double]
dataSet = ...

stats :: Covariance Vector Double
stats = foldMap observation dataSet

myPopulation :: Double
myPopulation = population stats

myMean :: Vector Double
myMean = mean stats

myVariance :: Double
myVariance = populationVariance stats

myDimensionVariances :: Vector Double
myDimensionVariances = populationVariances stats

myCovarianceMatrix :: Vector (Vector Double)
myCovarianceMatrix = populationCovariance stats

TODO

• Consider Kahan summation for better numerical stability. See Data.Kahan for a start.