random-fu-multivariate-0.1.2.1: Multivariate distributions for random-fu

Copyright (c) 2016 FP Complete Corporation MIT (see LICENSE) dominic@steinitz.org None Haskell2010

Data.Random.Distribution.Static.MultivariateNormal

Description

Sample from the multivariate normal distribution with a given vector-valued $$\mu$$ and covariance matrix $$\Sigma$$. For example, the chart below shows samples from the bivariate normal distribution. The dimension of the mean $$n$$ is statically checked to be compatible with the dimension of the covariance matrix $$n \times n$$.

Example code to generate the chart:

{-# LANGUAGE DataKinds #-}

import qualified Graphics.Rendering.Chart as C
import Graphics.Rendering.Chart.Backend.Diagrams

import Data.Random.Distribution.Static.MultivariateNormal

import qualified Data.Random as R
import Data.Random.Source.PureMT
import Numeric.LinearAlgebra.Static

nSamples :: Int
nSamples = 10000

sigma1, sigma2, rho :: Double
sigma1 = 3.0
sigma2 = 1.0
rho = 0.5

singleSample :: R.RVarT (State PureMT) (R 2)
singleSample = R.sample $Normal (vector [0.0, 0.0]) (sym$ matrix [ sigma1, rho * sigma1 * sigma2
, rho * sigma1 * sigma2, sigma2])

multiSamples :: [R 2]
multiSamples = evalState (replicateM nSamples $R.sample singleSample) (pureMT 3) pts = map f multiSamples where f z = (x, y) where (x, t) = headTail z (y, _) = headTail t chartPoint pointVals n = C.toRenderable layout where fitted = C.plot_points_values .~ pointVals$ C.plot_points_style  . C.point_color .~ opaque red
$C.plot_points_title .~ "Sample"$ def

layout = C.layout_title .~ "Sampling Bivariate Normal (" ++ (show n) ++ " samples)"
$C.layout_y_axis . C.laxis_generate .~ C.scaledAxis def (-3,3)$ C.layout_x_axis . C.laxis_generate .~ C.scaledAxis def (-3,3)

$C.layout_plots .~ [C.toPlot fitted]$ def

diagMS = do
denv <- defaultEnv C.vectorAlignmentFns 600 500
return $fst$ runBackend denv (C.render (chartPoint pts nSamples) (500, 500))

# Documentation

data family Normal k :: * Source #

Instances
 KnownNat n => Distribution Normal (R n) Source # Instance details Methodsrvar :: Normal (R n) -> RVar (R n) #rvarT :: Normal (R n) -> RVarT n0 (R n) # KnownNat n => PDF Normal (R n) Source # Instance details Methodspdf :: Normal (R n) -> R n -> Double #logPdf :: Normal (R n) -> R n -> Double # data Normal (R n) Source # Instance details data Normal (R n) = Normal (R n) (Sym n)