statistics-0.14.0.2: A library of statistical types, data, and functions

Copyright | (c) 2009 2010 Bryan O'Sullivan
License | BSD3
Maintainer | bos@serpentine.com
Stability | experimental
Portability | portable
Safe Haskell | None
Language | Haskell98

Statistics.Resampling

Contents

- Data types
- Resampling
- Jackknife
- Helper functions

Description

Resampling statistics.

Synopsis

- newtype Resample = Resample {
  - fromResample :: Vector Double
  }
- data Bootstrap v a = Bootstrap {
  - fullSample :: !a
  - resamples :: v a
  }
- data Estimator
  - = Mean
  - | Variance
  - | VarianceUnbiased
  - | StdDev
  - | Function (Sample -> Double)
- estimate :: Estimator -> Sample -> Double
- resampleST :: PrimMonad m => Gen (PrimState m) -> [Estimator] -> Int -> Vector Double -> m [Bootstrap Vector Double]
- resample :: GenIO -> [Estimator] -> Int -> Vector Double -> IO [(Estimator, Bootstrap Vector Double)]
- resampleVector :: (PrimMonad m, Vector v a) => Gen (PrimState m) -> v a -> m (v a)
- jackknife :: Estimator -> Sample -> Vector Double
- jackknifeMean :: Sample -> Vector Double
- jackknifeVariance :: Sample -> Vector Double
- jackknifeVarianceUnb :: Sample -> Vector Double
- jackknifeStdDev :: Sample -> Vector Double
- splitGen :: Int -> GenIO -> IO [GenIO]

# Data types

newtype Resample #

A resample drawn randomly, with replacement, from a set of data points. Distinct from a normal array to make it harder for your humble author's brain to go wrong.

Constructors

Resample |
Fields fromResample :: Vector Double

Instances

Eq Resample # |
Methods (==) :: Resample -> Resample -> Bool # (/=) :: Resample -> Resample -> Bool #
Data Resample # |
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Resample -> c Resample # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Resample # toConstr :: Resample -> Constr # dataTypeOf :: Resample -> DataType # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c Resample) # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Resample) # gmapT :: (forall b. Data b => b -> b) -> Resample -> Resample # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Resample -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Resample -> r # gmapQ :: (forall d. Data d => d -> u) -> Resample -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Resample -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Resample -> m Resample # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Resample -> m Resample # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Resample -> m Resample #
Read Resample # |
Methods readsPrec :: Int -> ReadS Resample # readList :: ReadS [Resample] # readPrec :: ReadPrec Resample # readListPrec :: ReadPrec [Resample] #
Show Resample # |
Methods showsPrec :: Int -> Resample -> ShowS # show :: Resample -> String # showList :: [Resample] -> ShowS #
Generic Resample # |
Associated Types type Rep Resample :: * -> * # Methods from :: Resample -> Rep Resample x # to :: Rep Resample x -> Resample #
ToJSON Resample # |
Methods toJSON :: Resample -> Value # toEncoding :: Resample -> Encoding # toJSONList :: [Resample] -> Value # toEncodingList :: [Resample] -> Encoding #
FromJSON Resample # |
Methods parseJSON :: Value -> Parser Resample # parseJSONList :: Value -> Parser [Resample] #
Binary Resample # |
Methods put :: Resample -> Put # get :: Get Resample # putList :: [Resample] -> Put #
type Rep Resample # |
type Rep Resample = D1 (MetaData "Resample" "Statistics.Resampling" "statistics-0.14.0.2-DwTksDozTf84s3a0u9j38y" True) (C1 (MetaCons "Resample" PrefixI True) (S1 (MetaSel (Just Symbol "fromResample") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Vector Double))))

data Bootstrap v a #

Constructors

Bootstrap |
Fields fullSample :: !a resamples :: v a

Instances

Functor v => Functor (Bootstrap v) # |
Methods fmap :: (a -> b) -> Bootstrap v a -> Bootstrap v b # (<$) :: a -> Bootstrap v b -> Bootstrap v a #
Foldable v => Foldable (Bootstrap v) # |
Methods fold :: Monoid m => Bootstrap v m -> m # foldMap :: Monoid m => (a -> m) -> Bootstrap v a -> m # foldr :: (a -> b -> b) -> b -> Bootstrap v a -> b # foldr' :: (a -> b -> b) -> b -> Bootstrap v a -> b # foldl :: (b -> a -> b) -> b -> Bootstrap v a -> b # foldl' :: (b -> a -> b) -> b -> Bootstrap v a -> b # foldr1 :: (a -> a -> a) -> Bootstrap v a -> a # foldl1 :: (a -> a -> a) -> Bootstrap v a -> a # toList :: Bootstrap v a -> [a] # null :: Bootstrap v a -> Bool # length :: Bootstrap v a -> Int # elem :: Eq a => a -> Bootstrap v a -> Bool # maximum :: Ord a => Bootstrap v a -> a # minimum :: Ord a => Bootstrap v a -> a # sum :: Num a => Bootstrap v a -> a # product :: Num a => Bootstrap v a -> a #
Traversable v => Traversable (Bootstrap v) # |
Methods traverse :: Applicative f => (a -> f b) -> Bootstrap v a -> f (Bootstrap v b) # sequenceA :: Applicative f => Bootstrap v (f a) -> f (Bootstrap v a) # mapM :: Monad m => (a -> m b) -> Bootstrap v a -> m (Bootstrap v b) # sequence :: Monad m => Bootstrap v (m a) -> m (Bootstrap v a) #
(Eq (v a), Eq a) => Eq (Bootstrap v a) # |
Methods (==) :: Bootstrap v a -> Bootstrap v a -> Bool # (/=) :: Bootstrap v a -> Bootstrap v a -> Bool #
(Data (v a), Data a, Typeable (* -> *) v) => Data (Bootstrap v a) # |
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Bootstrap v a -> c (Bootstrap v a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Bootstrap v a) # toConstr :: Bootstrap v a -> Constr # dataTypeOf :: Bootstrap v a -> DataType # dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Bootstrap v a)) # dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Bootstrap v a)) # gmapT :: (forall b. Data b => b -> b) -> Bootstrap v a -> Bootstrap v a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Bootstrap v a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Bootstrap v a -> r # gmapQ :: (forall d. Data d => d -> u) -> Bootstrap v a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Bootstrap v a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Bootstrap v a -> m (Bootstrap v a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Bootstrap v a -> m (Bootstrap v a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Bootstrap v a -> m (Bootstrap v a) #
(Read (v a), Read a) => Read (Bootstrap v a) # |
Methods readsPrec :: Int -> ReadS (Bootstrap v a) # readList :: ReadS [Bootstrap v a] # readPrec :: ReadPrec (Bootstrap v a) # readListPrec :: ReadPrec [Bootstrap v a] #
(Show (v a), Show a) => Show (Bootstrap v a) # |
Methods showsPrec :: Int -> Bootstrap v a -> ShowS # show :: Bootstrap v a -> String # showList :: [Bootstrap v a] -> ShowS #
Generic (Bootstrap v a) # |
Associated Types type Rep (Bootstrap v a) :: * -> * # Methods from :: Bootstrap v a -> Rep (Bootstrap v a) x # to :: Rep (Bootstrap v a) x -> Bootstrap v a #
(ToJSON a, ToJSON (v a)) => ToJSON (Bootstrap v a) # |
Methods toJSON :: Bootstrap v a -> Value # toEncoding :: Bootstrap v a -> Encoding # toJSONList :: [Bootstrap v a] -> Value # toEncodingList :: [Bootstrap v a] -> Encoding #
(FromJSON a, FromJSON (v a)) => FromJSON (Bootstrap v a) # |
Methods parseJSON :: Value -> Parser (Bootstrap v a) # parseJSONList :: Value -> Parser [Bootstrap v a] #
(Binary a, Binary (v a)) => Binary (Bootstrap v a) # |
Methods put :: Bootstrap v a -> Put # get :: Get (Bootstrap v a) # putList :: [Bootstrap v a] -> Put #
type Rep (Bootstrap v a) # |
type Rep (Bootstrap v a) = D1 (MetaData "Bootstrap" "Statistics.Resampling" "statistics-0.14.0.2-DwTksDozTf84s3a0u9j38y" False) (C1 (MetaCons "Bootstrap" PrefixI True) ((:*:) (S1 (MetaSel (Just Symbol "fullSample") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Just Symbol "resamples") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (v a)))))

data Estimator #

An estimator of a property of a sample, such as its `mean`.

The use of an algebraic data type here allows functions such as `jackknife` and `bootstrapBCA` to use more efficient algorithms when possible.

Constructors

Mean |
Variance |
VarianceUnbiased |
StdDev |
Function (Sample -> Double) |

estimate :: Estimator -> Sample -> Double #

Run an `Estimator` over a sample.

# Resampling

resampleST #

Arguments

:: PrimMonad m |
=> Gen (PrimState m) |
-> [Estimator] | Estimation functions.
-> Int | Number of resamples to compute.
-> Vector Double | Original sample.
-> m [Bootstrap Vector Double] |

Single threaded and deterministic version of resample.

resample #

Arguments

:: GenIO |
-> [Estimator] | Estimation functions.
-> Int | Number of resamples to compute.
-> Vector Double | Original sample.
-> IO [(Estimator, Bootstrap Vector Double)] |

O(e*r*s) Resample a data set repeatedly, with replacement, computing each estimate over the resampled data.

This function is expensive; it has to do work proportional to e*r*s, where e is the number of estimation functions, r is the number of resamples to compute, and s is the number of original samples.

To improve performance, this function will make use of all available CPUs. At least with GHC 7.0, parallel performance seems best if the parallel garbage collector is disabled (RTS option `-qg`).

resampleVector :: (PrimMonad m, Vector v a) => Gen (PrimState m) -> v a -> m (v a) #

Create vector using resamples

# Jackknife

jackknife :: Estimator -> Sample -> Vector Double #

O(n) or O(n^2) Compute a statistical estimate repeatedly over a sample, each time omitting a successive element.

jackknifeMean :: Sample -> Vector Double #

O(n) Compute the jackknife mean of a sample.

jackknifeVariance :: Sample -> Vector Double #

O(n) Compute the jackknife variance of a sample.

jackknifeVarianceUnb :: Sample -> Vector Double #

O(n) Compute the unbiased jackknife variance of a sample.

jackknifeStdDev :: Sample -> Vector Double #

O(n) Compute the jackknife standard deviation of a sample.

# Helper functions

splitGen :: Int -> GenIO -> IO [GenIO] #

Split a generator into several that can run independently.