Copyright	(c) 2009 2010 Bryan O'Sullivan
License	BSD3
Maintainer	bos@serpentine.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

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 Source #

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

Instances details

Eq Resample Source #
Instance details Defined in Statistics.Resampling Methods (==) :: Resample -> Resample -> Bool Source # (/=) :: Resample -> Resample -> Bool Source #
Data Resample Source #
Instance details Defined in Statistics.Resampling Methods gfoldl :: ( forall d b. Data d => c (d -> b) -> d -> c b) -> ( forall g. g -> c g) -> Resample -> c Resample Source # gunfold :: ( forall b r. Data b => c (b -> r) -> c r) -> ( forall r. r -> c r) -> Constr -> c Resample Source # toConstr :: Resample -> Constr Source # dataTypeOf :: Resample -> DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) -> Maybe (c Resample ) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) -> Maybe (c Resample ) Source # gmapT :: ( forall b. Data b => b -> b) -> Resample -> Resample Source # gmapQl :: (r -> r' -> r) -> r -> ( forall d. Data d => d -> r') -> Resample -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> ( forall d. Data d => d -> r') -> Resample -> r Source # gmapQ :: ( forall d. Data d => d -> u) -> Resample -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> Resample -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> Resample -> m Resample Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> Resample -> m Resample Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> Resample -> m Resample Source #
Read Resample Source #
Instance details Defined in Statistics.Resampling Methods readsPrec :: Int -> ReadS Resample Source # readList :: ReadS [ Resample ] Source # readPrec :: ReadPrec Resample Source # readListPrec :: ReadPrec [ Resample ] Source #
Show Resample Source #
Instance details Defined in Statistics.Resampling Methods showsPrec :: Int -> Resample -> ShowS Source # show :: Resample -> String Source # showList :: [ Resample ] -> ShowS Source #
Generic Resample Source #
Instance details Defined in Statistics.Resampling Associated Types type Rep Resample :: Type -> Type Source # Methods from :: Resample -> Rep Resample x Source # to :: Rep Resample x -> Resample Source #
ToJSON Resample Source #
Instance details Defined in Statistics.Resampling Methods toJSON :: Resample -> Value Source # toEncoding :: Resample -> Encoding Source # toJSONList :: [ Resample ] -> Value Source # toEncodingList :: [ Resample ] -> Encoding Source #
FromJSON Resample Source #
Instance details Defined in Statistics.Resampling Methods parseJSON :: Value -> Parser Resample Source # parseJSONList :: Value -> Parser [ Resample ] Source #
Binary Resample Source #
Instance details Defined in Statistics.Resampling Methods put :: Resample -> Put Source # get :: Get Resample Source # putList :: [ Resample ] -> Put Source #
type Rep Resample Source #
Instance details Defined in Statistics.Resampling type Rep Resample = D1 (' MetaData "Resample" "Statistics.Resampling" "statistics-0.16.1.2-IkOne9g3oJ1vhHVSRLPUO" ' True ) ( C1 (' MetaCons "Resample" ' PrefixI ' True ) ( S1 (' MetaSel (' Just "fromResample") ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) ( Rec0 ( Vector Double ))))

data Bootstrap v a Source #

Constructors

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

Instances

Instances details

Functor v => Functor ( Bootstrap v) Source #
Instance details Defined in Statistics.Resampling Methods fmap :: (a -> b) -> Bootstrap v a -> Bootstrap v b Source # (<$) :: a -> Bootstrap v b -> Bootstrap v a Source #
Foldable v => Foldable ( Bootstrap v) Source #
Instance details Defined in Statistics.Resampling Methods fold :: Monoid m => Bootstrap v m -> m Source # foldMap :: Monoid m => (a -> m) -> Bootstrap v a -> m Source # foldMap' :: Monoid m => (a -> m) -> Bootstrap v a -> m Source # foldr :: (a -> b -> b) -> b -> Bootstrap v a -> b Source # foldr' :: (a -> b -> b) -> b -> Bootstrap v a -> b Source # foldl :: (b -> a -> b) -> b -> Bootstrap v a -> b Source # foldl' :: (b -> a -> b) -> b -> Bootstrap v a -> b Source # foldr1 :: (a -> a -> a) -> Bootstrap v a -> a Source # foldl1 :: (a -> a -> a) -> Bootstrap v a -> a Source # toList :: Bootstrap v a -> [a] Source # null :: Bootstrap v a -> Bool Source # length :: Bootstrap v a -> Int Source # elem :: Eq a => a -> Bootstrap v a -> Bool Source # maximum :: Ord a => Bootstrap v a -> a Source # minimum :: Ord a => Bootstrap v a -> a Source # sum :: Num a => Bootstrap v a -> a Source # product :: Num a => Bootstrap v a -> a Source #
Traversable v => Traversable ( Bootstrap v) Source #
Instance details Defined in Statistics.Resampling Methods traverse :: Applicative f => (a -> f b) -> Bootstrap v a -> f ( Bootstrap v b) Source # sequenceA :: Applicative f => Bootstrap v (f a) -> f ( Bootstrap v a) Source # mapM :: Monad m => (a -> m b) -> Bootstrap v a -> m ( Bootstrap v b) Source # sequence :: Monad m => Bootstrap v (m a) -> m ( Bootstrap v a) Source #
( Eq a, Eq (v a)) => Eq ( Bootstrap v a) Source #
Instance details Defined in Statistics.Resampling Methods (==) :: Bootstrap v a -> Bootstrap v a -> Bool Source # (/=) :: Bootstrap v a -> Bootstrap v a -> Bool Source #
( Typeable v, Data a, Data (v a)) => Data ( Bootstrap v a) Source #
Instance details Defined in Statistics.Resampling 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) Source # gunfold :: ( forall b r. Data b => c (b -> r) -> c r) -> ( forall r. r -> c r) -> Constr -> c ( Bootstrap v a) Source # toConstr :: Bootstrap v a -> Constr Source # dataTypeOf :: Bootstrap v a -> DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) -> Maybe (c ( Bootstrap v a)) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) -> Maybe (c ( Bootstrap v a)) Source # gmapT :: ( forall b. Data b => b -> b) -> Bootstrap v a -> Bootstrap v a Source # gmapQl :: (r -> r' -> r) -> r -> ( forall d. Data d => d -> r') -> Bootstrap v a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> ( forall d. Data d => d -> r') -> Bootstrap v a -> r Source # gmapQ :: ( forall d. Data d => d -> u) -> Bootstrap v a -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> Bootstrap v a -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> Bootstrap v a -> m ( Bootstrap v a) Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> Bootstrap v a -> m ( Bootstrap v a) Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> Bootstrap v a -> m ( Bootstrap v a) Source #
( Read a, Read (v a)) => Read ( Bootstrap v a) Source #
Instance details Defined in Statistics.Resampling Methods readsPrec :: Int -> ReadS ( Bootstrap v a) Source # readList :: ReadS [ Bootstrap v a] Source # readPrec :: ReadPrec ( Bootstrap v a) Source # readListPrec :: ReadPrec [ Bootstrap v a] Source #
( Show a, Show (v a)) => Show ( Bootstrap v a) Source #
Instance details Defined in Statistics.Resampling Methods showsPrec :: Int -> Bootstrap v a -> ShowS Source # show :: Bootstrap v a -> String Source # showList :: [ Bootstrap v a] -> ShowS Source #
Generic ( Bootstrap v a) Source #
Instance details Defined in Statistics.Resampling Associated Types type Rep ( Bootstrap v a) :: Type -> Type Source # Methods from :: Bootstrap v a -> Rep ( Bootstrap v a) x Source # to :: Rep ( Bootstrap v a) x -> Bootstrap v a Source #
( ToJSON a, ToJSON (v a)) => ToJSON ( Bootstrap v a) Source #
Instance details Defined in Statistics.Resampling Methods toJSON :: Bootstrap v a -> Value Source # toEncoding :: Bootstrap v a -> Encoding Source # toJSONList :: [ Bootstrap v a] -> Value Source # toEncodingList :: [ Bootstrap v a] -> Encoding Source #
( FromJSON a, FromJSON (v a)) => FromJSON ( Bootstrap v a) Source #
Instance details Defined in Statistics.Resampling Methods parseJSON :: Value -> Parser ( Bootstrap v a) Source # parseJSONList :: Value -> Parser [ Bootstrap v a] Source #
( Binary a, Binary (v a)) => Binary ( Bootstrap v a) Source #
Instance details Defined in Statistics.Resampling Methods put :: Bootstrap v a -> Put Source # get :: Get ( Bootstrap v a) Source # putList :: [ Bootstrap v a] -> Put Source #
type Rep ( Bootstrap v a) Source #
Instance details Defined in Statistics.Resampling type Rep ( Bootstrap v a) = D1 (' MetaData "Bootstrap" "Statistics.Resampling" "statistics-0.16.1.2-IkOne9g3oJ1vhHVSRLPUO" ' False ) ( C1 (' MetaCons "Bootstrap" ' PrefixI ' True ) ( S1 (' MetaSel (' Just "fullSample") ' NoSourceUnpackedness ' SourceStrict ' DecidedStrict ) ( Rec0 a) :*: S1 (' MetaSel (' Just "resamples") ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) ( Rec0 (v a))))

data Estimator Source #

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 Source #

Run an Estimator over a sample.

Resampling

resampleST Source #

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 Source #

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) Source #

Create vector using resamples

Jackknife

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

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

jackknifeMean :: Sample -> Vector Double Source #

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

jackknifeVariance :: Sample -> Vector Double Source #

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

jackknifeVarianceUnb :: Sample -> Vector Double Source #

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

jackknifeStdDev :: Sample -> Vector Double Source #

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

Helper functions

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

Split a generator into several that can run independently.