statistics-0.16.2.1: 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 | Haskell2010

Statistics.Resampling

Contents

- Data types
- Resampling
- Jackknife
- Helper functions

Description

Resampling statistics.

Synopsis

- newtype Resample = Resample {
  - fromResample :: Vector Double
  }
- data Bootstrap (v :: Type -> Type) 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

Instances details

FromJSON Resample # |
Instance details Defined in Statistics.Resampling Methods parseJSON :: Value -> Parser Resample # parseJSONList :: Value -> Parser [Resample] # omittedField :: Maybe Resample #
ToJSON Resample # |
Instance details Defined in Statistics.Resampling Methods toJSON :: Resample -> Value # toEncoding :: Resample -> Encoding # toJSONList :: [Resample] -> Value # toEncodingList :: [Resample] -> Encoding # omitField :: Resample -> Bool #
Data Resample # |
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 # 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 :: forall r r'. (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 #
Generic Resample # |
Instance details Defined in Statistics.Resampling Associated Types
type Rep Resample |
Instance details Defined in Statistics.Resampling type Rep Resample = D1 ('MetaData "Resample" "Statistics.Resampling" "statistics-0.16.2.1-9EJt18csjGeB8Yk5f7eGk5" 'True) (C1 ('MetaCons "Resample" 'PrefixI 'True) (S1 ('MetaSel ('Just "fromResample") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Vector Double))))
Methods from :: Resample -> Rep Resample x # to :: Rep Resample x -> Resample #
Read Resample # |
Instance details Defined in Statistics.Resampling Methods readsPrec :: Int -> ReadS Resample # readList :: ReadS [Resample] # readPrec :: ReadPrec Resample # readListPrec :: ReadPrec [Resample] #
Show Resample # |
Instance details Defined in Statistics.Resampling Methods showsPrec :: Int -> Resample -> ShowS # show :: Resample -> String # showList :: [Resample] -> ShowS #
Binary Resample # |
Instance details Defined in Statistics.Resampling Methods put :: Resample -> Put # get :: Get Resample # putList :: [Resample] -> Put #
Eq Resample # |
Instance details Defined in Statistics.Resampling Methods (==) :: Resample -> Resample -> Bool # (/=) :: Resample -> Resample -> Bool #
type Rep Resample # |
Instance details Defined in Statistics.Resampling type Rep Resample = D1 ('MetaData "Resample" "Statistics.Resampling" "statistics-0.16.2.1-9EJt18csjGeB8Yk5f7eGk5" 'True) (C1 ('MetaCons "Resample" 'PrefixI 'True) (S1 ('MetaSel ('Just "fromResample") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Vector Double))))

data Bootstrap (v :: Type -> Type) a #

Constructors

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

#### Instances

Instances details

Foldable v => Foldable (Bootstrap v) # |
Instance details Defined in Statistics.Resampling Methods fold :: Monoid m => Bootstrap v m -> m # foldMap :: Monoid m => (a -> m) -> Bootstrap v a -> 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) # |
Instance details Defined in Statistics.Resampling 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) #
Functor v => Functor (Bootstrap v) # |
Instance details Defined in Statistics.Resampling Methods fmap :: (a -> b) -> Bootstrap v a -> Bootstrap v b # (<$) :: a -> Bootstrap v b -> Bootstrap v a #
(FromJSON a, FromJSON (v a)) => FromJSON (Bootstrap v a) # |
Instance details Defined in Statistics.Resampling Methods parseJSON :: Value -> Parser (Bootstrap v a) # parseJSONList :: Value -> Parser [Bootstrap v a] # omittedField :: Maybe (Bootstrap v a) #
(ToJSON a, ToJSON (v a)) => ToJSON (Bootstrap v a) # |
Instance details Defined in Statistics.Resampling Methods toJSON :: Bootstrap v a -> Value # toEncoding :: Bootstrap v a -> Encoding # toJSONList :: [Bootstrap v a] -> Value # toEncodingList :: [Bootstrap v a] -> Encoding # omitField :: Bootstrap v a -> Bool #
(Typeable v, Data a, Data (v a)) => Data (Bootstrap v a) # |
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) # 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 :: forall r r'. (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) #
Generic (Bootstrap v a) # |
Instance details Defined in Statistics.Resampling Associated Types
type Rep (Bootstrap v a) |
Instance details Defined in Statistics.Resampling type Rep (Bootstrap v a) = D1 ('MetaData "Bootstrap" "Statistics.Resampling" "statistics-0.16.2.1-9EJt18csjGeB8Yk5f7eGk5" '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))))
Methods from :: Bootstrap v a -> Rep (Bootstrap v a) x # to :: Rep (Bootstrap v a) x -> Bootstrap v a #
(Read a, Read (v a)) => Read (Bootstrap v a) # |
Instance details Defined in Statistics.Resampling Methods readsPrec :: Int -> ReadS (Bootstrap v a) # readList :: ReadS [Bootstrap v a] # readPrec :: ReadPrec (Bootstrap v a) # readListPrec :: ReadPrec [Bootstrap v a] #
(Show a, Show (v a)) => Show (Bootstrap v a) # |
Instance details Defined in Statistics.Resampling Methods showsPrec :: Int -> Bootstrap v a -> ShowS # show :: Bootstrap v a -> String # showList :: [Bootstrap v a] -> ShowS #
(Binary a, Binary (v a)) => Binary (Bootstrap v a) # |
Instance details Defined in Statistics.Resampling Methods put :: Bootstrap v a -> Put # get :: Get (Bootstrap v a) # putList :: [Bootstrap v a] -> Put #
(Eq a, Eq (v a)) => Eq (Bootstrap v a) # |
Instance details Defined in Statistics.Resampling Methods (==) :: Bootstrap v a -> Bootstrap v a -> Bool # (/=) :: Bootstrap v a -> Bootstrap v a -> Bool #
type Rep (Bootstrap v a) # |
Instance details Defined in Statistics.Resampling type Rep (Bootstrap v a) = D1 ('MetaData "Bootstrap" "Statistics.Resampling" "statistics-0.16.2.1-9EJt18csjGeB8Yk5f7eGk5" '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 #

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.