Package 'SBCK'

Description

Perform a multivariate (non stationary) bias correction.

Details

Use Quantiles shuffle in calibration and projection period with CDFt

Public fields

Methods

Public methods

• AR2D2$new()

• AR2D2$fit()

• AR2D2$predict()

• AR2D2$clone()

Method new()

Create a new AR2D2 object.

Usage

AR2D2$new(
  col_cond = base::c(1),
  lag_search = 1,
  lag_keep = 1,
  bc_method = SBCK::CDFt,
  shuffle = "quantile",
  reverse = FALSE,
  ...
)

Arguments

Returns

A new 'AR2D2' object.

Method fit()

Fit the bias correction method. If X1 is NULL, the method is considered as stationary

Usage

AR2D2$fit(Y0, X0, X1 = NULL)

Arguments

Returns

NULL

Method predict()

Predict the correction

Usage

AR2D2$predict(X1 = NULL, X0 = NULL)

Arguments

Returns

[matrix or list] Return the matrix of correction of X1 if X0 is NULL (and vice-versa), else return a list containing Z1 and Z0, the corrections of X1 and X0

Method clone()

The objects of this class are cloneable with this method.

Usage

AR2D2$clone(deep = FALSE)

Arguments

References

Vrac, M. et S. Thao (2020). “R2 D2 v2.0 : accounting for temporal dependences in multivariate bias correction via analogue rank resampling”. In : Geosci. Model Dev. 13.11, p. 5367-5387. doi :10.5194/gmd-13-5367-2020.

Examples

## Three 4-variate random variables
Y0 = matrix( stats::rnorm( n = 1000 ) , ncol = 4 ) ## Biased in calibration period
X0 = matrix( stats::rnorm( n = 1000 ) , ncol = 4 ) / 2 + 3 ## Reference in calibration period
X1 = matrix( stats::rnorm( n = 1000 ) , ncol = 4 ) * 2 + 6 ## Biased in projection period

## Bias correction
cond_col = base::c(2,4)
lag_search = 6
lag_keep = 3
## Step 1 : construction of the class AR2D2 
ar2d2 = SBCK::AR2D2$new( cond_col , lag_search , lag_keep ) 
## Step 2 : Fit the bias correction model
ar2d2$fit( Y0 , X0 , X1 )
## Step 3 : perform the bias correction
Z = ar2d2$predict(X1,X0)

Description

Lenght of cell to compute an histogram

Usage

bin_width_estimator(X, method = "auto")

Arguments

Value

[vector] Lenght of bins

Examples

X = base::cbind( stats::rnorm( n = 2000 ) , stats::rexp(2000) )
## Friedman Draconis is used
binw_width = SBCK::bin_width_estimator( X , method = "auto" ) 
X = stats::rnorm( n = 500 )
## Sturges is used
binw_width = SBCK::bin_width_estimator( X , method = "auto" )

Description

Perform an univariate bias correction of X with respect to Y.

Details

Correction is applied margins by margins.

Public fields

Methods

Public methods

• CDFt$new()

• CDFt$fit()

• CDFt$predict()

• CDFt$clone()

Method new()

Create a new CDFt object.

Usage

CDFt$new(...)

Arguments

Returns

A new 'CDFt' object.

Method fit()

Fit the bias correction method

Usage

CDFt$fit(Y0, X0, X1)

Arguments

Returns

NULL

Method predict()

Predict the correction

Usage

CDFt$predict(X1, X0 = NULL)

Arguments

Returns

[matrix or list] Return the matrix of correction of X1 if X0 is NULL, else return a list containing Z1 and Z0, the corrections of X1 and X0

Method clone()

The objects of this class are cloneable with this method.

Usage

CDFt$clone(deep = FALSE)

Arguments

References

Michelangeli, P.-A., Vrac, M., and Loukos, H.: Probabilistic downscaling approaches: Application to wind cumulative distribution functions, Geophys. Res. Lett., 36, L11708, https://doi.org/10.1029/2009GL038401, 2009.

Examples

## Three bivariate random variables (rnorm and rexp are inverted between ref and bias)
XY = SBCK::dataset_gaussian_exp_2d(2000)
X0 = XY$X0 ## Biased in calibration period
Y0 = XY$Y0 ## Reference in calibration period
X1 = XY$X1 ## Biased in projection period

## Bias correction
## Step 1 : construction of the class CDFt 
cdft = SBCK::CDFt$new() 
## Step 2 : Fit the bias correction model
cdft$fit( Y0 , X0 , X1 )
## Step 3 : perform the bias correction, Z is a list containing
## corrections
Z = cdft$predict(X1,X0) 
Z$Z0 ## Correction in calibration period
Z$Z1 ## Correction in projection period

Description

Compute Chebyshev distance between two dataset or SparseHist X and Y

Usage

chebyshev(X, Y)

Arguments

Value

[float] value of distance

Examples

X = base::cbind( stats::rnorm(2000) , stats::rnorm(2000)  )
Y = base::cbind( stats::rnorm(2000,mean=2)  , stats::rnorm(2000) )
bw = base::c(0.1,0.1)
muX = SBCK::SparseHist( X , bw )
muY = SBCK::SparseHist( Y , bw )

## The four are equals
d = SBCK::chebyshev(  X ,   Y )
d = SBCK::chebyshev(muX ,   Y )
d = SBCK::chebyshev(  X , muY )
d = SBCK::chebyshev(muX , muY )

Description

Pairwise distances between X and themselves with a R function (metric). DO NOT USE, use SBCK::pairwise_distances

Usage

cpp_pairwise_distances_XCall(X,metric)

Arguments

Description

Pairwise distances between X and themselves with a compiled str_metric. DO NOT USE, use SBCK::pairwise_distances

Usage

cpp_pairwise_distances_Xstr(X,str_metric)

Arguments

Description

Pairwise distances between X and Y with a R function (metric). DO NOT USE, use SBCK::pairwise_distances

Usage

cpp_pairwise_distances_XYCall(X,Y,metric)

Arguments

Description

Pairwise distances between two differents matrix X and Y with a compiled str_metric. DO NOT USE, use SBCK::pairwise_distances

Usage

cpp_pairwise_distances_XYstr(X,Y,str_metric)

Arguments

Description

Just a function to transform two datasets into SparseHist, if X or Y (or the both) are already a SparseHist, update just the second

Usage

data_to_hist(X, Y)

Arguments

Value

[list(muX,muY)] a list with the two SparseHist

Examples

X = base::cbind( stats::rnorm(2000) , stats::rexp(2000)  )
Y = base::cbind( stats::rexp(2000)  , stats::rnorm(2000) )

bw = base::c(0.1,0.1)
muX = SBCK::SparseHist( X , bw )
muY = SBCK::SparseHist( Y , bw )

## The four give the same result
SBCK::data_to_hist( X   , Y )
SBCK::data_to_hist( muX , Y )
SBCK::data_to_hist( X   , muY )
SBCK::data_to_hist( muX , muY )

Description

Generate a testing dataset from bimodale random bivariate Gaussian distribution

Usage

dataset_bimodal_reverse_2d(n_samples)

Arguments

Value

[list] a list containing X0, X1 (biased in calibration/projection) and Y0 (reference in calibration)

Examples

XY = SBCK::dataset_bimodal_reverse_2d(2000)
XY$X0 ## Biased in calibration period
XY$Y0 ## Reference in calibration period
XY$X1 ## Biased in projection period

Description

Generate a testing dataset from random bivariate Gaussian distribution

Usage

dataset_gaussian_2d(n_samples)

Arguments

Value

[list] a list containing X0, X1 (biased in calibration/projection) and Y0 (reference in calibration)

Examples

XY = SBCK::dataset_gaussian_2d(2000)
XY$X0 ## Biased in calibration period
XY$Y0 ## Reference in calibration period
XY$X1 ## Biased in projection period

Description

Generate a testing dataset such that the biased dataset is a distribution of the the form Normal x Exp and the reference of the the form Exp x Normal.

Usage

dataset_gaussian_exp_2d(n_samples)

Arguments

Value

[list] a list containing X0, X1 (biased in calibration/projection) and Y0 (reference in calibration)

Examples

XY = SBCK::dataset_gaussian_exp_2d(2000)
XY$X0 ## Biased in calibration period
XY$Y0 ## Reference in calibration period
XY$X1 ## Biased in projection period

Description

Generate a univariate testing dataset from a mixture of gaussian and exponential distribution

Usage

dataset_gaussian_exp_mixture_1d(n_samples)

Arguments

Value

[list] a list containing X0, X1 (biased in calibration/projection) and Y0 (reference in calibration)

Examples

XY = SBCK::dataset_gaussian_exp_mixture_1d(2000)
XY$X0 ## Biased in calibration period
XY$Y0 ## Reference in calibration period
XY$X1 ## Biased in projection period

Description

Generate a testing dataset such that the biased dataset is a normal distribution and reference a mixture a normal with a form in "L"

Usage

dataset_gaussian_L_2d(n_samples)

Arguments

Value

[list] a list containing X0, X1 (biased in calibration/projection) and Y0 (reference in calibration)

Examples

XY = SBCK::dataset_gaussian_L_2d(2000)
XY$X0 ## Biased in calibration period
XY$Y0 ## Reference in calibration period
XY$X1 ## Biased in projection period

Description

Generate a univariate testing dataset such that biased data follow an exponential law whereas reference follow a normal distribution

Usage

dataset_gaussian_VS_exp_1d(n_samples)

Arguments

Value

[list] a list containing X0, X1 (biased in calibration/projection) and Y0 (reference in calibration)

Examples

XY = SBCK::dataset_gaussian_VS_exp_1d(2000)
XY$X0 ## Biased in calibration period
XY$Y0 ## Reference in calibration period
XY$X1 ## Biased in projection period

Description

Generate a testing dataset similar to temperature and precipitation. The method is the following: - Data from a multivariate normal law (dim = 2) are drawn - The quantile mapping is used to map the last column into the exponential law - Values lower than a fixed quantile are replaced by 0

Usage

dataset_like_tas_pr(n_samples)

Arguments

Value

[list] a list containing X0, X1 (biased in calibration/projection) and Y0 (reference in calibration)

Examples

XY = SBCK::dataset_like_tas_pr(2000)
XY$X0 ## Biased in calibration period
XY$Y0 ## Reference in calibration period
XY$X1 ## Biased in projection period

Description

Class used by CDFt and QM to facilitate fit, do not use

Details

Used to parallel work for margins

Public fields

Methods

Public methods

• DistHelper$new()

• DistHelper$set_features()

• DistHelper$fit()

• DistHelper$is_frozen()

• DistHelper$is_parametric()

• DistHelper$clone()

Method new()

Create a new DistHelper object.

Usage

DistHelper$new(dist, kwargs)

Arguments

Returns

A new 'DistHelper' object.

Method set_features()

set the number of features

Usage

DistHelper$set_features(n_features)

Arguments

Returns

NULL

Method fit()

fit the laws

Usage

DistHelper$fit(X, i)

Arguments

Returns

NULL

Method is_frozen()

Test if margins i is frozen

Usage

DistHelper$is_frozen(i)

Arguments

Returns

[bool]

Method is_parametric()

Test if margins i is parametric

Usage

DistHelper$is_parametric(i)

Arguments

Returns

[bool]

Method clone()

The objects of this class are cloneable with this method.

Usage

DistHelper$clone(deep = FALSE)

Arguments

Examples

##

Description

Perform a multivariate (non stationary) bias correction.

Details

Three random variables are needed, Y0, X0 and X1. The dynamic between X0 and X1 is estimated, and applied to Y0 to estimate Y1. Finally, OTC is used between X1 and the Y1 estimated.

Super class

SBCK::OTC -> dOTC

Methods

Public methods

• dOTC$new()

• dOTC$fit()

• dOTC$predict()

• dOTC$clone()

Method new()

Create a new dOTC object.

Usage

dOTC$new(
  bin_width = NULL,
  bin_origin = NULL,
  cov_factor = "std",
  ot = SBCK::OTNetworkSimplex$new()
)

Arguments

Returns

A new 'dOTC' object.

Method fit()

Fit the bias correction method

Usage

dOTC$fit(Y0, X0, X1)

Arguments

Returns

NULL

Method predict()

Predict the correction

Note: Only the center of the bins associated to the corrected points are returned, but all corrections of the form: >> bw = dotc$bin_width / 2 >> n = base::prod(base::dim(X1)) >> Z1 = dotc$predict(X1) >> Z1 = Z1 + t(matrix(stats::runif( n = n min = - bw , max = bw ) , ncol = dim(X1)[1] )) are equivalent for OTC.

Usage

dOTC$predict(X1, X0 = NULL)

Arguments

Returns

[matrix or list] Return the matrix of correction of X1 if X0 is NULL, else return a list containing Z1 and Z0, the corrections of X1 and X0

Method clone()

The objects of this class are cloneable with this method.

Usage

dOTC$clone(deep = FALSE)

Arguments

References

Robin, Y., Vrac, M., Naveau, P., Yiou, P.: Multivariate stochastic bias corrections with optimal transport, Hydrol. Earth Syst. Sci., 23, 773–786, 2019, https://doi.org/10.5194/hess-23-773-2019

Examples

## Three bivariate random variables (rnorm and rexp are inverted between ref and bias)
XY = SBCK::dataset_gaussian_exp_2d(2000)
X0 = XY$X0 ## Biased in calibration period
Y0 = XY$Y0 ## Reference in calibration period
X1 = XY$X1 ## Biased in projection period

## Bin length
bin_width = c(0.2,0.2)

## Bias correction
## Step 1 : construction of the class dOTC 
dotc = SBCK::dOTC$new( bin_width ) 
## Step 2 : Fit the bias correction model
dotc$fit( Y0 , X0 , X1 )
## Step 3 : perform the bias correction, Z is a list containing
## corrections
Z = dotc$predict(X1,X0) 
Z$Z0 ## Correction in calibration period
Z$Z1 ## Correction in projection period

Description

Perform a bias correction of auto-correlation

Details

Correct auto-correlation with a shift approach, taking into account of non stationarity.

Public fields

Active bindings

Methods

Public methods

• dTSMBC$new()

• dTSMBC$fit()

• dTSMBC$predict()

• dTSMBC$clone()

Method new()

Create a new dTSMBC object.

Usage

dTSMBC$new(lag, bc_method = dOTC, method = "row", ref = "middle", ...)

Arguments

Returns

A new 'dTSMBC' object.

Method fit()

Fit the bias correction method

Usage

dTSMBC$fit(Y0, X0, X1)

Arguments

Returns

NULL

Method predict()

Predict the correction

Usage

dTSMBC$predict(X1, X0 = NULL)

Arguments

Returns

[matrix or list] Return the matrix of correction of X1 if X0 is NULL, else return a list containing Z1 and Z0, the corrections of X1 and X0

Method clone()

The objects of this class are cloneable with this method.

Usage

dTSMBC$clone(deep = FALSE)

Arguments

References

Robin, Y. and Vrac, M.: Is time a variable like the others in multivariate statistical downscaling and bias correction?, Earth Syst. Dynam. Discuss. [preprint], https://doi.org/10.5194/esd-2021-12, in review, 2021.

Examples

## arima model parameters
modelX0 = list( ar = base::c(  0.6 , 0.2 , -0.1 ) )
modelX1 = list( ar = base::c(  0.4 , 0.1 , -0.3 ) )
modelY0 = list( ar = base::c( -0.3 , 0.4 , -0.2 ) )

## arima random generator
rand.genX0 = function(n){ return(stats::rnorm( n , mean = 0.2 , sd = 1   )) }
rand.genX1 = function(n){ return(stats::rnorm( n , mean = 0.8 , sd = 1   )) }
rand.genY0 = function(n){ return(stats::rnorm( n , mean = 0   , sd = 0.7 )) }

## Generate two AR processes
X0 = stats::arima.sim( n = 1000 , model = modelX0 , rand.gen = rand.genX0 )
X1 = stats::arima.sim( n = 1000 , model = modelX1 , rand.gen = rand.genX1 )
Y0 = stats::arima.sim( n = 1000 , model = modelY0 , rand.gen = rand.genY0 )
X0 = as.vector( X0 )
X1 = as.vector( X1 )
Y0 = as.vector( Y0 + 5 )

## And correct it with 30 lags
dtsbc = SBCK::dTSMBC$new( 30 )
dtsbc$fit( Y0 , X0 , X1 )
Z = dtsbc$predict(X1,X0)

Description

Perform a multivariate (non stationary) bias correction.

Details

use Schaake shuffle

Super class

SBCK::CDFt -> ECBC

Methods

Public methods

• ECBC$new()

• ECBC$fit()

• ECBC$predict()

• ECBC$clone()

Method new()

Create a new ECBC object.

Usage

ECBC$new(...)

Arguments

Returns

A new 'ECBC' object.

Method fit()

Fit the bias correction method

Usage

ECBC$fit(Y0, X0, X1)

Arguments

Returns

NULL

Method predict()

Predict the correction

Usage

ECBC$predict(X1, X0 = NULL)

Arguments

Returns

[matrix or list] Return the matrix of correction of X1 if X0 is NULL, else return a list containing Z1 and Z0, the corrections of X1 and X0

Method clone()

The objects of this class are cloneable with this method.

Usage

ECBC$clone(deep = FALSE)

Arguments

References

Vrac, M. and P. Friederichs, 2015: Multivariate—Intervariable, Spatial, and Temporal—Bias Correction. J. Climate, 28, 218–237, https://doi.org/10.1175/JCLI-D-14-00059.1

Examples

## Three bivariate random variables (rnorm and rexp are inverted between ref
## and bias)
XY = SBCK::dataset_gaussian_exp_2d(2000)
X0 = XY$X0 ## Biased in calibration period
Y0 = XY$Y0 ## Reference in calibration period
X1 = XY$X1 ## Biased in projection period


## Bias correction
## Step 1 : construction of the class ECBC
ecbc = SBCK::ECBC$new() 
## Step 2 : Fit the bias correction model
ecbc$fit( Y0 , X0 , X1 )
## Step 3 : perform the bias correction
Z = ecbc$predict(X1,X0)

Description

Compute Energy distance between two dataset or SparseHist X and Y

Usage

energy(X, Y, p = 2, metric = "euclidean")

Arguments

Value

[float] value of distance

Examples

X = base::cbind( stats::rnorm(2000) , stats::rnorm(2000)  )
Y = base::cbind( stats::rnorm(2000,mean=10)  , stats::rnorm(2000) )
bw = base::c(0.1,0.1)
muX = SBCK::SparseHist( X , bw )
muY = SBCK::SparseHist( Y , bw )

## The four are equals
w2 = SBCK::energy(X,Y)
w2 = SBCK::energy(muX,Y)
w2 = SBCK::energy(X,muY)
w2 = SBCK::energy(muX,muY)

Description

Compute Euclidean distance between two dataset or SparseHist X and Y

Usage

euclidean(X, Y)

Arguments

Value

[float] value of distance

Examples

X = base::cbind( stats::rnorm(2000) , stats::rnorm(2000)  )
Y = base::cbind( stats::rnorm(2000,mean=2)  , stats::rnorm(2000) )
bw = base::c(0.1,0.1)
muX = SBCK::SparseHist( X , bw )
muY = SBCK::SparseHist( Y , bw )

## The four are equals
d = SBCK::euclidean(  X ,   Y )
d = SBCK::euclidean(muX ,   Y )
d = SBCK::euclidean(  X , muY )
d = SBCK::euclidean(muX , muY )

Description

Always return X1 / X0 as correction.

Details

Only for comparison.

Methods

Public methods

• IdBC$new()

• IdBC$fit()

• IdBC$predict()

• IdBC$clone()

Method new()

Create a new IdBC object.

Usage

IdBC$new()

Returns

A new 'IdBC' object.

Method fit()

Fit the bias correction method

Usage

IdBC$fit(Y0, X0, X1 = NULL)

Arguments

Returns

NULL

Method predict()

Predict the correction. Use named keywords to use stationary or non-stationary method.

Usage

IdBC$predict(X1 = NULL, X0 = NULL)

Arguments

Returns

[matrix or list] Return X1 and / or X0

Method clone()

The objects of this class are cloneable with this method.

Usage

IdBC$clone(deep = FALSE)

Arguments

Examples

## Three bivariate random variables (rnorm and rexp are inverted between ref
## and bias)
XY = SBCK::dataset_gaussian_exp_2d(2000)
X0 = XY$X0 ## Biased in calibration period
Y0 = XY$Y0 ## Reference in calibration period
X1 = XY$X1 ## Biased in projection period


## Bias correction
## Step 1 : construction of the class IdBC
idbc = SBCK::IdBC$new() 
## Step 2 : Fit the bias correction model
idbc$fit( Y0 , X0 , X1 )
## Step 3 : perform the bias correction
Z = idbc$predict(X1,X0) 
## Z$Z0 # == X0
## Z$Z1 # == X1

Description

Compute Manhattan distance between two dataset or SparseHist X and Y

Usage

manhattan(X, Y)

Arguments

Value

[float] value of distance

Examples

X = base::cbind( stats::rnorm(2000) , stats::rnorm(2000)  )
Y = base::cbind( stats::rnorm(2000,mean=2)  , stats::rnorm(2000) )
bw = base::c(0.1,0.1)
muX = SBCK::SparseHist( X , bw )
muY = SBCK::SparseHist( Y , bw )

## The four are equals
d = SBCK::manhattan(  X ,   Y )
d = SBCK::manhattan(muX ,   Y )
d = SBCK::manhattan(  X , muY )
d = SBCK::manhattan(muX , muY )

Description

Perform a multivariate bias correction.

Details

BC is performed with an alternance of rotation and univariate BC.

Public fields

Methods

Public methods

• MBCn$new()

• MBCn$fit()

• MBCn$predict()

• MBCn$clone()

Method new()

Create a new MBCn object.

Usage

MBCn$new(
  bc = QDM,
  metric = wasserstein,
  stopping_criteria = SlopeStoppingCriteria,
  stopping_criteria_params = list(minit = 20, maxit = 100, tol = 0.001),
  ...
)

Arguments

Returns

A new 'MBCn' object.

Method fit()

Fit the bias correction method

Usage

MBCn$fit(Y0, X0, X1)

Arguments

Returns

NULL

Method predict()

Predict the correction

Usage

MBCn$predict(X1, X0 = NULL)

Arguments

Returns

[matrix or list] Return the matrix of correction of X1 if X0 is NULL, else return a list containing Z1 and Z0, the corrections of X1 and X0

Method clone()

The objects of this class are cloneable with this method.

Usage

MBCn$clone(deep = FALSE)

Arguments

References

Cannon, A. J., Sobie, S. R., and Murdock, T. Q.: Bias correction of simulated precipitation by quantile mapping: how well do methods preserve relative changes in quantiles and extremes?, J. Climate, 28, 6938–6959, https://doi.org/10.1175/JCLI-D-14- 00754.1, 2015.

Examples

## Three bivariate random variables (rnorm and rexp are inverted between ref
## and bias)
XY = SBCK::dataset_gaussian_exp_2d(200)
X0 = XY$X0 ## Biased in calibration period
Y0 = XY$Y0 ## Reference in calibration period
X1 = XY$X1 ## Biased in projection period

## Bias correction
## Step 1 : construction of the class MBCn
mbcn = SBCK::MBCn$new() 
## Step 2 : Fit the bias correction model
mbcn$fit( Y0 , X0 , X1 )
## Step 3 : perform the bias correction, Z is a list containing
## corrections
Z = mbcn$predict(X1,X0) 
Z$Z0 ## Correction in calibration period
Z$Z1 ## Correction in projection period

Description

Compute Minkowski distance between two dataset or SparseHist X and Y. If p = 2, it is the Euclidean distance, for p = 1, it is the manhattan distance, if p = Inf, chebyshev distance is called.

Usage

minkowski(X, Y, p = 2)

Arguments

Value

[float] value of distance

Examples

X = base::cbind( stats::rnorm(2000) , stats::rnorm(2000)  )
Y = base::cbind( stats::rnorm(2000,mean=2)  , stats::rnorm(2000) )
bw = base::c(0.1,0.1)
muX = SBCK::SparseHist( X , bw )
muY = SBCK::SparseHist( Y , bw )

## The four are equals
d = SBCK::minkowski(  X ,   Y , p = 3 )
d = SBCK::minkowski(muX ,   Y , p = 3 )
d = SBCK::minkowski(  X , muY , p = 3 )
d = SBCK::minkowski(muX , muY , p = 3 )

Description

Perform a multivariate bias correction with Gaussian assumption.

Details

Only pearson correlations are corrected.

Public fields

Methods

Public methods

• MRec$new()

• MRec$fit()

• MRec$predict()

• MRec$clone()

Method new()

Create a new MRec object.

Usage

MRec$new(distY = NULL, distX = NULL)

Arguments

Returns

A new 'MRec' object.

Method fit()

Fit the bias correction method

Usage

MRec$fit(Y0, X0, X1)

Arguments

Returns

NULL

Method predict()

Predict the correction

Usage

MRec$predict(X1, X0 = NULL)

Arguments

Returns

[matrix or list] Return the matrix of correction of X1 if X0 is NULL, else return a list containing Z1 and Z0, the corrections of X1 and X0

Method clone()

The objects of this class are cloneable with this method.

Usage

MRec$clone(deep = FALSE)

Arguments

References

Bárdossy, A. and Pegram, G.: Multiscale spatial recorrelation of RCM precipitation to produce unbiased climate change scenarios over large areas and small, Water Resources Research, 48, 9502–, https://doi.org/10.1029/2011WR011524, 2012.

Examples

## Three bivariate random variables (rnorm and rexp are inverted between ref
## and bias)
XY = SBCK::dataset_gaussian_exp_2d(2000)
X0 = XY$X0 ## Biased in calibration period
Y0 = XY$Y0 ## Reference in calibration period
X1 = XY$X1 ## Biased in projection period

## Bias correction
## Step 1 : construction of the class MRec 
mrec = SBCK::MRec$new() 
## Step 2 : Fit the bias correction model
mrec$fit( Y0 , X0 , X1 )
## Step 3 : perform the bias correction, Z is a list containing corrections.
Z = mrec$predict(X1,X0) ## X0 is optional, in this case Z0 is NULL
Z$Z0 ## Correction in calibration period
Z$Z1 ## Correction in projection period

Description

Multivariate Schaake shuffle using the quantiles.

Details

Used to reproduce the dependence structure of a dataset to another dataset

Public fields

Methods

Public methods

• MVQuantilesShuffle$new()

• MVQuantilesShuffle$fit()

• MVQuantilesShuffle$transform()

• MVQuantilesShuffle$clone()

Method new()

Create a new MVQuantilesShuffle object.

Usage

MVQuantilesShuffle$new(col_cond = base::c(1), lag_search = 1, lag_keep = 1)

Arguments

Returns

A new 'MVQuantilesShuffle' object.

Method fit()

Fit method

Usage

MVQuantilesShuffle$fit(Y)

Arguments

Returns

NULL

Method transform()

Transform method

Usage

MVQuantilesShuffle$transform(X)

Arguments

Returns

Z The X with the quantiles structure of Y

Method clone()

The objects of this class are cloneable with this method.

Usage

MVQuantilesShuffle$clone(deep = FALSE)

Arguments

References

Vrac, M. et S. Thao (2020). “R2 D2 v2.0 : accounting for temporal dependences in multivariate bias correction via analogue rank resampling”. In : Geosci. Model Dev. 13.11, p. 5367-5387. doi :10.5194/gmd-13-5367-2020.

Examples

## Generate sample
X = matrix( stats::rnorm( n = 100 ) , ncol = 4 )
Y = matrix( stats::rnorm( n = 100 ) , ncol = 4 )

## Fit dependence structure
## Assume that the link beween column 2 and 4 is correct, and change also
## the auto-correlation structure until lag 3 = lag_keep - 1
mvq = MVQuantilesShuffle$new( base::c(2,4) , lag_search = 6 , lag_keep = 4 )
mvq$fit(Y)
Z = mvq$transform(X)

Description

Multivariate Schaake shuffle using the ranks.

Details

Used to reproduce the dependence structure of a dataset to another dataset

Public fields

Methods

Public methods

• MVRanksShuffle$new()

• MVRanksShuffle$fit()

• MVRanksShuffle$transform()

• MVRanksShuffle$clone()

Method new()

Create a new MVRanksShuffle object.

Usage

MVRanksShuffle$new(col_cond = base::c(1), lag_search = 1, lag_keep = 1)

Arguments

Returns

A new 'MVRanksShuffle' object.

Method fit()

Fit method

Usage

MVRanksShuffle$fit(Y)

Arguments

Returns

NULL

Method transform()

Transform method

Usage

MVRanksShuffle$transform(X)

Arguments

Returns

Z The X with the quantiles structure of Y

Method clone()

The objects of this class are cloneable with this method.

Usage

MVRanksShuffle$clone(deep = FALSE)

Arguments

References

Vrac, M. et S. Thao (2020). “R2 D2 v2.0 : accounting for temporal dependences in multivariate bias correction via analogue rank resampling”. In : Geosci. Model Dev. 13.11, p. 5367-5387. doi :10.5194/gmd-13-5367-2020.

Examples

## Generate sample
X = matrix( stats::rnorm( n = 100 ) , ncol = 4 )
Y = matrix( stats::rnorm( n = 100 ) , ncol = 4 )

## Fit dependence structure
## Assume that the link beween column 2 and 4 is correct, and change also
## the auto-correlation structure until lag 3 = lag_keep - 1
mvr = MVRanksShuffle$new( base::c(2,4) , lag_search = 6 , lag_keep = 4 )
mvr$fit(Y)
Z = mvr$transform(X)

Description

Perform a multivariate bias correction of X0 with respect to Y0.

Details

Joint distribution, i.e. all dependence are corrected.

Public fields

Methods

Public methods

• OTC$new()

• OTC$fit()

• OTC$predict()

• OTC$clone()

Method new()

Create a new OTC object.

Usage

OTC$new(bin_width = NULL, bin_origin = NULL, ot = SBCK::OTNetworkSimplex$new())

Arguments

Returns

A new 'OTC' object.

Method fit()

Fit the bias correction method

Usage

OTC$fit(Y0, X0)

Arguments

Returns

NULL

Method predict()

Predict the correction

Note: Only the center of the bins associated to the corrected points are returned, but all corrections of the form: >> bw = otc$bin_width / 2 >> n = base::prod(base::dim(X0)) >> Z0 = otc$predict(X0) >> Z0 = Z0 + t(matrix(stats::runif( n = n min = - bw , max = bw ) , ncol = dim(X0)[1] )) are equivalent for OTC.

Usage

OTC$predict(X0)

Arguments

Returns

[matrix] Return the corrections of X0

Method clone()

The objects of this class are cloneable with this method.

Usage

OTC$clone(deep = FALSE)

Arguments

References

Robin, Y., Vrac, M., Naveau, P., Yiou, P.: Multivariate stochastic bias corrections with optimal transport, Hydrol. Earth Syst. Sci., 23, 773–786, 2019, https://doi.org/10.5194/hess-23-773-2019

Examples

## Two bivariate random variables (rnorm and rexp are inverted between ref 
## and bias)
XY = SBCK::dataset_gaussian_exp_2d(2000)
X0 = XY$X0 ## Biased in calibration period
Y0 = XY$Y0 ## Reference in calibration period

## Bin length
bin_width = SBCK::bin_width_estimator( list(X0,Y0) )

## Bias correction
## Step 1 : construction of the class OTC 
otc = SBCK::OTC$new( bin_width ) 
## Step 2 : Fit the bias correction model
otc$fit( Y0 , X0 )
## Step 3 : perform the bias correction, Z0 is the correction of
## X0 with respect to the estimation of Y0
Z0 = otc$predict(X0)

Description

Histogram

Details

Just a generic class which contains two arguments, p (probability) and c (center of bins)

Public fields

Methods

Public methods

• OTHist$new()

• OTHist$clone()

Method new()

Create a new OTHist object.

Usage

OTHist$new(p, c)

Arguments

Returns

A new 'OTHist' object.

Method clone()

The objects of this class are cloneable with this method.

Usage

OTHist$clone(deep = FALSE)

Arguments

Examples

## Build a random discrete probability distribution
p = stats::rnorm(100)
p = p / base::sum(p)
c = base::seq( -1 , 1 , length = 100 )
mu = OTHist$new( p , c )

Description

Solve the optimal transport problem with the package 'transport'

Details

use the network simplex algorithm

Public fields

Methods

Public methods

• OTNetworkSimplex$new()

• OTNetworkSimplex$fit()

• OTNetworkSimplex$clone()

Method new()

Create a new OTNetworkSimplex object.

Usage

OTNetworkSimplex$new(p = 2)

Arguments

Returns

A new 'OTNetworkSimplex' object.

Method fit()

Fit the OT plan

Usage

OTNetworkSimplex$fit(muX0, muX1, C = NULL)

Arguments

Returns

NULL

Method clone()

The objects of this class are cloneable with this method.

Usage

OTNetworkSimplex$clone(deep = FALSE)

Arguments

References

Bazaraa, M. S., Jarvis, J. J., and Sherali, H. D.: Linear Programming and Network Flows, 4th edn., John Wiley & Sons, 2009.

Examples

## Define two dataset
X = stats::rnorm(2000)
Y = stats::rnorm(2000 , mean = 5 )
bw = base::c(0.1)
muX = SBCK::SparseHist( X , bw )
muY = SBCK::SparseHist( Y , bw )

## Find solution
ot = OTNetworkSimplex$new()
ot$fit( muX , muY )

print( sum(ot$plan) ) ## Must be equal to 1
print( ot$success )   ## If solve is success
print( sqrt(sum(ot$plan * ot$C)) ) ## Cost of plan

Description

Compute the matrix of pairwise distances between a matrix X and a matrix Y

Usage

pairwise_distances(X,Y,metric)

Arguments

Value

distXY [matrix] Pairwise distances. distXY[i,j] is the distance between X[i,] and Y[j,]

Examples

X = matrix( stats::rnorm(200) , ncol = 100 , nrow = 2 )
Y = matrix( stats::rexp(300)  , ncol = 150 , nrow = 2 )

distXY = SBCK::pairwise_distances( X , Y )

Description

Apply the diff w.r.t. a ref transformation.

Details

Transform a dataset such that all 'lower' dimensions are replaced by the 'ref' dimension minus the 'lower'; and all 'upper' dimensions are replaced by 'upper' minus 'ref'.

Super class

SBCK::PrePostProcessing -> PPPDiffRef

Public fields

Methods

Public methods

• PPPDiffRef$new()

• PPPDiffRef$transform()

• PPPDiffRef$itransform()

• PPPDiffRef$clone()

Method new()

Create a new PPPDiffRef object.

Usage

PPPDiffRef$new(ref, lower = NULL, upper = NULL, ...)

Arguments

Returns

A new 'PPPDiffRef' object.

Method transform()

Apply the DiffRef transform.

Usage

PPPDiffRef$transform(X)

Arguments

Returns

Xt a transformed matrix

Method itransform()

Apply the DiffRef inverse transform.

Usage

PPPDiffRef$itransform(Xt)

Arguments

Returns

X a transformed matrix

Method clone()

The objects of this class are cloneable with this method.

Usage

PPPDiffRef$clone(deep = FALSE)

Arguments

Examples

## Parameters
size  = 2000
nfeat = 5
sign  = base::sample( base::c(-1,1) , nfeat - 1 , replace = TRUE )

## Build data
X     = matrix( stats::rnorm( n = size ) , ncol = 1 )
for( s in sign )
{
	X = base::cbind( X , X[,1] + s * base::abs(matrix( stats::rnorm(n = size) , ncol = 1 )) )
}

## PPP
lower = which( sign ==  1 ) + 1
upper = which( sign == -1 ) + 1
ppp   = SBCK::PPPDiffRef$new( ref = 1 , lower = lower , upper = upper )
Xt    = ppp$transform(X)
Xti   = ppp$itransform(Xt)

print( base::max( base::abs( X - Xti ) ) )

Description

Base class to build link function pre-post processing class. See also the PrePostProcessing documentation

Details

This class is used to define pre/post processing class with a link function and its inverse. See example.

Super class

SBCK::PrePostProcessing -> PPPFunctionLink

Methods

Public methods

• PPPFunctionLink$new()

• PPPFunctionLink$transform()

• PPPFunctionLink$itransform()

• PPPFunctionLink$clone()

Method new()

Create a new PPPFunctionLink object.

Usage

PPPFunctionLink$new(transform_, itransform_, cols = NULL, ...)

Arguments

Returns

A new 'PPPFunctionLink' object.

Method transform()

Apply the transform.

Usage

PPPFunctionLink$transform(X)

Arguments

Returns

Xt a transformed matrix

Method itransform()

Apply the inverse transform.

Usage

PPPFunctionLink$itransform(Xt)

Arguments

Returns

X a transformed matrix

Method clone()

The objects of this class are cloneable with this method.

Usage

PPPFunctionLink$clone(deep = FALSE)

Arguments

Examples

## Start with data
XY = SBCK::dataset_like_tas_pr(2000)
X0 = XY$X0
X1 = XY$X1
Y0 = XY$Y0

## Define the link function
transform  = function(x) { return(x^3) }
itransform = function(x) { return(x^(1/3)) }

## And the PPP method
ppp = PPPFunctionLink$new( bc_method = CDFt , transform = transform ,
                                             itransform = itransform )

## And now the correction
## Bias correction
ppp$fit(Y0,X0,X1)
Z = ppp$predict(X1,X0)

Description

Log linear link function. See also the PrePostProcessing documentation.

Details

Log linear link function. The transform is log(x) if 0 < x < 1, else x -1, and the inverse transform exp(x) if x < 0, else x + 1.

Super classes

SBCK::PrePostProcessing -> SBCK::PPPFunctionLink -> PPPLogLinLink

Methods

Public methods

• PPPLogLinLink$new()

• PPPLogLinLink$clone()

Method new()

Create a new PPPLogLinLink object.

Usage

PPPLogLinLink$new(s = 1e-05, cols = NULL, ...)

Arguments

Returns

A new 'PPPLogLinLink' object.

Method clone()

The objects of this class are cloneable with this method.

Usage

PPPLogLinLink$clone(deep = FALSE)

Arguments

Examples

## Start with data
XY = SBCK::dataset_like_tas_pr(2000)
X0 = XY$X0
X1 = XY$X1
Y0 = XY$Y0

## Define the PPP method
ppp = PPPLogLinLink$new( bc_method = CDFt , cols = 2 ,
                         pipe = list(PPPSSR),
                         pipe_kwargs = list(list(cols=2)) )

## And now the correction
## Bias correction
ppp$fit(Y0,X0,X1)
Z = ppp$predict(X1,X0)

Description

Set an order between cols, and preserve it by swapping values after the correction

Details

Set an order between cols, and preserve it by swapping values after the correction

Super class

SBCK::PrePostProcessing -> PPPPreserveOrder

Methods

Public methods

• PPPPreserveOrder$new()

• PPPPreserveOrder$transform()

• PPPPreserveOrder$itransform()

• PPPPreserveOrder$clone()

Method new()

Create a new PPPPreserveOrder object.

Usage

PPPPreserveOrder$new(cols = NULL, ...)

Arguments

Returns

A new 'PPPPreserveOrder' object.

Method transform()

nothing occur here

Usage

PPPPreserveOrder$transform(X)

Arguments

Returns

Xt a transformed matrix

Method itransform()

sort along cols

Usage

PPPPreserveOrder$itransform(Xt)

Arguments

Returns

X a transformed matrix

Method clone()

The objects of this class are cloneable with this method.

Usage

PPPPreserveOrder$clone(deep = FALSE)

Arguments

Examples

## Build data
X = matrix( stats::rnorm( n = 20 ) , ncol = 2 )

## PPP
ppp   = SBCK::PPPPreserveOrder$new( cols = base::c(1,2) )
Xt    = ppp$transform(X) ## Nothing
Xti   = ppp$itransform(Xt) ## Order

Description

Square link function. See also the PrePostProcessing documentation.

Details

Square link function. The transform is x^2, and the sign(x)*sqrt(abs(x)) its inverse.

Super classes

SBCK::PrePostProcessing -> SBCK::PPPFunctionLink -> PPPSquareLink

Methods

Public methods

• PPPSquareLink$new()

• PPPSquareLink$clone()

Method new()

Create a new PPPSquareLink object.

Usage

PPPSquareLink$new(cols = NULL, ...)

Arguments

Returns

A new 'PPPSquareLink' object.

Method clone()

The objects of this class are cloneable with this method.

Usage

PPPSquareLink$clone(deep = FALSE)

Arguments

Examples

## Start with data
XY = SBCK::dataset_like_tas_pr(2000)
X0 = XY$X0
X1 = XY$X1
Y0 = XY$Y0

## Define the PPP method
ppp = PPPSquareLink$new( bc_method = CDFt , cols = 2 )

## And now the correction
## Bias correction
ppp$fit(Y0,X0,X1)
Z = ppp$predict(X1,X0)

Description

Apply the SSR transformation.

Details

Apply the SSR transformation. The SSR transformation replace the 0 by a random values between 0 and the minimal non zero value (the threshold). The inverse transform replace all values lower than the threshold by 0. The threshold used for inverse transform is given by the keyword 'isaved', which takes the value 'Y0' (reference in calibration period), or 'X0' (biased in calibration period), or 'X1' (biased in projection period)

Super class

SBCK::PrePostProcessing -> PPPSSR

Public fields

Methods

Public methods

• PPPSSR$new()

• PPPSSR$transform()

• PPPSSR$itransform()

• PPPSSR$clone()

Method new()

Create a new PPPSSR object.

Usage

PPPSSR$new(cols = NULL, isaved = "Y0", ...)

Arguments

Returns

A new 'PPPSSR' object.

Method transform()

Apply the SSR transform, i.e. all 0 are replaced by random values between 0 (excluded) and the minimal non zero value.

Usage

PPPSSR$transform(X)

Arguments

Returns

Xt a transformed matrix

Method itransform()

Apply the inverse SSR transform, i.e. all values lower than the threshold found in the transform function are replaced by 0.

Usage

PPPSSR$itransform(Xt)

Arguments

Returns

X a transformed matrix

Method clone()

The objects of this class are cloneable with this method.

Usage

PPPSSR$clone(deep = FALSE)

Arguments

Examples

## Start with data
XY = SBCK::dataset_like_tas_pr(2000)
X0 = XY$X0
X1 = XY$X1
Y0 = XY$Y0

## Define the PPP method
ppp = PPPSSR$new( bc_method = CDFt , cols = 2 )

## And now the correction
## Bias correction
ppp$fit(Y0,X0,X1)
Z = ppp$predict(X1,X0)

Description

Base class to pre/post process data before/after a bias correction

Details

This base class can be considered as the identity pre-post processing, and is used to be herited by others pre/post processing class. The key ideas are:
- A PrePostProcessing based class contains a bias correction method, initalized by the 'bc_method' argument, always available for all herited class
- The 'pipe' keyword is a list of pre/post processing class, applied one after the other.

Try with an example, start with a dataset similar to tas/pr:
>>> XY = SBCK::dataset_like_tas_pr(2000)
>>> X0 = XY$X0
>>> X1 = XY$X1
>>> Y0 = XY$Y0

The first column is Gaussian, but the second is an exponential law with a Dirac mass at 0, represented the 0 of precipitations. For a quantile mapping correction in the calibration period, we just apply
>>> qm = SBCK::QM$new()
>>> qm$fit(Y0,X0)
>>> Z0 = qm$predict(X0)

Now, if we want to pre-post process with the SSR method (0 are replaced by random values between 0 (excluded) and the minimal non zero value), we write:
>>> ppp = SBCK::PPPSSR$new( bc_method = QM , cols = 2 )
>>> ppp$fit(Y0,X0)
>>> Z0 = ppp$predict(X0)

The SSR approach is applied only on the second column (the precipitation), and the syntax is the same than for a simple bias correction method.

Imagine now that we want to apply the SSR, and to ensure the positivity of CDFt for precipitation, we also want to use the LogLinLink pre-post processing method. This can be done with the following syntax:
>>> ppp = PPPLogLinLink$new( bc_method = CDFt , cols = 2 ,
>>> pipe = list(PPPSSR) ,
>>> pipe_kwargs = list( list(cols = 2) ) )
>>> ppp$fit(Y0,X0,X1)
>>> Z = ppp$predict(X1,X0)

With this syntax, the pre processing operation is PPPLogLinLink$transform(PPPSSR$transform(data)) and post processing operation PPPSSR$itransform(PPPLogLinLink$itransform(bc_data)). So the formula can read from right to left (as the mathematical composition). Note it is equivalent to define:
>>> ppp = PrePostProcessing$new( bc_method = CDFt,
>>> pipe = list(PPPLogLinLink,PPPSSR),
>>> pipe_kwargs = list( list(cols=2) , list(cols=2) ) )

Methods

Public methods

• PrePostProcessing$new()

• PrePostProcessing$transform()

• PrePostProcessing$itransform()

• PrePostProcessing$fit()

• PrePostProcessing$predict()

• PrePostProcessing$clone()

Method new()

Create a new PrePostProcessing object.

Usage

PrePostProcessing$new(
  bc_method = NULL,
  bc_method_kwargs = list(),
  pipe = list(),
  pipe_kwargs = list()
)

Arguments

Returns

A new 'PrePostProcessing' object.

Method transform()

Transformation applied to data before the bias correction. Just the identity for this class

Usage

PrePostProcessing$transform(X)

Arguments

Returns

Xt [matrix: n_samples * n_features]

Method itransform()

Transformation applied to data after the bias correction. Just the identity for this class

Usage

PrePostProcessing$itransform(Xt)

Arguments

Returns

X [matrix: n_samples * n_features]

Method fit()

Apply the pre processing and fit the bias correction method. If X1 is NULL, the method is considered as stationary

Usage

PrePostProcessing$fit(Y0, X0, X1 = NULL)

Arguments

Returns

NULL

Method predict()

Predict the correction, apply pre-processing before, and post-processing after

Usage

PrePostProcessing$predict(X1 = NULL, X0 = NULL)

Arguments

Returns

[matrix or list] Return the matrix of correction of X1 if X0 is NULL (and vice-versa), else return a list containing Z1 and Z0, the corrections of X1 and X0

Method clone()

The objects of this class are cloneable with this method.

Usage

PrePostProcessing$clone(deep = FALSE)

Arguments

Examples

## Start with data
XY = SBCK::dataset_like_tas_pr(2000)
X0 = XY$X0
X1 = XY$X1
Y0 = XY$Y0

## Define pre/post processing method
ppp = PrePostProcessing$new( bc_method = CDFt,
                             pipe = list(PPPLogLinLink,PPPSSR),
                             pipe_kwargs = list( list(cols=2) , list(cols=2) ) )

## Bias correction
ppp$fit(Y0,X0,X1)
Z = ppp$predict(X1,X0)

Description

Perform a bias correction.

Details

Mix of delta and quantile method

Methods

Public methods

• QDM$new()

• QDM$fit()

• QDM$predict()

• QDM$clone()

Method new()

Create a new QDM object.

Usage

QDM$new(delta = "additive", ...)

Arguments

Returns

A new 'QDM' object.

Method fit()

Fit the bias correction method

Usage

QDM$fit(Y0, X0, X1)

Arguments

Returns

NULL

Method predict()

Predict the correction

Usage

QDM$predict(X1, X0 = NULL)

Arguments

Returns

[matrix or list] Return the matrix of correction of X1 if X0 is NULL, else return a list containing Z1 and Z0, the corrections of X1 and X0

Method clone()

The objects of this class are cloneable with this method.

Usage

QDM$clone(deep = FALSE)

Arguments

References

Cannon, A. J., Sobie, S. R., and Murdock, T. Q.: Bias correction of simulated precipitation by quantile mapping: how well do methods preserve relative changes in quantiles and extremes?, J. Climate, 28, 6938–6959, https://doi.org/10.1175/JCLI-D-14- 00754.1, 2015.

Examples

## Three bivariate random variables (rnorm and rexp are inverted between ref
## and bias)
XY = SBCK::dataset_gaussian_exp_2d(2000)
X0 = XY$X0 ## Biased in calibration period
Y0 = XY$Y0 ## Reference in calibration period
X1 = XY$X1 ## Biased in projection period

## Bias correction
## Step 1 : construction of the class QDM
qdm = SBCK::QDM$new() 
## Step 2 : Fit the bias correction model
qdm$fit( Y0 , X0 , X1 )
## Step 3 : perform the bias correction, Z is a list containing
## corrections
Z = qdm$predict(X1,X0) 
Z$Z0 ## Correction in calibration period
Z$Z1 ## Correction in projection period

Description

Perform an univariate bias correction of X0 with respect to Y0

Details

Correction is applied margins by margins.

Public fields

Methods

Public methods

• QM$new()

• QM$fit()

• QM$predict()

• QM$clone()

Method new()

Create a new QM object.

Usage

QM$new(distX0 = ROOPSD::rv_histogram, distY0 = ROOPSD::rv_histogram, ...)

Arguments

Returns

A new 'QM' object.

Method fit()

Fit the bias correction method

Usage

QM$fit(Y0 = NULL, X0 = NULL)

Arguments

Returns

NULL

Method predict()

Predict the correction

Usage

QM$predict(X0)

Arguments

Returns

[matrix] Return the corrections of X0

Method clone()

The objects of this class are cloneable with this method.

Usage

QM$clone(deep = FALSE)

Arguments

References

Panofsky, H. A. and Brier, G. W.: Some applications of statistics to meteorology, Mineral Industries Extension Services, College of Mineral Industries, Pennsylvania State University, 103 pp., 1958.

Wood, A. W., Leung, L. R., Sridhar, V., and Lettenmaier, D. P.: Hydrologic Implications of Dynamical and Statistical Approaches to Downscaling Climate Model Outputs, Clim. Change, 62, 189–216, https://doi.org/10.1023/B:CLIM.0000013685.99609.9e, 2004.

Déqué, M.: Frequency of precipitation and temperature extremes over France in an anthropogenic scenario: Model results and statistical correction according to observed values, Global Planet. Change, 57, 16–26, https://doi.org/10.1016/j.gloplacha.2006.11.030, 2007.

Examples

## Three bivariate random variables (rnorm and rexp are inverted between ref
## and bias)
XY = SBCK::dataset_gaussian_exp_2d(2000)
X0 = XY$X0 ## Biased in calibration period
Y0 = XY$Y0 ## Reference in calibration period

## Bias correction
## Step 1 : construction of the class QM 
qm = SBCK::QM$new() 
## Step 2 : Fit the bias correction model
qm$fit( Y0 , X0 )
## Step 3 : perform the bias correction, Z0 is the correction of
## X0 with respect to the estimation of Y0
Z0 = qm$predict(X0)

# ## But in fact the laws are known, we can fit parameters:
distY0 = list( ROOPSD::Exponential , ROOPSD::Normal )
distX0 = list( ROOPSD::Normal , ROOPSD::Exponential )
qm_fix = SBCK::QM$new( distY0 = distY0 , distX0 = distX0 )
qm_fix$fit( Y0 , X0 )
Z0 = qm_fix$predict(X0)

Description

Perform a multivariate bias correction of X with respect to Y

Details

Dependence is corrected with multi_schaake_shuffle.

Super class

SBCK::QM -> QMrs

Public fields

Methods

Public methods

• QMrs$new()

• QMrs$fit()

• QMrs$predict()

• QMrs$clone()

Method new()

Create a new QMrs object.

Usage

QMrs$new(irefs = base::c(1), ...)

Arguments

Returns

A new 'QMrs' object.

Method fit()

Fit the bias correction method

Usage

QMrs$fit(Y0, X0)

Arguments

Returns

NULL

Method predict()

Predict the correction

Usage

QMrs$predict(X0)

Arguments

Returns

[matrix] Return the corrections of X0

Method clone()

The objects of this class are cloneable with this method.

Usage

QMrs$clone(deep = FALSE)

Arguments

References

Vrac, M.: Multivariate bias adjustment of high-dimensional climate simulations: the Rank Resampling for Distributions and Dependences (R2 D2 ) bias correction, Hydrol. Earth Syst. Sci., 22, 3175–3196, https://doi.org/10.5194/hess-22-3175-2018, 2018.

Examples

## Three bivariate random variables (rnorm and rexp are inverted between ref
## and bias)
XY = SBCK::dataset_gaussian_exp_2d(2000)
X0 = XY$X0 ## Biased in calibration period
Y0 = XY$Y0 ## Reference in calibration period

## Bias correction
## Step 1 : construction of the class QMrs 
qmrs = SBCK::QMrs$new() 
## Step 2 : Fit the bias correction model
qmrs$fit( Y0 , X0 )
## Step 3 : perform the bias correction
Z0 = qmrs$predict(X0)

Description

Perform a multivariate (non stationary) bias correction.

Details

Use rankshuffle in calibration and projection period with CDFt

Super class

SBCK::CDFt -> R2D2

Public fields

Methods

Public methods

• R2D2$new()

• R2D2$fit()

• R2D2$predict()

• R2D2$clone()

Method new()

Create a new R2D2 object.

Usage

R2D2$new(irefs = base::c(1), ...)

Arguments

Returns

A new 'R2D2' object.

Method fit()

Fit the bias correction method

Usage

R2D2$fit(Y0, X0, X1)

Arguments

Returns

NULL

Method predict()

Predict the correction

Usage

R2D2$predict(X1, X0 = NULL)

Arguments

Returns

[matrix or list] Return the matrix of correction of X1 if X0 is NULL, else return a list containing Z1 and Z0, the corrections of X1 and X0

Method clone()

The objects of this class are cloneable with this method.

Usage

R2D2$clone(deep = FALSE)

Arguments

References

Vrac, M.: Multivariate bias adjustment of high-dimensional climate simulations: the Rank Resampling for Distributions and Dependences (R2 D2 ) bias correction, Hydrol. Earth Syst. Sci., 22, 3175–3196, https://doi.org/10.5194/hess-22-3175-2018, 2018.

Examples

## Three bivariate random variables (rnorm and rexp are inverted between ref
## and bias)
XY = SBCK::dataset_gaussian_exp_2d(2000)
X0 = XY$X0 ## Biased in calibration period
Y0 = XY$Y0 ## Reference in calibration period
X1 = XY$X1 ## Biased in projection period

## Bias correction
## Step 1 : construction of the class R2D2 
r2d2 = SBCK::R2D2$new() 
## Step 2 : Fit the bias correction model
r2d2$fit( Y0 , X0 , X1 )
## Step 3 : perform the bias correction
Z = r2d2$predict(X1,X0)

Description

Perform a multivariate bias correction of X with respect to Y randomly.

Details

Only for comparison.

Methods

Public methods

• RBC$new()

• RBC$fit()

• RBC$predict()

• RBC$clone()

Method new()

Create a new RBC object.

Usage

RBC$new()

Returns

A new 'RBC' object.

Method fit()

Fit the bias correction method

Usage

RBC$fit(Y0, X0, X1 = NULL)

Arguments

Returns

NULL

Method predict()

Predict the correction. Use named keywords to use stationary or non-stationary method.

Usage

RBC$predict(X1 = NULL, X0 = NULL)

Arguments

Returns

[matrix or list] Return the matrix of correction of X1 if X0 is NULL, else return a list containing Z1 and Z0, the corrections of X1 and X0

Method clone()

The objects of this class are cloneable with this method.

Usage

RBC$clone(deep = FALSE)

Arguments

Examples

## Three bivariate random variables (rnorm and rexp are inverted between ref
## and bias)
XY = SBCK::dataset_gaussian_exp_2d(2000)
X0 = XY$X0 ## Biased in calibration period
Y0 = XY$Y0 ## Reference in calibration period
X1 = XY$X1 ## Biased in projection period


## Bias correction
## Step 1 : construction of the class RBC
rbc = SBCK::RBC$new() 
## Step 2 : Fit the bias correction model
rbc$fit( Y0 , X0 , X1 )
## Step 3 : perform the bias correction
Z = rbc$predict(X1,X0) 
## Z$Z0 # BC of X0
## Z$Z1 # BC of X1

Description

Statistical Bias Correction Kit

Author(s)

Yoann Robin Maintainer: Yoann Robin <[email protected]>

Description

Apply the Schaake shuffle to transform the rank of X0 such that its correspond to the rank of Y0

Usage

schaake_shuffle(Y0,X0)

Arguments

Value

Z0 [vector] X shuffled.

Examples

X0 = stats::runif(10)
Y0 = stats::runif(10)
Z0 = SBCK::schaake_shuffle( Y0 , X0 )

Description

Perform the Schaake Shuffle

Details

as fit/predict mode

Methods

Public methods

• SchaakeShuffle$new()

• SchaakeShuffle$fit()

• SchaakeShuffle$predict()

• SchaakeShuffle$clone()

Method new()

Create a new ShaakeShuffle object.

Usage

SchaakeShuffle$new(Y0 = NULL)

Arguments

Returns

A new 'ShaaleShuffle' object.

Method fit()

Fit the model

Usage

SchaakeShuffle$fit(Y0)

Arguments

Returns

NULL

Method predict()

Fit the model

Usage

SchaakeShuffle$predict(X0)

Arguments

Returns

Z0 [vector] data shuffled

Method clone()

The objects of this class are cloneable with this method.

Usage

SchaakeShuffle$clone(deep = FALSE)

Arguments

Examples

X0 = matrix( stats::runif(20) , ncol = 2 )
Y0 = matrix( stats::runif(20) , ncol = 2 )
ss = SchaakeShuffle$new()
ss$fit(Y0)
Z0 = ss$predict(X0)

Description

Match the rank structure of X with them of Y by reordering X.

Details

Can keep multiple features to keep the structure of X.

Public fields

Methods

Public methods

• SchaakeShuffleMultiRef$new()

• SchaakeShuffleMultiRef$fit()

• SchaakeShuffleMultiRef$predict()

• SchaakeShuffleMultiRef$clone()

Method new()

Create a new ShaakeShuffleMultiRef object.

Usage

SchaakeShuffleMultiRef$new(lag_search, lag_keep, cond_cols = base::c(1))

Arguments

Returns

A new 'ShaaleShuffleMultiRef' object.

Method fit()

Fit the model

Usage

SchaakeShuffleMultiRef$fit(Y0)

Arguments

Returns

NULL

Method predict()

Fit the model

Usage

SchaakeShuffleMultiRef$predict(X0)

Arguments

Returns

Z0 [vector] data shuffled

Method clone()

The objects of this class are cloneable with this method.

Usage

SchaakeShuffleMultiRef$clone(deep = FALSE)

Arguments

Examples

X0 = matrix( stats::runif(50) , ncol = 2 )
Y0 = matrix( stats::runif(50) , ncol = 2 )
ssmr = SchaakeShuffleMultiRef$new( lag_search = 3 , lag_keep = 1 , cond_cols = 1 )
ssmr$fit(Y0)
Z0 = ssmr$predict(X0)

Description

Match the rank structure of X with them of Y by reordering X.

Details

Fix one features to keep the structure of X.

Super class

SBCK::SchaakeShuffle -> SchaakeShuffleRef

Public fields

Methods

Public methods

• SchaakeShuffleRef$new()

• SchaakeShuffleRef$fit()

• SchaakeShuffleRef$predict()

• SchaakeShuffleRef$clone()

Method new()

Create a new ShaakeShuffleRef object.

Usage

SchaakeShuffleRef$new(ref, Y0 = NULL)

Arguments

Returns

A new 'ShaaleShuffleRef' object.

Method fit()

Fit the model

Usage

SchaakeShuffleRef$fit(Y0)

Arguments

Returns

NULL

Method predict()

Fit the model

Usage

SchaakeShuffleRef$predict(X0)

Arguments

Returns

Z0 [vector] data shuffled

Method clone()

The objects of this class are cloneable with this method.

Usage

SchaakeShuffleRef$clone(deep = FALSE)

Arguments

Examples

X0 = matrix( stats::runif(20) , ncol = 2 )
Y0 = matrix( stats::runif(20) , ncol = 2 )
ss = SchaakeShuffleRef$new( ref = 1 )
ss$fit(Y0)
Z0 = ss$predict(X0)

Description

Class to shift a dataset.

Format

R6Class object.

Details

Transform autocorrelations to intervariables correlations

Value

Object of R6Class

Methods

new(lag,method,ref,)

This method is used to create object of this class with Shift

transform(X)

Method to shift a dataset

inverse(Xs)

Method to inverse the shift of a dataset

Public fields

Active bindings

Methods

Public methods

• Shift$new()

• Shift$transform()

• Shift$inverse()

• Shift$clone()

Method new()

Create a new Shift object.

Usage

Shift$new(lag, method = "row", ref = 1)

Arguments

Returns

A new 'Shift' object.

Method transform()

Shift the data

Usage

Shift$transform(X)

Arguments

Returns

[matrix] Matrix shifted

Method inverse()

Inverse the shift of the data

Usage

Shift$inverse(Xs)

Arguments

Returns

[matrix] Matrix un shifted

Method clone()

The objects of this class are cloneable with this method.

Usage

Shift$clone(deep = FALSE)

Arguments

Examples

X = base::t(matrix( 1:20 , nrow = 2 , ncol = 10 ))

sh = Shift$new(1)
Xs = sh$transform(X)
Xi = sh$inverse(Xs)

Description

Class which send a stop signal when a time series stay constant.

Details

Test the slope.

Public fields

Methods

Public methods

• SlopeStoppingCriteria$new()

• SlopeStoppingCriteria$reset()

• SlopeStoppingCriteria$append()

• SlopeStoppingCriteria$clone()

Method new()

Create a new SlopeStoppingCriteria object.

Usage

SlopeStoppingCriteria$new(minit, maxit, tol)

Arguments

Returns

A new 'SlopeStoppingCriteria' object.

Method reset()

Reset the class

Usage

SlopeStoppingCriteria$reset()

Returns

NULL

Method append()

Add a new value

Usage

SlopeStoppingCriteria$append(value)

Arguments

Returns

NULL

Method clone()

The objects of this class are cloneable with this method.

Usage

SlopeStoppingCriteria$clone(deep = FALSE)

Arguments

Examples

stop_slope = SlopeStoppingCriteria$new( 20 , 500 , 1e-3 )
x = 0
while(!stop_slope$stop)
{
	stop_slope$append(base::exp(-x))
	x = x + 0.1
}
print(stop_slope$nit)

Description

Return the Rcpp Class SparseHistBase initialized

Usage

SparseHist(X, bin_width = NULL, bin_origin = NULL)

Arguments

Value

[SparseHist] SparseHist class

Examples

## Data
X = base::matrix( stats::rnorm( n = 10000 ) , nrow = 5000 , ncol = 2 )
muX = SparseHist(X)

print(muX$p) ## Vector of probabilities
print(muX$c) ## Matrix of coordinates of each bins
print(muX$argwhere(X)) ## Index of bins of dataset X

Description

Perform a bias correction of auto-correlation

Details

Correct auto-correlation with a shift approach.

Public fields

Active bindings

Methods

Public methods

• TSMBC$new()

• TSMBC$fit()

• TSMBC$predict()

• TSMBC$clone()

Method new()

Create a new TSMBC object.

Usage

TSMBC$new(lag, bc_method = OTC, method = "row", ref = "middle", ...)

Arguments

Returns

A new 'TSMBC' object.

Method fit()

Fit the bias correction method

Usage

TSMBC$fit(Y0, X0)

Arguments

Returns

NULL

Method predict()

Predict the correction

Usage

TSMBC$predict(X0)

Arguments

Returns

[matrix] Return the corrections of X0

Method clone()

The objects of this class are cloneable with this method.

Usage

TSMBC$clone(deep = FALSE)

Arguments

References

Robin, Y. and Vrac, M.: Is time a variable like the others in multivariate statistical downscaling and bias correction?, Earth Syst. Dynam. Discuss. [preprint], https://doi.org/10.5194/esd-2021-12, in review, 2021.

Examples

## arima model parameters
modelX0 = list( ar = base::c(  0.6 , 0.2 , -0.1 ) )
modelY0 = list( ar = base::c( -0.3 , 0.4 , -0.2 ) )

## arima random generator
rand.genX0 = function(n){ return(stats::rnorm( n , mean = 0.2 , sd = 1   )) }
rand.genY0 = function(n){ return(stats::rnorm( n , mean = 0   , sd = 0.7 )) }

## Generate two AR processes
X0 = stats::arima.sim( n = 1000 , model = modelX0 , rand.gen = rand.genX0 )
Y0 = stats::arima.sim( n = 1000 , model = modelY0 , rand.gen = rand.genY0 )
X0 = as.vector( X0 )
Y0 = as.vector( Y0 + 5 )

## And correct it with 30 lags
tsbc = SBCK::TSMBC$new( 30 )
tsbc$fit( Y0 , X0 )
Z0 = tsbc$predict(X0)

Description

Compute wasserstein distance between two dataset or SparseHist X and Y

Usage

wasserstein(X, Y, p = 2, ot = SBCK::OTNetworkSimplex$new())

Arguments

Value

[float] value of distance

References

Wasserstein, L. N. (1969). Markov processes over denumerable products of spaces describing large systems of automata. Problems of Information Transmission, 5(3), 47-52.

Examples

X = base::cbind( stats::rnorm(2000) , stats::rnorm(2000)  )
Y = base::cbind( stats::rnorm(2000,mean=10)  , stats::rnorm(2000) )
bw = base::c(0.1,0.1)
muX = SBCK::SparseHist( X , bw )
muY = SBCK::SparseHist( Y , bw )

## The four are equals
w2 = SBCK::wasserstein(X,Y)
w2 = SBCK::wasserstein(muX,Y)
w2 = SBCK::wasserstein(X,muY)
w2 = SBCK::wasserstein(muX,muY)

Description

This function return a vector / matrix / array of the same shape than cond / x / y such that if(cond) values are x, and else y.

Usage

where(cond,x,y)

Arguments

Value

z [vector/matrix/array].

Examples

x = base::seq( -2 , 2 , length = 100 )
y = where( x < 1 , x , exp(x) ) ## y = x if x < 1, else exp(x)