dOTC {SBCK}

dOTC (dynamical Optimal Transport Correction) method

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

bin_width

[vector or NULL] A vector of lengths of the cells discretizing R^numbers of variables. If NULL, it is estimating during the fit

bin_origin

[vector or NULL] Coordinate of lower corner of one cell. If NULL, c(0,...,0) is used

cov_factor

[string or matrix] Covariance factor to correct the dynamic transferred between X0 and Y0. For string, available values are "std" and "cholesky"

ot

[OTSolver] Optimal Transport solver, default is the network simplex

Returns

A new 'dOTC' object.

Method fit()

Fit the bias correction method

Usage

dOTC$fit(Y0, X0, X1)

Arguments

Y0

[matrix: n_samples * n_features] Observations in calibration

X0

[matrix: n_samples * n_features] Model in calibration

X1

[matrix: n_samples * n_features] Model in projection

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

X1

[matrix: n_samples * n_features] Model in projection

X0

[matrix: n_samples * n_features or NULL] Model in calibration

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

deep

Whether to make a deep clone.

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