weightTSA | R Documentation |
Transformation function of one variable (vector sample)
weightTSA(Y, c, upper = TRUE, type="indicTh", param=1)
Y |
The output vector |
c |
The threshold |
upper |
TRUE for upper threshold and FALSE for lower threshold |
type |
The weight function type ("indicTh", "zeroTh", logistic", "exp1side"):
|
param |
The parameter value for "logistic" and "exp1side" types |
The weight functions depend on a threshold c
and/or a smooth relaxation. These functions are defined as follows
if type = "indicTh": w = 1_{Y>c}
(upper threshold) and w = 1_{Y<c}
(lower threshold),
if type = "zeroTh": w = Y 1_{Y>c}
(upper threshold) and w = Y 1_{Y<c}
(lower threshold),
if type = "logistic":
w = \left[ 1 + \exp{\left( -param\frac{Y-c}{|c|}\right)}\right]^{-1}
(upper threshold) and
w = \left[ 1 + \exp{\left( -param\frac{c-Y}{|c|}\right)}\right]^{-1}
(lower threshold),
if type = "exp1side":
w = \left[ 1 + \exp{\left( -\frac{\max(c - Y, 0)}{\frac{param}{5} \sigma(Y)}\right)}\right]
(upper threshold) and
w = \left[ 1 + \exp{\left( -\frac{\max(Y - c, 0)}{\frac{param}{5} \sigma(Y)}\right) }\right]
(lower threshold), where \sigma(Y)
is an estimation of the standard deviation of Y and param = 1
is a parameter tuning the smoothness.
The vector sample of the transformed variable
B. Iooss
H. Raguet and A. Marrel, Target and conditional sensitivity analysis with emphasis on dependence measures, Preprint, https://hal.archives-ouvertes.fr/hal-01694129
A. Marrel and V. Chabridon, 2021, Statistical developments for target and conditional sensitivity analysis: Application on safety studies for nuclear reactor, Reliability Engineering & System Safety, 214:107711.
A. Spagnol, Kernel-based sensitivity indices for high-dimensional optimization problems, PhD Thesis, Universite de Lyon, 2020
Spagnol A., Le Riche R., Da Veiga S. (2019), Global sensitivity analysis for optimization with variable selection, SIAM/ASA J. Uncertainty Quantification, 7(2), 417–443.
n <- 100 # sample size
c <- 1.5
Y <- rnorm(n)
Yt <- weightTSA(Y, c)
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