SALib.analyze.rsa module#
- SALib.analyze.rsa.analyze(problem: Dict, X: ndarray, Y: ndarray, bins: int = 20, target: str = 'Y', print_to_console: bool = False, seed: int = None)[source]#
Perform Regional Sensitivity Analysis (RSA), also known as Monte Carlo Filtering.
In a usual RSA, a desirable region of output space is defined. Outputs which fall within this region is categorized as being “behavioral” (\(B\)), and those outside are described as being “non-behavioral” (\(\bar{B}\)). The input factors are also partitioned into behavioral and non-behavioral subsets, such that \(f(X_{i}|B) \rightarrow (Y|B)\) and \(f(X_{i}|\bar{B}) \rightarrow (Y|\bar{B})\). The distribution between the two sub-samples are compared for each factor. The greater the difference between the two distributions, the more important the given factor is in driving model outputs.
The approach implemented in SALib partitions factor or output space into \(b\) bins (default: 20) according to their percentile values. Output space is targeted for analysis by default (
target="Y"), such that \((Y|b_{i})\) is mapped back to \((X_{i}|b_{i})\). In other words, we treat outputs falling within a given bin (\(b_{i}\)) corresponding to their inputs as behavioral, and those outside the bin as non-behavioral. This aids in answering the question “Which \(X_{i}\) contributes most toward a given range of outputs?”. Factor space can also be assessed (target="X"), such that \(f(X_{i}|b_{i}) \rightarrow (Y|b_{i})\) and \(f(X_{i}|b_{\sim i}) \rightarrow (Y|b_{\sim i})\). This aids in answering the question “where in factor space are outputs most sensitive to?”The two-sample Cramér-von Mises (CvM) test is used to compare distributions. Results of the analysis indicate sensitivity across factor/output space. As the Cramér-von Mises criterion ranges from 0 to \(\infty\), a value of zero will indicates the two distributions being compared are identical, with larger values indicating greater differences.
Notes
- Compatible with:
all samplers
When applied to grouped factors, the analysis is conducted on each factor individually, and the mean of the results for a group are reported.
Increasing the value of
binsincreases the granularity of the analysis (across factor space), but necessitates larger sample sizes.This analysis will produce NaNs, indicating areas of factor space that did not have any samples, or for which the outputs were constant.
Analysis results are normalized against the maximum value such that 1.0 indicates the greatest sensitivity.
- Parameters:
problem (dict) – The problem definition
X (numpy.array) – A NumPy array containing the model inputs
Y (numpy.array) – A NumPy array containing the model outputs
bins (int) – The number of bins to use (default: 20)
target (str) – Assess factor space (“X”) or output space (“Y”) (default: “Y”)
print_to_console (bool) – Print results directly to console (default False)
seed (int) – Seed value to ensure deterministic results Unused, but defined to maintain compatibility.
References
- Hornberger, G. M., and R. C. Spear. 1981.
Approach to the preliminary analysis of environmental systems. Journal of Environmental Management 12:1. https://www.osti.gov/biblio/6396608-approach-preliminary-analysis-environmental-systems
- Pianosi, F., K. Beven, J. Freer, J. W. Hall, J. Rougier, D. B. Stephenson, and
T. Wagener. 2016. Sensitivity analysis of environmental models: A systematic review with practical workflow. Environmental Modelling & Software 79:214-232. https://dx.doi.org/10.1016/j.envsoft.2016.02.008
- Saltelli, A., M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli,
M. Saisana, and S. Tarantola. 2008. Global Sensitivity Analysis: The Primer. Wiley, West Sussex, U.K. https://dx.doi.org/10.1002/9780470725184 Accessible at: http://www.andreasaltelli.eu/file/repository/Primer_Corrected_2022.pdf