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Added references to bibliography for Sobol
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Prateek Bhustali committed May 23, 2022
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27 changes: 27 additions & 0 deletions docs/source/bibliography.bib
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Expand Up @@ -801,3 +801,30 @@ @article{GSI
doi = {10.1214/14-EJS895},
URL = {https://doi.org/10.1214/14-EJS895}
}

# Sobol
@book{saltelli_2008,
author = {Saltelli, A.},
description = {Global sensitivity analysis: the primer - Andrea Saltelli},
isbn = {9780470059975},
keywords = {sensitivity statistics},
lccn = {2007045551},
publisher = {John Wiley},
title = {Global sensitivity analysis: the primer},
url = {https://onlinelibrary.wiley.com/doi/book/10.1002/9780470725184},
year = 2008
}

@article{saltelli_2002,
title = {Making best use of model evaluations to compute sensitivity indices},
journal = {Computer Physics Communications},
volume = {145},
number = {2},
pages = {280-297},
year = {2002},
issn = {0010-4655},
doi = {https://doi.org/10.1016/S0010-4655(02)00280-1},
url = {https://www.sciencedirect.com/science/article/pii/S0010465502002801},
author = {Andrea Saltelli},
keywords = {Sensitivity analysis, Sensitivity measures, Sensitivity indices, Importance measures},
}
15 changes: 5 additions & 10 deletions docs/source/sensitivity/sobol.rst
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Expand Up @@ -31,38 +31,33 @@ Here, :math:`N` is the number of Monte Carlo samples and :math:`m` being the num
Compared to "Sobol1993", the "Janon2014" estimator makes more efficient use of model evaluations and produces smaller (better) confidence intervals.

- Sobol1993: Requires :math:`N(m + 1)` model evaluations [1]_.
- Sobol1993: Requires :math:`N(m + 1)` model evaluations :cite:`saltelli_2008`.

.. math::
S_{i} = \frac{\mathbb{V}\left[E\left(Y \mid X_{i}\right)\right]}{\mathbb{V}(Y)} = \frac{ (1/N) Y_{A} \cdot Y_{C_{i}}-f_{0}^{2}}{(1 / N) Y_{A} \cdot Y_{A}-f_{0}^{2}}
.. math::
y_{A}=f(A), \quad y_{C_{i}}=f(C_{i}), \quad f_{0}^{2}=\left(\frac{1}{N} \sum_{j=1}^{N} y_{A}^{(j)} \right)^{2}
- Saltelli2002: Requires :math:`N(2m + 2)` model evaluations [2]_.
- Saltelli2002: Requires :math:`N(2m + 2)` model evaluations :cite:`saltelli_2002`.

2. **Second order indices** (:math:`S_{ij}`)

- Saltelli2002: Requires :math:`N(2m + 2)` model evaluations [2]_.
- Saltelli2002: Requires :math:`N(2m + 2)` model evaluations :cite:`saltelli_2002`.

3. **Total order indices** (:math:`S_{T_{i}}`)

- Homma1996: Requires :math:`N(m + 1)` model evaluations [1]_.
- Homma1996: Requires :math:`N(m + 1)` model evaluations :cite:`saltelli_2008`.

.. math::
S_{T_{i}} = 1 - \frac{\mathbb{V}\left[E\left(Y \mid \mathbf{X}_{\sim_{i}}\right)\right]}{\mathbb{V}(Y)} = 1 - \frac{ (1 / N) Y_{B} \cdot Y_{C_{i}}-f_{0}^{2}}{(1 / N) Y_{A} \cdot Y_{A}-f_{0}^{2}}
.. math::
y_{A}=f(A), \quad y_{B}=f(B), \quad y_{C_{i}}=f(C_{i}), \quad f_{0}^{2}=\left(\frac{1}{2N} \sum_{j=1}^{N} y_{A}^{(j)} + y_{B}^{(j)} \right)^{2}
- Saltelli2002: Requires :math:`N(2m + 2)` model evaluations [2]_.
- Saltelli2002: Requires :math:`N(2m + 2)` model evaluations :cite:`saltelli_2002`.


.. [1] Saltelli, A. (2008). Global sensitivity analysis: the primer.
John Wiley. ISBN: 9780470059975
.. [2] Saltelli, A. (2002). Making best use of model evaluations to compute sensitivity indices. (`Link <http://www.andreasaltelli.eu/file/repository/Making_best_use.pdf>`_)
Sobol Class
^^^^^^^^^^^^^^^^^^

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