no, but that’s a good point. We should have that information in the docs pages.
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Yes, I fully agree with @xztt wrt this Springer Primer - that’s my favorite book on this topic. I believe also “Sensitivity and Uncertainty Analysis – Volume I – Theory”; Dan G. Cacuci; Chapman & Hall/CRC 2003 [link] and “Sensitivity and Uncertainty Analysis – Volume II - Applications to Large-Scale Systems”; Dan G. Cacuci, Mihaela Ionescu-Bujor, Ionel Michael Navon; CRC Press 2005 [link] could be to your interest as well. If you plan a trip into ai/ml/rl: “Stochastic Learning And Optimization - A Sensitivity-Based Approach”; Xi-Ren Cao, Hong Kong University of Science and Technology; Springer Science+Business Media 2007 [link] and “Sensitivity Analysis for Neural Networks”; Daniel S. Yeung, Ian Cloete, Daming Shi, Wing W.Y. Ng; Springer-Verlag Berlin Heidelberg 2010 [link]. In my opinion, it should be noted that there is a lot going on in the fields closely related to quantum computing that in about 5 years (more probably in 10 to 30) could completely change the perception about the subject of sensitivity analysis. However, as for now, there are almost no books on those topics and most of the things are in lengthy papers that, as far as I know, are regarded as dangerous even by persons skilled in reading various advanced notations. BTW, I also believe that even not straight about discussed subject a book “Chaos: Making a New Science” by James Gleick [link] and some short videos like Educational video (3b1b style) on chaos or Educational video (3b1b style) on chaos - #9 by j_u could make a time enjoyable for a person with a curious mind. And of course some of the local posts by @ChrisRackauckas I am finding interesting (but usually more advanced that my current coding skills). However, my perception is [first hand knowledge dated a few months back] that he is not that easily approachable.
We should have a mod split this into a separate thread titled Uncertainty Quantification vs Global Sensitivity Analysis, but anyways.
Many of those books are still not quite global sensitivity analysis, most are focused on local sensitivity analysis and adjoints. It’s basically a difference of questions:
- Local sensitivity analysis: If I change x, how does y change? It’s derivatives.
- Global sensitivity analysis: how does y change on “average” for x in some domain (with some measure on input probability/uncertainty)? The definition of average is what then gives you the various GSA methods.
- Uncertainty quantification: given a distributional input for x, what is the distributional input for y?
Now Sobol’s method does state GSA in a form of uncertainty quantification, where it has a precise definition in terms of an input distribution and defining some “average” output by integrals of the output distribution (the Sobol indices), but that’s different from direct UQ which would then ask “but what are the output distributions?” while Sobol sensitivity analysis answers its question just by giving the integral results.
(This is where the issue with Morris’s method comes in. It’s not rigorously defined as a probabilistic problem. There’s no definite sense of what input probability distribution it’s assuming, but it is still some kind of measure of “average change”. But this is why it’s then wonky and doesn’t really “converge”)
For details then, see the 18.337 lecture notes on the two.
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Happy to contribute to the docs if you think it can add value
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It would add a lot of value since it right now assumes the user just knows how to interpret the result structure, which is a bit much.
https://gsa.sciml.ai/dev/methods/sobol/#Sobol-Method
That should be moved to a docstring,
https://gsa.sciml.ai/dev/methods/sobol/#API
should be a docstring (and formatting fixed)
should have a docstring, and that page should be generated from the docstrings.
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That’s a good point re the content of the books I listed especially with regard to your question, however, I believe they are somehow closely related and most of them make a good reading even for an outsider or a newbie. Besides I think its always useful to have a little bit broader view on the subject - this is just my personal opinion.