Chapter 1: Uncertainty quantification in computer experiments

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[x] The progress of computer simulation gradually ~allows the virtual resolution~ solves Virtually veut dire presque en anglais
[x] to pursue these studies ~for~ at a reasonable computational cost.
[x] Section 1.2 describes the ~context of the~ model specification step
[x] SectionS 1.4 and 1.5 introduce various methods
[x] is hereafter ~considered~ viewed

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[x] knowledge of the underlying physics ~doesn’t~ does not inform the UQ methods
[x] numerical models ~might~ can actually be a ~sequence~ chain of codes executed in ~series~ sequence
[x] they ~may also be qualified as~ can also be
[x] their ~confidence~ domain of validity and predictive accuracy Plus précis à mon avis
[x] The studied outputs ~studied~
[x] Unlike data scientists who work with the typical machine learning input-output dataset framework, ~the~ UQ analystS

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[x] the industrialISTs
[x] ~Contrarily to~ Unlike
[x] ~Note that an event is defined as a set of outcomes in the sample space.~ Then, a σ -algebra A, also called event space, is a set of subsets of $\Omega$ called events.
[x] The main objectS will be measurable functions defined over this probability space: these are called random variables.
[x] Dans l'équation 1.2, je supprimerais le "=x".
[x] will be ~considered~ assumed to be
[x] denoted by P_X
[x] Dans l'équation 1.3 : P(ω ∈ Ω : X(ω) ∈ B) : il faut mettre des accolades pour indiquer que c'est un ensemble

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[ ] (CDF) is a common tool to manipulate ~random variables~ probability distributions.
[ ] In the continuous case _(i.e. if PX is absolutely continuous with respect to the Lebesgue measure on R^d)
[ ] ~with f_X(x) = ∂^d F_X(x) / ∂x1 ...∂xd~. _This means that for any event B ∈ A, $\int f_X(x) \mathbb{1}_B(x) dx = \mathcal{P}_X(B)$. Plus général, et évite de faire l'hypothèse de la différentiabilité de F
[ ] the ~two~ first two moments

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[ ] ~Then,~ Second,
[ ] ~A~ Sklar's theorem states (tu le nommes juste après)

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[ ] ~misuse of language~ abuse of terminology

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[ ] ~To ease the reading, a few~ Techniques ~for estimating~ designed to estimate
[ ] ~therefore, Appendices~ therefore Appendix A ~recall~ lists
[ ] of ~a~ probabilistic uncertainty modeling
[ ] the _available knowledge ~available~
[ ] contrasts with the uncertainty propagation approach
[ ] related to any uncertainty propagation task
[ ] each representS a challenge
[ ] affordable computational budget ~affordable~
[ ] of this probabilistic integration problem
[ ] A quadrature ~establishes a~ rule select~ing~s

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[ ] denoted by l_n

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[ ] of the first kind. Fejér's Remplacer le point par une virgule

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[ ] The lowe~st~r the discrepancy of a design is, the “closest” it is to uniformity.
[ ] The function’s variation V (g) in Eq. (??) référence à corriger
[ ] définition de $V(g)$ : quelque chose m'échappe : que se passerait-il pour une fonction $g : [0,1]^2 \rightarrow \mathbb{R}$ telle que $g(x_1,x_2) = 0$ si $\max(x_1,x_2) \geq 1/2$ ? Que vaudrait $V(g)$ ?

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[ ] A randomization overlay ~fades~ removes the deterministic property of these designs,

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[ ] is ~qualified as~ called space-filling
[ ] ~As well as in integration~ : je ne comprends pas bien ce que tu veux dire
[ ] ~as they get their~ when their initial computational budget is extended
[ ] Some might request a sampling method ~conserving~ that preserves its properties
[ ] to optimize their performance~S~
[ ] ~However,~ While the L ∞ star discrepancy is hard to estimate, ~fortunately,~ Warnock (1972) elaborated an explicit expression specific to the L 2 star discrepancy
[ ] while ~satisfying the Koksma-Hlawka inequality with a modification of~ diminishing the total variation component of the Koksma-Hlawka bound.

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[ ] the ϕ p criterion defined below is often
[ ] The ~following~ ϕ p criterion
[ ] Dans la définition de ϕ p il faut s'assurer que $j \neq i$ car sinon on a une division par 0.
[ ] Many different sampling techniques are designed to optimize one of these space-filling metrics ~are widely used to optimize different sampling techniques.~
[ ] in the 1970s ~for~ as a numerical integration method
[ ] ~forces~ aims to force soyons modestes !
[ ] within a ~segment~ cell*
[ ] Various contributions proposed a variance que veut dire "proposer une variance" ?
[ ] ~Where~ In the equation above, C is a positive constant, showing that ~the~ LHS ~usually~ asymptotically ne s'agit-il pas d'un résultat asymptotique ?

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[ ] It also shows that these designs keep this property for dimensions larger than 10, while scrambled Sobol’ sequences lose it. Il faudra que je lise le papier, j'ai du mal à comprendre pourquoi.
[ ] the uniform projection designs from Sun et al. (2019) ~is~ also ~a method to~ optimize LHS

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[ ] Central tendency estimation ~is a~ can be viewed as numerical integration with respect to any input distribution
[ ] making the interpretation of the last discrepancy easier qu'est-ce que la "dernière discrépance" ?
[ ] a versatile generation algorithm
[ ] . One may generate remplacer la virgule par un point
[ ] and only retain ~from this sample~ the points under the PDF
[ ] are ~not well~ ill suited
[ ] ~The~ Uncertainty propagation with the three following goals
[ ] ~which is simply a~ i.e. to perform numerical integration against a nonuniform density
[ ] areas of the output random variables distribution

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[ ] Hence, ~the usage of~ the ~equivalent~ terms reliability analysis and rare event estimation are used interchangeably.
[ ] The notion of risk associated with an event is often decomposed as a product of its likelihood and its consequences. Je trouve cette phrase étrange, ne peux-tu pas dire que le risque est l'espérance du coût des dommages ? En fait, cette phrase contredit ce qui suit, ou tu définis le risque soit comme un quantile, soit comme une probabilité.
[ ] Quantiles are a ~first~ conservative measure
[ ] An interesting reflection on the use and the interpretation of risk measures including measures from the finance domain such as the conditional value-at-risk (also called superquantile) is presented in Rockafellar and Royset (2015). Il me semble que tu pourrais donner la définition des superquantiles ici.

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[ ] ~Depending on the sign of its images,~ this function splits the input space
[ ] a system of sequential and parallel problems ~in series and parallel.~ Simple suggestion, je ne sais pas quelle est la fréquence de l'expression "in series" dans les textes anglophones.
[ ] ~A~ rare event estimation ~results from a particular~ boils down to propagating uncertainty ~propagation~ through the LSF.
[ ] ~The~ This so-called failure probability, this parce que c'est exactement la probabilité d'être négatif dont tu parles dans la phrase précédente.

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[ ] ~where the indicator function applied to the failure domain returns 1 {F X } (x) = 1 if x ∈ F X and 1 {F X } (x) = 0 otherwise~ Précision inutile, tu as déjà défini la fonction indicatrice page 17.
[ ] an order of magnitude between 10−2 ≤ pf ≤ 10−9 Non, 10-2 est plus grand que 10-9 !
[ ] Since this transformation is a diffeomorphism Non, tu n'as pas pris assez d'hypothèses pour garantir qu'il s'agit d'un difféomorphisme : si ça se trouve $g$ n'est pas dérivable !

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[ ] . This section introduce~d~S
[ ] look for this MPFP, denoted by P∗,
[ ] ~This problem then becomes~ Such a quadratic optimization under nonlinear constraint ~. It~ is classically solved
[ ] but ~can~ also ~use~ by
[ ] This point defines the smallest Euclidian distance Quel point ? je ne comprends pas ce que tu veux dire.

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[ ] the standard normal distribution presents
[ ] exponential decay in its radial and tangential directions C'est vrai, mais je ne comprends pas l'intérêt de le dire, qu'est-ce que ça apporte dans la démonstration ? Ne suffit-il pas de dire que P étoile est le point de la zone de défaillance de plus grande densité de probabilité ?
[ ] P∗ is the point with the biggest contribution to the failure probability Je dirais plutôt : the failure point with the largest probability density
[ ] ~Then,~ FORM aims Pas vraiment de lien d'implication entre les deux
[ ] the MPFP, denoted by ˇg1(u∗):
[ ] $g(u) = ˇg1(u∗) +o ∥u − u∗ ∥_2^2$ Sauf erreur, g1 n'a pas encore été introduit à ce stade.

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[ ] by removing a nudge Pas clair, il faut que tu explicites davantage.
[ ] ~Only~ the estimator is ~now~ written

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[ ] this unbiased estimator converges ~toward it~ almost le fait qu'il soit non biaisé implique qu'en cas de convergence, la convergence se fait vers la vraie valeur
[ ] are overshadowed by its slow convergence

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[ ] to integrate against the auxiliary distribution Petit doute, il me semble que les anglophones préfèrent "average over" à "integrate against". A vérifier
[ ] drawn ~on~ from the auxiliary distribution
[ ] Note that comparing the results from FORM and FORM-IS allows us to assess the nonlinearity of the LSF in the vicinity of the design point. Ce point n'est pas clair pour moi, mais je ne sais pas s'il faut détailler davantage. A voir.
[ ] , progressively leading the sampl~ing~E towards the failure domain
[ ] ~The~ cross-entropy-based adaptive importance sampling

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[ ] space Dblambda ⊆ Rp as: erreur de formatage
[ ] which ~was overcome~ can be avoided by using a different approach

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[ ] pf should not be too ~rare~ low ~which allows~ because we want
[ ] ~Eventually,~ this optimization can be solved
[ ] is then ~considered~ used for importance sampling

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[ ] lat~t~er followed by
[ ] the nonparametric importance sampling method
[ ] Sur l'équation 1.58, comment peux-tu savoir si la densité est normalisée ou non puisque K n'est pas donné explicitement ? Tu dis que c'est commonly gaussien, mais si c'était autre chose ?
[ ] Après l'équation 1.58, tu ne peux pas commencer une phrase par "Where"
[ ] the normalization constant ensures Quelle est la constante de normalisation ?

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[ ] samples exceeding the threshold qkp0 ~such that ~
[ ] Overall, ~the~ NAIS
[ ] ~seriously~ significantly decrease for problems trop familier

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[ ] as ~seeds~ initialization points
[ ] Even if the problem is generic rare event estimation requires tailored solutions Cette phrase n'apporte pas grand chose de mon point de vue, je serais favorable à sa suppression.

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[ ] such as ~the~ directional sampling ~or~ line sampling or moving particles
[ ] ~the direct use of~ directly using rare event
[ ] were dedicated to ~the~ coupling ~of~ surrogate

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[ ] which was studied ~from~ within probabilistic and extra-probabilistic frameworks
[ ] to drop the irrelevant variables ~to the learning~.
[ ] not only looks for ~the~ irrelevant ~features to the learning~ but also ~the~ redundant features
[ ] The global ~sensitivity~ variation of an output ça fait bizarre de parler de sensibilité de manière intransitive
[ ] Two variables present interactions when their simultaneous effect on an output is not additive il s'agit 'une définition, n'est-ce pas ? Je pense qu'il serait bien de le préciser.

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[ ] Screening methods allow to discriminat~ing~E
[ ] which can afterwards be ~considered afterward~ treated as deterministIC to simplify

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[ ] attributing variance shareS to the inputs
[ ] Consider~ing~ a squared-integrable
[ ] with the previous terms defined according to this recurrence: en fait la récurrence n'est pas claire car tu ne donnes pas le terme générique. Ce terme est donné ici, section "Extension to any input distribution with independent marginals" : https://openturns.github.io/openturns/latest/theory/reliability_sensitivity/sensitivity_sobol.html
[ ] can be ~transposed in terms of~ used to derive a functional decomposition of the variance

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[ ] Même remarque que précédemment sur la récurrence qui n'est pas clairement définie.
[ ] By jointly analyzing ~jointly~

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[ ] equal to the first order indices
[ ] from ~the~ cooperative game~s’~ theory
[ ] This method is an alternative to ~the~ Sobol’ indices
[ ] In ~the~ game theory

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[ ] The Shapley effects adapted this concept to perform ~a~ GSA by considering the variables as players and by using the closed Sobol’ indices ~for the~ as value function
[ ] Unlike ~the~ Sobol’ indices

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[ ] Equation 1.81 : k n'a pas été défini (même si on peut deviner que c'est le noyau du RKHS)
[ ] and ~assumes~ the RKHS H induced by the tensor product

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[ ] ~or~ while others rely on extra-probabilistic methods
[ ] to replac~ing~E a costly numerical model

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[ ] This n-sized set is usually called learning set and written:

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[ ] GP is also called ~k~Kriging en anglais quand un nom est dérivé d'un nom propre il prend une majuscule. Cette remarque est valable à plein d'endroits, je recommande une recherche et correction globale.

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[ ] ~consider~ assume the hyperparameters σ,θ are fully known and the trend is ~a~ zero: ~trend~ β = 0.
[ ] offer ~its~ the explicit expression of the parameters of this distribution:

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[ ] Je ne sais plus si tu utilises cette version de la PVA (celle de Bachoc) ou celle sans la valeur absolue ?

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[ ] before ~evaluating~ the true function is evaluated.
[ ] Consider~ing~ an initial learning set

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[ ] and ~allows a progressive enhancement of~ is used to progressively enhance the Gaussian process in order to

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[ ] this problem can be seen as ~a~ binary classification.
[ ] Consider~ing~ an initial learning set
[ ] and a sampling technique~s~ Sans S
[ ] paired with ~a~ subset simulation
[ ] ~The~ AK methods present the advantage~s~
[ ] Alternatively, ~the~ stepwise uncertainty reduction (SUR)

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[ ] although their error is often much smaller than the modeling error peux-tu étayer cela ? Je veux bien le croire, mais ce genre d'affirmation peut avoir du mal à passer...

efekhari27 commented 10 months ago

Hi Joseph, I have taken into account all your remarks, thanks for this very good feedback. Regards, Elias

efekhari27 / thesis