Finalise une première version

calibration2024/calibration2024.bib

@@ -1,19 +1,12 @@
 
 @inproceedings{Baudin2021,
- title={Linear algebra of linear and nonlinear bayesian calibration},
+ title={Linear algebra of linear and nonlinear {Bayesian} calibration},
  author={Baudin, Michaël and Lebrun, Régis},
  year={2021},
  booktitle = {UNCECOMP 2021},
  pages = {339--353},
  organization = "4th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering M. Papadrakakis, V. Papadopoulos, G. Stefanou (eds.) Streamed from Athens, Greece, 28-30 June 2021",
 }
-@book{BinghamFry2010,
-  title={Regression, Linear Models in Statistics},
-  author={N. H. Bingham and John M. Fry},
-  series={Springer Undergraduate Mathematics Series},
-  year={2010},
-  publisher={Springer}
-}
 
 @Book{Bjorck1996,
   author =   {Ake Björck},
@@ -22,14 +15,6 @@ @Book{Bjorck1996
   year =     {1996},
 }
 
-@book{BinghamFry,
-  title={Regression, Linear Models in Statistics},
-  author={N. H. Bingham and John M. Fry},
-  series={Springer Undergraduate Mathematics Series},
-  year={2010},
-  publisher={Springer}
-}
-
 @INPROCEEDINGS{Hansen00thelcurve,
     author = {P. C. Hansen},
     title = {The {L}-Curve and its Use in the Numerical Treatment of Inverse Problems},
@@ -64,20 +49,6 @@ @book{Evensen2009
 publisher = {SIAM}
 }
 
-@book{Sen1990,
-    author       = "Ashish Sen and Muni Srivastava",
-    title        = "Regression analysis",
-    year         = "1990",
-    publisher    = "Springer",
-}
-
-@book{Draper1988,
-    author       = "Norman R. Draper and Harry Smith",
-    title        = "Applied Regression Analysis, Third Edition",
-    year         = "1988",
-    publisher    = "John Wiley \& Sons, Inc.",
-}
-
 @book{Tarantola2005,
     author       = "Albert Tarantola",
     title        = "Inverse problem theory",
@@ -92,14 +63,6 @@ @book{Asch2016
   publisher={SIAM}
 }
 
-@incollection{iooss2015review,
-  title={A review on global sensitivity analysis methods},
-  author={Iooss, Bertrand and Lema{\^\i}tre, Paul},
-  booktitle={Uncertainty management in simulation-optimization of complex systems},
-  pages={101--122},
-  year={2015},
-  publisher={Springer}
-}
 
 @Inbook{Baudin2016,
 author="Baudin, Micha{\"e}l and Dutfoy, Anne and Iooss, Bertrand and Popelin, Anne-Laure",
@@ -129,13 +92,6 @@ @techreport{BaudinMethodes2022
 number={6125-3119-2022-00175-FR}
 }
 
-@unpublished{OpenTURNSCalibrationFlooding, 
-author = "{Consortium OpenTURNS}",
-title = "Calibration of the flooding model",
-year = "2022",
-note = "\url{http://openturns.github.io/openturns/master/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_flooding.html}",
-}
-
 @techreport{garbow1980implementation,
   title={Implementation guide for {MINPACK}-1.},
   author={Garbow, Burton S. and Hillstrom, Kenneth E. and More, Jorge J.},
@@ -151,21 +107,23 @@ @book{kern2016methodes
 }
 
 
-@book{hastie2009elements,
-  title={The elements of statistical learning: data mining, inference, and prediction},
-  author={Hastie, Trevor and Tibshirani, Robert and Friedman, Jerome H and Friedman, Jerome H},
-  volume={2},
-  year={2009},
-  publisher={Springer}
+@book{lawson1995solving,
+  title={Solving least squares problems},
+  author={Lawson, Charles L. and Hanson, Richard J.},
+  year={1995},
+  publisher={SIAM}
 }
 
-@article{Rocquigny2006LaMaitrise,
-  title={La maîtrise des incertitudes dans un contexte industriel. 1re partie: une approche méthodologique globale basée sur des exemples.},
-  author={de Rocquigny, Etienne.},
-  journal={Journal de la Société française de statistique},
-  volume={147},
-  number={3},
-  pages={33-71},
-  year={2006}
+@book{idier2013bayesian,
+  title={Bayesian approach to inverse problems},
+  author={Idier, J{\'e}r{\^o}me},
+  year={2013},
+  publisher={John Wiley \& Sons}
 }
 
+@book{hansen2013least,
+  title={Least squares data fitting with applications},
+  author={Hansen, Per Christian and Pereyra, Victor and Scherer, Godela},
+  year={2013},
+  publisher={JHU Press}
+}

calibration2024/calibration2024.tex

@@ -59,28 +59,83 @@
 \begin{frame}
 \frametitle{Introduction}
 
-On dispose :
+We have:
 \begin{itemize}
-\item d'observations,
-\item d'un modèle paramétrique.
+\item a dataset,
+\item a parametric model with unknown parameters.
 \end{itemize}
 
-On cherche :
+We search for:
 \begin{itemize}
-\item des paramètres, 
-\item tels que les prédictions du modèle soient 
-\emph{proches} des observations. 
+\item parameter values,
+\item such that the predictions of the model are as close as possible to the data.
 \end{itemize}
 
+Since the dataset is random, we want the distribution of the parameters.
+
+From there, we can compute confidence intervals of the parameters.
+
 \begin{figure}
 \begin{center}
 \includegraphics[width=0.5\textwidth]{flooding_before_calibration.pdf}
 \end{center}
-\caption{Des observations comparées à des prédictions.}
+\caption{Observations compared to the predictions of a model.}
 \end{figure}
 
 \end{frame}
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}[fragile]
+\section{Overview}
+\frametitle{Overview}
+
+In OpenTURNS, we have several calibration features:
+\begin{itemize}
+\item \href{https://openturns.github.io/openturns/latest/theory/data_analysis/data_analysis.html#calibration}{theory help pages}
+\item \href{https://openturns.github.io/openturns/latest/user_manual/calibration.html}{API help pages}
+\item \href{https://openturns.github.io/openturns/latest/auto_calibration/index.html}{examples}.
+\end{itemize}
+
+
+There are two types of features :
+\begin{itemize}
+\item linear and non linear least squares, Gaussian linear and non linear calibration : \pyvar{*Calibration} classes. These classes compute the \textbf{posterior distribution of the parameters}.
+\item Monte Carlo Markov Chain (MCMC) algorithms : \pyvar{*MetropolisHastings}, etc. These classes \textbf{generate a sample from the posterior distribution of the parameters}.
+\end{itemize}
+
+The simplest example is \href{https://openturns.github.io/openturns/latest/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_quickstart.html#sphx-glr-auto-calibration-least-squares-and-gaussian-calibration-plot-calibration-quickstart-py}{Calibrate a parametric model: a quick-start guide to calibration}
+
+Here, we are going to review the \href{https://openturns.github.io/openturns/latest/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_flooding.html#sphx-glr-auto-calibration-least-squares-and-gaussian-calibration-plot-calibration-flooding-py}{Calibration of the flooding model}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}[fragile]
+\section{Conclusion}
+\frametitle{Conclusion}
+
+Other tools :
+\begin{itemize}
+\item Calibration methods are also available in \href{https://persalys.fr}{Persalys} : linear and non linear least squares, Gaussian linear and non linear calibration.
+\end{itemize}
+
+Perspectives:
+\begin{itemize}
+\item provide bounds to the optimization algorithms (return truncated normal distribution if necessary);
+\item unify the \pyvar{ParametricFunction} in \pyvar{*Calibration} and \pyvar{*MetropolisHastings} classes (exchange the roles of $x$ and $\theta$);
+\item calibrate parametric functions with field output more easily;
+\item provide algorithms to automatically compute finite difference steps (not specific to calibration);
+\item provide the covariance matrix of the parameters as a diagonal matrix;
+\item scale the parameters to calibrate (not specific to calibration);
+\item implement \pyvar{CalibrationResult.isBayesian()} (see \href{https://github.com/openturns/openturns/issues/2560}{2560});
+\item implement a `CalibrationResult` structure for M.-H. classes.
+\end{itemize}
+\end{frame}
+
+
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \section{References}

calibration2024/macros.tex

@@ -18,6 +18,8 @@
 \unitlength=1cm
 \graphicspath{{./figures/}}
 
+\usepackage{hyperref}
+\hypersetup{colorlinks=true, linkcolor=blue, linktocpage, urlcolor=blue}
 
 \def\bx{{\bf x}}
 \def\RR{\mathbb{R}}