From 8a0932974ed87fd5a5d5ac448cc364355b5b5e44 Mon Sep 17 00:00:00 2001 From: Louis Lacoste Date: Tue, 26 Mar 2024 10:08:14 +0100 Subject: [PATCH] =?UTF-8?q?Diff=C3=A9rentes=20corrections?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- prez.Rnw | 153 ++++++++++++++++++++++++++++++++----------------------- prez.pdf | Bin 3245148 -> 3228256 bytes 2 files changed, 88 insertions(+), 65 deletions(-) diff --git a/prez.Rnw b/prez.Rnw index 194901b..690eb31 100644 --- a/prez.Rnw +++ b/prez.Rnw @@ -62,7 +62,7 @@ alsoletter={.} \newcommand{\dd}{\mathrm{d}} \title{Projet: ANOVA Phylogénétique} -\subtitle{Présentation du Mardi 26 Mars. 2024} +\subtitle{Présentation du Mardi 26 Mars 2024} \date{} \author{Alizée Geffroy, Louis Lacoste, encadrés par Mélina Gallopin et Paul Bastide} \institute{M2 MathSV Université Paris-Saclay} @@ -97,59 +97,55 @@ source(here("R","utils.R")) \tableofcontents[hideallsubsections] \end{frame} -\begin{frame}[allowframebreaks]{Idée structure} - TODO Supprimer cette slide temporaire - \begin{itemize} - \item \textbf{Intro/Contexte} : biologique avec l'exemple de Chen (mettre l'arbre) + figure de l'article ? -> trouver les gènes différentiellement exprimés - \item Il existe déjà des méthodes statistiques pour cette problématique (EVEmodel ? State of the Art) - \item Transition avec le pourquoi du projet, trouver d'autres méthodes statistiques, adaptées de méthodes classiques qui pourraient bien marcher - \item \textbf{Méthode pas par nous} : 1 slide par tiret - \begin{itemize} - \item Reprendre la forme matricielle de l'ANOVA phylo (mettre en rouge les diffs) - \item Présenter le MB qui évolue sur l'arbre + lien matrice K - \item Mettre la statistique de test (mettre en rouge la projection (donc diffs)) - \end{itemize} - \item Transition vers notre travail - \begin{itemize} - \item Mettre la formule avec erreur de mesure avec justification de l'ajout de l'erreur de mesure, formule transfo $V_{\lambda}$, pointer la limite qui est l'erreur dûe à l'estimation du $\lambda$ - \end{itemize} - \item \textbf{Méthode par nous} : - \begin{itemize} - \item Satterthwaite : préciser que c'est nos calculs à partir de résultats sur modèle mixte (faire slide en appendice) + stat approximée + df formule une méthode possible parmi tant d'autres: Kenward Roger classique - \end{itemize} - \item \textbf{Simulations} : - \begin{itemize} - \item les 2 arbres avec les groupes - \item Modalités de simulations, bien préciser que l'idée de simuler c'est pour voir erreur de type I et puissance - \item Les résultats de simulations: pour les résultats Mettre ANOVA , ANOVA phylo Satterthwaite LRT - \end{itemize} - \item \textbf{Applications aux données réelles} : - \begin{itemize} - \item Rappel du type de données, RNA-seq sur pleins de gènes (éventuellement un extrait du tableau ?) - \item Mentionner toutes les méthodes rapidement et présenter l'UpSet diagramme avec son analyse et la remarque sur Satterthwaite ML qui sur-sélectionne - \end{itemize} - \item \textbf{Conclusions/Ouvertures}: - \begin{itemize} - \item \textbf{Conclusions} : - \begin{itemize} - \item Récap du projet sur son contenu scientifique - \end{itemize} - \item \textbf{Ouvertures} : - \begin{itemize} - \item Utiliser un autre processus stochastique Ornstein-Uhlenbeck - \item Comprendre pourquoi Satterthwaite a sur-sélectionné dans l'application: mauvaise implémentation ? évaluer l'impact de l'approx - \item Prendre un autre arbre ou ré-échantillonner les groupes dans les simus - \item Agrandir le cadre de simulations - \item Appliquer les méthodes à d'autres données - \item modèle qui fait gène par gène: imaginer en prenant tous les gènes : Limma - \end{itemize} - \end{itemize} -\end{itemize} - - - - -\end{frame} +% \begin{frame}[allowframebreaks]{Idée structure} +% TODO Supprimer cette slide temporaire +% \begin{itemize} +% \item \textbf{Intro/Contexte} : biologique avec l'exemple de Chen (mettre l'arbre) + figure de l'article ? -> trouver les gènes différentiellement exprimés +% \item Il existe déjà des méthodes statistiques pour cette problématique (EVEmodel ? State of the Art) +% \item Transition avec le pourquoi du projet, trouver d'autres méthodes statistiques, adaptées de méthodes classiques qui pourraient bien marcher +% \item \textbf{Méthode pas par nous} : 1 slide par tiret +% \begin{itemize} +% \item Reprendre la forme matricielle de l'ANOVA phylo (mettre en rouge les diffs) +% \item Présenter le MB qui évolue sur l'arbre + lien matrice K +% \item Mettre la statistique de test (mettre en rouge la projection (donc diffs)) +% \end{itemize} +% \item Transition vers notre travail +% \begin{itemize} +% \item Mettre la formule avec erreur de mesure avec justification de l'ajout de l'erreur de mesure, formule transfo $V_{\lambda}$, pointer la limite qui est l'erreur dûe à l'estimation du $\lambda$ +% \end{itemize} +% \item \textbf{Méthode par nous} : +% \begin{itemize} +% \item Satterthwaite : préciser que c'est nos calculs à partir de résultats sur modèle mixte (faire slide en appendice) + stat approximée + df formule une méthode possible parmi tant d'autres: Kenward Roger classique +% \end{itemize} +% \item \textbf{Simulations} : +% \begin{itemize} +% \item les 2 arbres avec les groupes +% \item Modalités de simulations, bien préciser que l'idée de simuler c'est pour voir erreur de type I et puissance +% \item Les résultats de simulations: pour les résultats Mettre ANOVA , ANOVA phylo Satterthwaite LRT +% \end{itemize} +% \item \textbf{Applications aux données réelles} : +% \begin{itemize} +% \item Rappel du type de données, RNA-seq sur pleins de gènes (éventuellement un extrait du tableau ?) +% \item Mentionner toutes les méthodes rapidement et présenter l'UpSet diagramme avec son analyse et la remarque sur Satterthwaite ML qui sur-sélectionne +% \end{itemize} +% \item \textbf{Conclusions/Ouvertures}: +% \begin{itemize} +% \item \textbf{Conclusions} : +% \begin{itemize} +% \item Récap du projet sur son contenu scientifique +% \end{itemize} +% \item \textbf{Ouvertures} : +% \begin{itemize} +% \item Utiliser un autre processus stochastique Ornstein-Uhlenbeck +% \item Comprendre pourquoi Satterthwaite a sur-sélectionné dans l'application: mauvaise implémentation ? évaluer l'impact de l'approx +% \item Prendre un autre arbre ou ré-échantillonner les groupes dans les simus +% \item Agrandir le cadre de simulations +% \item Appliquer les méthodes à d'autres données +% \item modèle qui fait gène par gène: imaginer en prenant tous les gènes : Limma +% \end{itemize} +% \end{itemize} +% \end{itemize} +% \end{frame} \section[Introduction]{Introduction} @@ -207,7 +203,10 @@ article de Chen: \end{figure} \note{ - Pour un arbre phylo donné ça nous renseigne sur les instants de spéciation, donc moment de divergence entre 2 espèces représenté ici par les ronds + Pour un arbre phylo donné ça nous renseigne sur les instants de spéciation, + donc moment de divergence entre 2 espèces représenté ici par les ronds. \\ + IMPORTANT : l'arbre phylogénétique est supposé connu, calibré\footnote{Il s'agit de pouvoir calibrer l'horloge moléculaire.} en temps et + on n'y touche pas, nous. \begin{itemize} \item Ici représenté l'évolution d'un trait cad d'une valeur quantitaive qu'on considère : ex comptage du nombre d'ARN exprimé pour un gène donné. \item La valeur du trait peut diverger pour chaque espèce à partir du moment de spéciation. @@ -314,7 +313,8 @@ En posant $\lambda = \frac{\sigma^2_{phy}}{\sigma^2_{err}}$ et $E=u+\epsilon$, o &Y = X\beta + E \text{, où } Var(E)=V(\theta)=\sigma^2_{phy}(K-\lambda I_n)=\sigma^2_{phy}V_\lambda \\ &E \sim \mathcal{N}_n(0, \sigma^2_{phy}V_\lambda) \notag \end{align} -Problème: $\lambda$ n'est souvent pas connu et il faut l'estimer. Dans ce cas, le test n'est pas exact et $F$ ne suit plus la même de Fisher. +Problème: $\lambda$ n'est en général pas connu et il faut l'estimer. Dans ce cas, +le test n'est pas exact et $F$ ne suit plus la même loi de Fisher. \note{ \begin{itemize} @@ -329,7 +329,9 @@ Problème: $\lambda$ n'est souvent pas connu et il faut l'estimer. Dans ce cas, \section{Calculs} \note{ \begin{itemize} - \item Jusqu'ici nous avons étudier le modèle d'ANOVA phylo, ça a été un apprentissage. A partir d'ici ce sont nos calculs avec pour but leur implémentation. + \item Jusqu'ici nous avons étudier le modèle d'ANOVA phylo, + ça a été un apprentissage. A partir d'ici ce sont nos calculs avec + pour but leur implémentation. \end{itemize} } @@ -339,7 +341,9 @@ Problème: $\lambda$ n'est souvent pas connu et il faut l'estimer. Dans ce cas, \begin{align} &F_{approx}=\frac{||\hat{Y} - \bar{Y}||^2_{V_\lambda^{-1}}df_{approx}}{||Y - \hat{Y}||^2_{V_\lambda^{-1}}} \underset{\mathcal{H}_0}{\sim}\mathcal{F}\text{isher} (1, df_{approx})\\ \text{Avec } &df_{approx} = \frac{2(f(\hat{\theta}))^2}{[\nabla f(\hat{\theta})]^T A[\nabla f(\hat{\theta})]} \\ - \text{où } &f(\theta) = \ell^TC(\theta)\ell \text{ et A matrice de variance-covariance de } \hat{\theta}=(\hat{\sigma}^2_{phy}, \hat{\sigma}^2_{err}) \notag + \text{où } f(\theta) &= \ell^TC(\theta)\ell \text{ et A matrice de variance-covariance de } \hat{\theta}=(\hat{\sigma}^2_{phy}, \hat{\sigma}^2_{err}) \notag\\ + C(\theta) &= (Cov(\beta_i , \beta_j))_{i,j}\notag \\ + &= (X^TV(\theta)^{-1}X)^{-1} = (X^T(\sigma^2_{phy}K + \sigma^2_{err}I_n)^{-1}X)^{-1} \notag \end{align} \note{ @@ -604,7 +608,9 @@ Et nous avons réalisé des simulations pour $h \in \{\Sexpr{heri}\}$. \item groupe pas phylo: h=0.3 l'ANOVA se trompe legerement, elle depasse le seuil, les autres sont en dessous à 0.03 \item pour h =0.9 l'ANOVA se trompe plus, elle depasse le seuil, les autres sont en dessous \item touk, avec faible héritabilité on est dasn un résultat proche de l'attendu : l'ANOVA se trompe à peine, avec forte héritabilité l'erreur est plus marquée ce qui est étonnant au vu des groupes selectionnes - \item On suspecte que la manièere dont on a constitue les groupes n'a pas suffisamment cassé la phylogénie + \item Tout d'abord nos données ne respectent les hypothèses de l'ANOVA. + On suspecte que la manière dont on a constitué les groupes n'a pas + suffisamment cassé la phylogénie. \end{itemize} } @@ -979,18 +985,31 @@ evemodel_dataframe$test_method <- as.factor(evemodel_dataframe$test_method) \section{Conclusions et ouvertures} \begin{frame}{Conclusions} \begin{itemize} - \item La méthode d'ANOVA phylogénétique avec Satterthwaite parait intéressante, en particulier elle permet de bien contrôler l'erreur de type I. + \item La méthode d'ANOVA phylogénétique avec Satterthwaite parait + intéressante, notamment pour le contrôle de l'erreur de type I. Mais il + faudra creuser pour essayer de comprendre la dégradation de la puissance. - \item Utilisation de l'approx de la Hessienne -> expression analytique + \item Au début nous utilisions une approximation de l'hessienne, + remplacée par la forme analytique une fois celle-ci obtenue. \end{itemize} + \note{ + \begin{itemize} + \item Approximation Hessienne : calculée par approximation numérique, méthode de + Richardson. + \end{itemize} + } \end{frame} \begin{frame}{Ouvertures} \begin{itemize} - \item Utilisation du processus d'Ornstein-Uhlenbeck - \item Pourquoi Satterthwaite a surselectionné ? Creuser - \item Prendre un autre arbre, autres données, ou ré-échantillonner les groupes dans les simus - \item Modèle qui fait gène par gène: imaginer en prenant tous les gènes -> méthode LIMMA + \item Changer de processus stochastique ? Le processus d'Ornstein-Uhlenbeck. + \item Comprendre pourquoi avec l'approximation de Satterthwaite sur les + données réelles il y a eu une sur-sélection. + \item Changer les conditions de simulations : prendre un autre arbre, + autres données, ou ré-échantillonner les groupes. + \item Ces méthodes test gène par gène puis corrige pour faire un test + multiple. On pourrait développer des méthodes qui font sur tous les gènes + en même temps (adaptation phylogénétique de la méthode LIMMA). \end{itemize} \end{frame} @@ -1047,6 +1066,10 @@ $$\dd r_t = -\theta(r_t - \mu)+\sigma\dd W_t$$ } \end{frame} +\begin{frame}{Lien modèle mixte} + TODO Ajouter la formule canonique du modèle mixte +\end{frame} + \begin{frame}[allowframebreaks]{questions posables} % - comment obtenir la stat de test pour anova phylo (Cholesky) % - en quoi c'est un modèle mixte pour Satterthwaite ? diff --git a/prez.pdf b/prez.pdf index d52b7e0d6d8bd54b4c8a525665a0f4a2f0887344..07d615644cc876e359755be0ea05037ef443c472 100644 GIT binary patch delta 128778 zcmY(pV{j!-)a@PH_QXymwr$(SOl+Un)`_i&eS(Q?8xxxo`=Rc%=50GHZ^jteYU{?~Ok=H%%6*Q>wXF*L*otE*#Shs77I z^i`H?Z4n51^3GRf7fLqzImi;r+*|zpUH$$2{ggVSD5BxXKmR=bD$`NHq!`Dhma_>z z;yWZtZ7h-2Us>B$6;5< z6qAf*mR=}lW}$pIUY{&zxhU8YqU!-qFJ3!&;Gagr&OjWRy})3#?*u~#hHh?xekI7k zsk*j(p^gpZ>U$m-NnF?w;NZZEK-YG5^6>{oaOfC@Ekfaj-l_ykci17zCZ_Ks*MMxF 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