.. De-planète, 40 Introduction, Etude statistique qualitative des données simulées en l'absence 40 Description statistique des données, p.43

.. Modèle-gaussien-des-données, 55 Description qualitative d'une image, 55 Discrimination entre signal (planète) et bruit (´ etoile) . . . . . . . . . . . . . . . . . . . . . 57

P. De-la, 58 Estimation d'intensitéintensité? intensité??(r) (et estimation conjointe du fond), p.61

.. Probabilité-a-priori-de-l-'intensité-de-la-planète-dans-les-différents-canaux-spectraux...-niveau, 175 A priori de premier 175 A priori marginal, p.176

. Dans-cette-section and . Dempster, et comme le suggère Royall [1986] notamment , on effectue le test binaire en attribuant une interprétation directe des seuils ? et p (voir la section 7.3 p. 128) et en les fixantàfixantà un certain couple de valeurs (? 0 , p 0 ) De la même façon, l'approche de Neyman consisteraitàconsisteraità fixer une valeur de PFA, grandeur dont l'interprétation est naturelle aussi. Il s'agit ainsi de rejeter l'hypothèse nulle H 0 lorsque la vraisemblance p(x|?) est " souvent, 1974.

. Ici, Cependantx|?) soit plus de 10 fois plus grande que p(x|? = 0) ne peut pas se produire avec une probabilité 1 puisque l'intensité ? de la planète n'est pas connue de façon certaine On choisit en l'occurrence que l'´ evénement qui nous intéresse (p(x|?) ? 10p(x|? 0 )) se produit " souvent " si cela survient pour une probabilité a posteriori sous H 1 supérieurè a p 0 = 0.8. On vérifie si le test binaire ainsi défini rejète l'hypothèse nulle ou non en lisant directement la figure 12.6 qui représente PLR(x, ?) en fonction de ?, le graphe de gauché etant obtenù a partir des données x avec planète et le graphe de droitè a partir des données x sans planète. On lit pour les données sous H 1 que PLR(x, 0.1) = 0.94, c'est-` a-dire que la probabilité a posteriori sous H 1 que la vraisemblance p(x|?) sous H 1 soit plus de 10 fois supérieurè a celle sous H 0 estégalèestégalè a 0.94. Cette valeur estélevéeestélevée et en particulier supérieurè a p 0 = 0.8, de sorte que le test rejète bien H 0 . On constate pour les données sous H 0 que PLR(x, 0.1) = 0, c'est-` a-dire qu'il y a une probabilité a posteriori nulle (` a l'erreur d'´ echantillonnage près) sous H 1 que la vraisemblance p(x|?) sous H 1 soit plus de 10 fois supérieurè a celle sous H 0 . Plus généralement, le PLR, sorte de p-value bayésienne, indique les couples limites

L. Comme-pour and . Plr, ´ echelle dite de Jeffreys associe ainsi, par convention, des termes qualitatifsàqualitatifsà des valeurs prises par le BF (Kass and Raftery La correspondance, ` a x fixé, avec un test construitàconstruità partir du PLR, est indiquée dans la sous-section 8.2 p. 138, 50<3=04 ! 0>0!"& ,1205:;50<3=0! ! 0>0' -?-0345678905, 1205.

F. Courbes, R. Du, and P. , PD est calculée pour une valeur ? 1 fixée. nellè a l'identité) est extrêmement peu performant : ce test revient ici, pour PFA=0.5, ` a détecter ou non selon l'issue d'un jeu de pile ou face. Il faut cependant bien noter que ce GLR n'est pas calculécalculéà partir de la vraisemblance marginale p(x|?)

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