E. Stéphanie-allassonnière, A. Kuhn, and . Trouvé, Construction of bayesian deformable models via a stochastic approximation algorithm: a convergence study, Bernoulli, vol.16, issue.3, pp.641-678, 2010.

V. Arsigny, P. Fillard, X. Pennec, and N. Ayache, Log-euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic resonance in medicine, vol.56, pp.411-421, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00502678

Y. F. Atchadé, An adaptive version for the metropolis adjusted langevin algorithm with a truncated drift, Methodology and Computing in applied Probability, vol.8, issue.2, pp.235-254, 2006.

L. G. Bandini, A. Must, J. L. Spadano, and W. H. Dietz, Relation of body composition, parental overweight, pubertal stage, and race-ethnicity to energy expenditure among premenarcheal girls, The American Journal Of Clinical Nutrition, vol.76, issue.5, pp.1040-1047, 2002.

T. F. Coleman and D. C. Sorensen, A note on the computation of an orthonormal basis for the null space of a matrix, Mathematical Programming, vol.29, issue.2, pp.234-242, 1984.

I. Delor, J. E. Charoin, R. Gieschke, S. Retout, and P. Jacqmin, Modeling alzheimer's disease progression using disease onset time and disease trajectory concepts applied to cdr-sob scores from adni, CPT: pharmacometrics & systems pharmacology, vol.2, p.78, 2013.

P. Arthur, N. M. Dempster, D. Laird, and . Rubin, Maximum likelihood from incomplete data via the em algorithm, Journal of the royal statistical society. Series B (methodological), pp.1-38, 1977.

M. , Do Carmo Valero. Riemannian geometry. Birkhäuser, 1992.

S. Durrleman, X. Pennec, A. Trouvé, G. Gerig, and N. Ayache, Spatiotemporal atlas estimation for developmental delay detection in longitudinal datasets, International Conference on Medical Image Computing and Computer-Assisted Intervention, pp.297-304, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00408293

S. Durrleman, X. Pennec, A. Trouvé, J. Braga, G. Gerig et al., Toward a comprehensive framework for the spatiotemporal statistical analysis of longitudinal shape data, International Journal of Computer Vision, vol.103, issue.1, pp.22-59, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00813825

C. Eisenhart, The assumptions underlying the analysis of variance, Biometrics, vol.3, issue.1, pp.1-21, 1947.

G. M. Fitzmaurice, N. M. Laird, and J. H. Ware, Applied longitudinal analysis, vol.998, 2012.

T. Fletcher, Geodesic regression on riemannian manifolds, Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy-Geometrical and Statistical Methods for Modelling Biological Shape Variability, pp.75-86, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00623920

M. Hubert-m-fonteijn, . Modat, J. Matthew, J. Clarkson, M. Barnes et al., An event-based model for disease progression and its application in familial alzheimer's disease and huntington's disease, NeuroImage, vol.60, issue.3, pp.1880-1889, 2012.

M. D. Hoffman and A. Gelman, The no-u-turn sampler: adaptively setting path lengths in hamiltonian monte carlo, Journal of Machine Learning Research, vol.15, issue.1, pp.1593-1623, 2014.

Y. Hong, N. Singh, R. Kwitt, and M. Niethammer, Time-warped geodesic regression, International Conference on Medical Image Computing and Computer-Assisted Intervention, pp.105-112, 2014.
DOI : 10.1007/978-3-319-10470-6_14
URL : http://europepmc.org/articles/pmc4885123?pdf=render

A. Hyvärinen, J. Karhunen, and E. Oja, Independent component analysis, vol.46, 2004.

B. M. Jedynak, A. Lang, B. Liu, E. Katz, Y. Zhang et al., A computational neurodegenerative disease progression score: method and results with the alzheimer's disease neuroimaging initiative cohort, Neuroimage, vol.63, issue.3, pp.1478-1486, 2012.

I. Koval, J. Schiratti, A. Routier, M. Bacci, O. Colliot et al., Statistical learning of spatiotemporal patterns from longitudinal manifold-valued networks, Medical Image Computing and Computer-Assisted Intervention, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01540828

E. Kuhn and M. Lavielle, Coupling a stochastic approximation version of em with an mcmc procedure, ESAIM: Probability and Statistics, vol.8, pp.115-131, 2004.

M. Nan, J. Laird, and . Ware, Random-effects models for longitudinal data, Biometrics, pp.963-974, 1982.

M. Lavielle and F. Mentré, Estimation of population pharmacokinetic parameters of saquinavir in hiv patients with the monolix software, Journal of pharmacokinetics and pharmacodynamics, vol.34, issue.2, pp.229-249, 2007.
URL : https://hal.archives-ouvertes.fr/inserm-00156907

C. Lenglet, M. Rousson, R. Deriche, and O. Faugeras, Statistics on the manifold of multivariate normal distributions: Theory and application to diffusion tensor mri processing, Journal of Mathematical Imaging and Vision, vol.25, issue.3, pp.423-444, 2006.

M. Lorenzi, X. Pennec, G. Frisoni, and N. Ayache, Disentangling normal aging from alzheimer's disease in structural magnetic resonance images, Neurobiology of aging, vol.36, pp.42-52, 2015.

M. Moakher and M. Zéraï, The riemannian geometry of the space of positive-definite matrices and its application to the regularization of positive-definite matrix-valued data, Journal of Mathematical Imaging and Vision, vol.40, issue.2, pp.171-187, 2011.

R. C. Mohs, D. Knopman, R. Petersen, S. H. Ferris, C. Ernesto et al., Development of cognitive instruments for use in clinical trials of antidementia drugs: additions to the alzheimer's disease assessment scale that broaden its scope, Alzheimer Disease & Associated Disorders, vol.11, pp.13-21, 1997.

X. Pennec, P. Fillard, and N. Ayache, A riemannian framework for tensor computing, International Journal of Computer Vision, vol.66, issue.1, pp.41-66, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00070743

P. Petersen, Riemannian geometry, vol.171, 2006.

M. Phillips, L. G. Bandini, D. V. Compton, E. N. Naumova, and A. Must, A longitudinal comparison of body composition by total body water and bioelectrical impedance in adolescent girls, The Journal of nutrition, vol.133, issue.5, pp.1419-1425, 2003.

G. O. Roberts, A. Gelman, and W. R. Gilks, Weak convergence and optimal scaling of random walk metropolis algorithms. The annals of applied probability, vol.7, pp.110-120, 1997.

J. Schiratti, S. Allassonnière, O. Colliot, and S. Durrleman, Mixed-effects model for the spatiotemporal analysis of longitudinal manifold-valued data, 5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01245905

J. Schiratti, S. Allassonnière, O. Colliot, and S. Durrleman, Learning spatiotemporal trajectories from manifold-valued longitudinal data, Advances in Neural Information Processing Systems, pp.2404-2412, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01245909

J. Schiratti, S. Allassonnière, A. Routier, O. Colliot, and S. Durrleman, A mixed-effects model with time reparametrization for longitudinal univariate manifoldvalued data, International Conference on Information Processing in Medical Imaging, pp.564-575, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01163213

N. Singh, J. Hinkle, S. Joshi, and P. T. Fletcher, An efficient parallel algorithm for hierarchical geodesic models in diffeomorphisms, 2014 IEEE 11th International Symposium on Biomedical Imaging (ISBI), pp.341-344, 2014.

N. Singh, J. Hinkle, S. Joshi, and P. Fletcher, A hierarchical geodesic model for diffeomorphic longitudinal shape analysis, Information Processing in Medical Imaging, pp.560-571, 2013.

L. T. Skovgaard, A riemannian geometry of the multivariate normal model, Scandinavian Journal of Statistics, pp.211-223, 1984.

J. Su, S. Kurtek, E. Klassen, and A. Srivastava, Statistical analysis of trajectories on riemannian manifolds: Bird migration, hurricane tracking and video surveillance, The Annals of Applied Statistics, vol.8, issue.1, pp.530-552, 2014.

G. Verbeke and G. Molenberghs, Linear mixed models for longitudinal data, 2009.

E. Yang, M. Farnum, V. Lobanov, T. Schultz, N. Raghavan et al., Quantifying the pathophysiological timeline of alzheimer's disease, Journal of Alzheimer's Disease, vol.26, issue.4, pp.745-753, 2011.