A. , K. Allassonniere, S. Kuhn, and E. , Convergent stochastic expectation maximization algorithm with ecient sampling in high dimension . application to deformable template model estimation, Computational Statistics & Data Analysis, vol.91, p.419, 2015.

. Andrieu, Stability of stochastic approximation under veriable conditions, SIAM Journal on control and optimization, vol.44, issue.1, p.283312, 2005.
DOI : 10.1109/cdc.2005.1583231

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

. Arsigny, Logeuclidean metrics for fast and simple calculus on diusion tensors, Magnetic resonance in medicine, vol.56, issue.2, p.411421, 2006.
DOI : 10.1002/mrm.20965

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

Y. F. Atchadé, An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift, Methodology and Computing in Applied Probability, vol.22, issue.2, p.235254, 2006.
DOI : 10.1007/s11009-006-8550-0

. Bandini, Relation of body composition, parental overweight, pubertal stage, and race-ethnicity to energy expenditure among premenarcheal girls, The American Journal Of Clinical Nutrition, issue.5, p.7610401047, 2002.

. Benzinger, Regional variability of imaging biomarkers in autosomal dominant Alzheimer's disease, Proceedings of the National Academy of Sciences, pp.110-4502, 2013.
DOI : 10.2307/2533558

A. Beskos, A stable manifold MCMC method for high dimensions, Statistics & Probability Letters, vol.90, p.4652, 2014.
DOI : 10.1016/j.spl.2014.03.016

URL : http://arxiv.org/abs/1403.7711

M. Betancourt, A General Metric for Riemannian Manifold Hamiltonian Monte Carlo, Geometric science of information, p.327334, 2013.
DOI : 10.1007/978-3-642-40020-9_35

URL : http://arxiv.org/abs/1212.4693

P. Billingsley, Convergence of probability measures, 2013.
DOI : 10.1002/9780470316962

. References, . Booth, . Hobert, J. G. Booth, and J. P. Hobert, Maximizing generalized linear mixed model likelihoods with an automated monte carlo em algorithm, Journal of the Royal Statistical Society: Series B (Statistical Methodology), issue.1, p.61265285, 1999.

. Braak, . Braak, H. Braak, and E. Braak, Staging of alzheimer's disease-related neurobrillary changes, Neurobiology of aging, vol.16, issue.3, p.271278, 1995.

. Chi, E. M. Chi, and G. C. Reinsel, Models for longitudinal data with random eects and ar (1) errors, Journal of the American Statistical Association, vol.84, issue.406, p.452459, 1989.
DOI : 10.2307/2289929

. Consonni, . Marin, G. Consonni, and J. Marin, Mean-eld variational approximate bayesian inference for latent variable models, Computational Statistics & Data Analysis, vol.52, issue.2, p.790798, 2007.
DOI : 10.1016/j.csda.2006.10.028

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

. Corder, Gene dose of apolipoprotein E type 4 allele and the risk of Alzheimer's disease in late onset families, Science, vol.261, issue.5123, p.261921923, 1993.
DOI : 10.1126/science.8346443

C. Cowles, M. K. Cowles, and B. P. Carlin, Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review, Journal of the American Statistical Association, vol.90, issue.434, p.91883904, 1996.
DOI : 10.1080/01621459.1996.10476956

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

. Davidian, . Gallant, M. Davidian, and A. R. Gallant, Smooth nonparametric maximum likelihood estimation for population pharmacokinetics, with application to quinidine, Journal of Pharmacokinetics and Biopharmaceutics, vol.11, issue.60, p.529556, 1992.
DOI : 10.1007/BF01061470

. Delor, Modeling Alzheimer???s Disease Progression Using Disease Onset Time and Disease Trajectory Concepts Applied to CDR-SOB Scores From ADNI, CPT: pharmacometrics & systems pharmacology, p.78, 2013.
DOI : 10.1186/1471-2377-12-46

URL : http://doi.org/10.1038/psp.2013.54

. Delyon, Convergence of a stochastic approximation version of the em algorithm, Annals of statistics, p.94128, 1999.

. Dempster, Maximum likelihood from incomplete data via the em algorithm, Journal of the royal statistical society. Series B, p.138, 1977.

. Desikan, An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest, NeuroImage, vol.31, issue.3, p.31968980, 2006.
DOI : 10.1016/j.neuroimage.2006.01.021

. Diggle, Analysis of Longitudinal Data., Biometrics, vol.53, issue.2, 2002.
DOI : 10.2307/2533983

. Dryden, Noneuclidean statistics for covariance matrices, with applications to diusion tensor imaging. The Annals of Applied Statistics, p.11021123, 2009.
DOI : 10.1214/09-aoas249

URL : http://arxiv.org/abs/0910.1656

. Durrleman, Registration, atlas estimation and variability analysis of white matter ber bundles modeled as currents, NeuroImage, issue.3, p.5510731090, 2011.

. Durrleman, Toward a Comprehensive Framework for the Spatiotemporal Statistical Analysis of Longitudinal Shape Data, International Journal of Computer Vision, vol.31, issue.3, p.2259, 2013.
DOI : 10.1007/s11263-012-0592-x

URL : https://hal.archives-ouvertes.fr/hal-00813825

C. Eisenhart, The Assumptions Underlying the Analysis of Variance, Biometrics, vol.3, issue.1, p.121, 1947.
DOI : 10.2307/3001534

. Fitzmaurice, Longitudinal data analysis, 2008.

. Fitzmaurice, Applied longitudinal analysis, 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, p.7586, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00623920

W. Förstner and B. Moonen, A Metric for Covariance Matrices, Geodesy-The Challenge of the 3rd Millennium, p.299309, 2003.
DOI : 10.1007/978-3-662-05296-9_31

. Gallot, Riemannian geometry, 1990.
URL : https://hal.archives-ouvertes.fr/hal-00002870

R. Gelman, A. Gelman, and D. B. Rubin, Inference from iterative simulation using multiple sequences. Statistical science, p.457472, 1992.
DOI : 10.1214/ss/1177011136

J. Geweke, Getting It Right, Journal of the American Statistical Association, vol.99, issue.467, p.99799804, 2004.
DOI : 10.1198/016214504000001132

. Girolami, . Calderhead, M. Girolami, and B. Calderhead, Riemann manifold Langevin and Hamiltonian Monte Carlo methods, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.13, issue.10, p.73123214, 2011.
DOI : 10.1111/j.1467-9868.2010.00765.x

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

D. Harville, Extension of the gauss-markov theorem to include the estimation of random eects. The Annals of Statistics, p.384395, 1976.

D. A. Harville, Bayesian inference for variance components using only error contrasts, Biometrika, vol.61, issue.2, p.61383385, 1974.
DOI : 10.1093/biomet/61.2.383

D. A. Harville, Maximum likelihood approaches to variance component estimation and to related problems, Journal of the American Statistical Association, issue.358, p.72320338, 1977.
DOI : 10.2307/2286796

C. R. Henderson, Estimation of genetic parameters, In Biometrics, vol.6, p.186187, 1950.

G. Homan, M. D. Homan, 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, p.15931623, 2014.

. Hong, Timewarped geodesic regression, International Conference on Medical Image Computing and Computer-Assisted Intervention, p.105112, 2014.
DOI : 10.1007/978-3-319-10470-6_14

. Hyvärinen, Independent component analysis, 2004.

. Kheyfets, Schild's ladder parallel transport procedure for an arbitrary connection, International Journal of Theoretical Physics, issue.12, p.3928912898, 2000.

L. Kuhn, E. Kuhn, and M. Lavielle, Coupling a stochastic approximation version of EM with an MCMC procedure, ESAIM: Probability and Statistics, p.115131, 2004.
DOI : 10.1051/ps:2004007

. Laird, Maximum Likelihood Computations with Repeated Measures: Application of the EM Algorithm, Journal of the American Statistical Association, vol.39, issue.397, p.8297105, 1987.
DOI : 10.1080/01621459.1987.10478395

W. Laird, N. M. Laird, and J. H. Ware, Random-eects models for longitudinal data, Biometrics, p.963974, 1982.

S. Lang, Dierential manifolds, 1972.

. Lavielle, M. Mentré-]-lavielle, and F. Mentré, Estimation of Population Pharmacokinetic Parameters of Saquinavir in HIV Patients with the MONOLIX Software, Journal of Pharmacokinetics and Pharmacodynamics, vol.32, issue.2, p.229249, 2007.
DOI : 10.1007/s10928-006-9043-z

URL : https://hal.archives-ouvertes.fr/inserm-00156907

J. M. Lee, Smooth manifolds, Introduction to Smooth Manifolds, p.129, 2003.

J. M. Lee, Riemannian manifolds: an introduction to curvature, 2006.
DOI : 10.1007/b98852

. Liang, Advanced Markov chain Monte Carlo methods: learning from past samples, 2011.
DOI : 10.1002/9780470669723

B. Lindstrom, M. J. Lindstrom, and D. M. Bates, Newtonraphson and em algorithms for linear mixed-eects models for repeatedmeasures data, Journal of the American Statistical Association, issue.404, p.8310141022, 1988.

B. Lindstrom, M. J. Lindstrom, and D. M. Bates, Nonlinear mixed eects models for repeated measures data, Biometrics, p.673687, 1990.
DOI : 10.2307/2532087

. Lorenzi, Schild???s Ladder for the Parallel Transport of Deformations in Time Series of Images, Information Processing in Medical Imaging, p.463474, 2011.
DOI : 10.1007/978-3-642-22092-0_38

. Lorenzi, Disentangling normal aging from Alzheimer's disease in structural magnetic resonance images, Neurobiology of Aging, vol.36, pp.42-52, 2015.
DOI : 10.1016/j.neurobiolaging.2014.07.046

A. Maclaurin, D. Maclaurin, and R. P. Adams, Firey monte carlo: Exact mcmc with subsets of data. arXiv preprint, 2014.

. Marin, Bayesian modeling and inference on mixtures of distributions, Handbook of statistics, pp.459-507, 2005.

P. W. Michor, Topics in dierential geometry, 2008.

. Mohs, Development of Cognitive Instruments for Use in Clinical Trials of Antidementia Drugs, Alzheimer Disease & Associated Disorders, vol.11, 1997.
DOI : 10.1097/00002093-199700112-00003

F. Muralidharan, P. Muralidharan, and P. T. Fletcher, Sasaki metrics for analysis of longitudinal data on manifolds, 2012 IEEE Conference on Computer Vision and Pattern Recognition, p.10271034, 2012.
DOI : 10.1109/CVPR.2012.6247780

T. Musso, E. Musso, and F. Tricerri, Riemannian metrics on tangent bundles, Annali di Matematica Pura ed Applicata, vol.13, issue.1, p.119, 1988.
DOI : 10.1007/BF01761461

. Ng, Transport on riemannian manifold for functional connectivitybased classication, International Conference on Medical Image Computing and Computer-Assisted Intervention, p.405412, 2014.
DOI : 10.1007/978-3-319-10470-6_51

X. Pennec, Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements, Journal of Mathematical Imaging and Vision, vol.20, issue.10, p.127154, 2006.
DOI : 10.1007/s10851-006-6228-4

URL : https://hal.archives-ouvertes.fr/inria-00614994

. Pennec, A Riemannian Framework for Tensor Computing, International Journal of Computer Vision, vol.6, issue.2, p.4166, 2006.
DOI : 10.1007/s11263-005-3222-z

URL : https://hal.archives-ouvertes.fr/inria-00070743

P. Petersen, Riemannian geometry, 2006.

. Phillips, 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.

. Pinheiro, . Bates, J. Pinheiro, and D. Bates, Mixed-eects models in S and S-PLUS, 2006.
DOI : 10.1007/978-1-4419-0318-1

J. C. Pinheiro, Topics in mixed eects models, 1994.

. Pinheiro, . Bates, J. C. Pinheiro, and D. M. Bates, Unconstrained parametrizations for variance-covariance matrices, Statistics and Computing, vol.46, issue.2, p.289296, 1996.
DOI : 10.1007/BF00140873

W. Ring, W. Ring, and B. Wirth, Optimization Methods on Riemannian Manifolds and Their Application to Shape Space, SIAM Journal on Optimization, vol.22, issue.2, p.596627, 2012.
DOI : 10.1137/11082885X

M. Robbins, H. Robbins, and S. Monro, A stochastic approximation method. The annals of mathematical statistics, p.400407, 1951.

R. , C. Robert, C. Casella, and G. , Introducing Monte Carlo Methods with R, 2009.
DOI : 10.1007/978-1-4419-1576-4

URL : https://hal.archives-ouvertes.fr/hal-00450502

R. , C. Robert, C. Casella, and G. , Monte Carlo statistical methods, 2013.

. Roberts, Weak convergence and optimal scaling of random walk metropolis algorithms. The annals of applied probability, p.110120, 1997.
DOI : 10.1214/aoap/1034625254

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

G. K. Robinson, That blup is a good thing: the estimation of random eects. Statistical science, p.1532, 1991.

. Rumpf, . Wirth, M. Rumpf, and B. Wirth, Discrete geodesic calculus in the space of viscous uidic objects. arXiv preprint, 2012.

. Savic, Implementation and evaluation of the saem algorithm for longitudinal ordered categorical data with an illustration in pharmacokineticspharmacodynamics, The AAPS journal, vol.13, issue.1, p.4453, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00637400

H. Scheé, A "mixed model" for the analysis of variance. The Annals of Mathematical Statistics, p.2336, 1956.

. Schiratti, Learning spatiotemporal trajectories from manifold-valued longitudinal data, Advances in Neural Information Processing Systems, p.24042412, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01163373

. Schiratti, Mixed-eects model for the spatiotemporal analysis of longitudinal manifold-valued data, 5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy, 2015.

. References and . Schiratti, Estimating proles of disease progression using mixed-eects models with time reparametrization, Organisation for Human Brain Mapping, 2015.

. Schiratti, A mixed-eects model with time reparametrization for longitudinal univariate manifold-valued data, International Conference on Information Processing in Medical Imaging, p.564575, 2015.
DOI : 10.1007/978-3-319-19992-4_44

URL : https://hal.archives-ouvertes.fr/hal-01163213/document

. Sheiner, . Beal, L. B. Sheiner, and S. L. Beal, Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis-menten model: Routine clinical pharmacokinetic data, Journal of Pharmacokinetics and Biopharmaceutics, vol.39, issue.6, p.553571, 1980.
DOI : 10.1007/BF01060053

C. L. Siegel, Symplectic Geometry, American Journal of Mathematics, vol.65, issue.1, p.186, 1964.
DOI : 10.2307/2371774

. Singh, A hierarchical geodesic model for dieomorphic longitudinal shape analysis, Information Processing in Medical Imaging, p.560571, 2013.
DOI : 10.1007/978-3-642-38868-2_47

. Singh, An ecient parallel algorithm for hierarchical geodesic models in dieomorphisms, 2014 IEEE 11th International Symposium on Biomedical Imaging (ISBI), pp.341-344, 2014.
DOI : 10.1109/isbi.2014.6867878

L. T. Skovgaard, A riemannian geometry of the multivariate normal model, Scandinavian Journal of Statistics, p.211223, 1984.

S. T. Smith, Optimization techniques on riemannian manifolds. Fields institute communications, p.113135, 1994.
DOI : 10.1090/fic/003/09

URL : http://arxiv.org/abs/1407.5965

. Thompson-jr and W. A. Thompson-jr, The problem of negative estimates of variance components. The Annals of Mathematical Statistics, p.273289, 1962.

K. Tierney, L. Tierney, and J. B. Kadane, Accurate Approximations for Posterior Moments and Marginal Densities, Journal of the American Statistical Association, vol.31, issue.393, p.818286, 1986.
DOI : 10.1080/01621459.1974.10480130

G. Verbeke and G. Molenberghs, Linear Mixed Models for Longitudinal Data, 2009.
DOI : 10.1007/978-1-4612-2294-1_3

C. F. Wu, On the Convergence Properties of the EM Algorithm, The Annals of Statistics, vol.11, issue.1, 1983.
DOI : 10.1214/aos/1176346060