A. Abdelwahab, O. Amor, and T. Abdelwahed, The analysis of the interdependence structure in international financial markets by graphical models, International research journal of finance and economics, vol.15, pp.291-306, 2008.

S. Andersson and G. Wojnar, Wishart Distributions on Homogeneous Cones, Journal of Theoretical Probability, vol.17, issue.2, pp.781-818, 2004.
DOI : 10.1090/conm/261/04137
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.1053

S. A. Andersson and T. Klein, On Riesz and Wishart distributions associated with decomposable undirected graphs, Journal of Multivariate Analysis, vol.101, issue.4, pp.789-810, 2010.
DOI : 10.1016/j.jmva.2009.12.005
URL : http://doi.org/10.1016/j.jmva.2009.12.005

T. Andersson and P. Handel, Cramer-Rao bound and the parsimony principle, Instrumentation and Measurement, IEEE Transactions, vol.55, issue.1, pp.44-53, 2006.

E. Avventi, A. G. Lindquist, and B. Wahlberg, ARMA identification of graphical models, Automatic Control, IEEE Transactions on, vol.58, issue.5, pp.1167-1178, 2013.
DOI : 10.1109/tac.2012.2231551
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.309.9295

O. Banerjee, L. Ghaoui, and A. Aspremont, Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data, The Journal of Machine Learning Research, vol.9, pp.485-516, 2008.

O. E. Barndorff-nielsen, Information and Exponential Families in Statistical Theory, 1978.

E. Ben-david and B. Rajaratnam, The Letac-Massam conjecture and existence of high dimensional Bayes estimators for graphical models, arXiv preprint, 2014.

J. F. Bercher and C. Vignat, On minimum Fisher information distributions with restricted support and fixed variance, Information Sciences, vol.179, issue.22, pp.3832-3842, 2009.
DOI : 10.1016/j.ins.2009.07.013
URL : https://hal.archives-ouvertes.fr/hal-00621947

A. Berrington, Y. Hu, P. W. Smith, and P. Sturgis, A graphical chain model for reciprocal relationships between women's gender role attitudes and labour force participation, Journal of the Royal Statistical Society: Series A (Statistics in Society), vol.52, issue.0, pp.89-108, 2008.
DOI : 10.1177/0958928704042003
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.129.8916

D. M. Bressoud, Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture, 1999.
DOI : 10.1017/CBO9780511613449

L. D. Brown, Fundamentals of statistical exponential families with applications in statistical decision theory, Lecture Notes-monograph, 1986.

M. F. Bru, Diffusions of perturbed principal component analysis, Journal of Multivariate Analysis, vol.29, issue.1, pp.127-136, 1989.
DOI : 10.1016/0047-259X(89)90080-8
URL : http://doi.org/10.1016/0047-259x(89)90080-8

M. F. Bru, Wishart processes, Journal of Theoretical Probability, vol.20, issue.4, pp.725-751, 1991.
DOI : 10.1007/BF01259552

U. Callies, D. Kurowicka, and R. Cooke, Graphical models for the evaluation of multisite temperature forecasts: comparison of vines and independence graphs, Proc. of ESREL 2003, Safety and Reliability, pp.363-371, 2003.

A. Caputo, R. Foraita, S. Klasen, and I. Pigeot, Undernutrition in Benin???an analysis based on graphical models, Social Science & Medicine, vol.56, issue.8, pp.1677-1691, 2003.
DOI : 10.1016/S0277-9536(02)00162-4

C. Carvalho and M. West, Dynamic matrix-variate graphical models, Bayesian Analysis, vol.2, issue.1, pp.69-98, 2007.
DOI : 10.1214/07-BA204
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.62.6120

C. M. Carvalho, H. Massam, and M. West, Simulation of hyper-inverse Wishart distributions in graphical models, Biometrika, vol.94, issue.3, pp.647-659, 2007.
DOI : 10.1093/biomet/asm056

M. Casalis and G. Letac, The Lukacs-Olkin-Rubin characterization of Wishart distributions on symmetric cones, The Annals of Statistics, pp.763-786, 1996.

L. S. Chandran, L. Ibarra, F. Ruskey, and J. Sawada, Generating and characterizing the perfect elimination orderings of a chordal graph, Theoretical Computer Science, vol.307, issue.2, pp.303-317, 2003.
DOI : 10.1016/S0304-3975(03)00221-4

G. Chenevier and D. Renard, Characters of speh representations and lewis caroll identity, Representation Theory of the, pp.447-452, 2008.

R. Dahlhaus, Graphical interaction models for multivariate time series 1, Metrika, vol.51, issue.2, pp.157-172, 2000.
DOI : 10.1007/s001840000055

J. N. Darroch, S. L. Lauritzen, and T. P. Speed, Markov fields and log-linear interaction models for contingency tables, The Annals of Statistics, pp.522-539, 1980.

A. P. Dawid and S. L. Lauritzen, Hyper Markov laws in the statistical analysis of decomposable graphical models, The Annals of Statistics, pp.1272-1317, 1993.

A. P. Dempster, Covariance Selection, Biometrics, vol.28, issue.1, pp.157-175, 1972.
DOI : 10.2307/2528966

P. Diaconis and D. Ylvisaker, Conjugate priors for exponential families, The Annals of statistics, pp.269-281, 1979.

A. Dobra, T. S. Eicher, and A. Lenkoski, Modeling uncertainty in macroeconomic growth determinants using Gaussian graphical models, Statistical Methodology, vol.7, issue.3, pp.292-306, 2010.
DOI : 10.1016/j.stamet.2009.11.003

D. Edwards, Introduction to graphical modelling, 2000.
DOI : 10.1007/978-1-4612-0493-0

M. Eichler, Graphical modelling of multivariate time series, Probability Theory and Related Fields, pp.233-268, 2012.

J. Faraut and A. Korányi, Analysis on symmetric cones, 1994.

B. R. Frieden, Science from Fisher information: a unification, 2004.
DOI : 10.1017/CBO9780511616907

J. Friedman, T. Hastie, and R. Tibshirani, Sparse inverse covariance estimation with the graphical lasso, Biostatistics, vol.9, issue.3, pp.432-441, 2008.
DOI : 10.1093/biostatistics/kxm045
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3019769

U. Gather, M. Imhoff, and R. Fried, Graphical models for multivariate time series from intensive care monitoring, Statistics in Medicine, vol.40, issue.18, pp.2685-2701, 2002.
DOI : 10.1002/aic.690400509
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.4409

J. W. Gibbs, Elementary principles in statistical mechanics, 1902.
DOI : 10.1017/CBO9780511686948

W. Glunt, T. Hayden, C. R. Johnson, and P. Tarazaga, Positive definite completions and determinant maximization, Positive definite completions and determinant maximization, pp.1-10, 1999.
DOI : 10.1016/S0024-3795(98)10211-2
URL : http://doi.org/10.1016/s0024-3795(98)10211-2

L. A. Goodman, The Multivariate Analysis of Qualitative Data: Interactions among Multiple Classifications, Journal of the American Statistical Association, vol.20, issue.329, pp.226-256, 1970.
DOI : 10.2307/2283825

P. Graczyk and H. Ishi, Riesz measures and Wishart laws associated to quadratic maps, Journal of the Mathematical Society of Japan, vol.66, issue.1, pp.317-348, 2014.
DOI : 10.2969/jmsj/06610317
URL : https://hal.archives-ouvertes.fr/hal-00605146

P. Graczyk, H. Ishi, S. Mamane, and H. Ochiai, On the Letac-Massam Conjecture on cones $Q_{A_{n}}$, Proc. Japan Acad, pp.16-21, 2017.
DOI : 10.3792/pjaa.93.16

P. Graczyk and S. Mamane, Fisher information and exponential families parametrized by a segment of means, Probability and Mathematical Statistics, vol.35, issue.1, pp.73-90, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00942218

R. D. Gupta and D. Kundu, On the comparison of Fisher information of the Weibull and GE distributions, Journal of Statistical Planning and Inference, vol.136, issue.9, pp.3130-3144, 2006.
DOI : 10.1016/j.jspi.2004.11.013

E. Gutiérrez-peña and . Smith, Exponential and bayesian conjugate families: Review and extensions, Test, vol.11, issue.1, pp.1-90, 1997.
DOI : 10.1002/9780470316870

D. Hand, K. Mcconway, and E. Stanghellini, Graphical models of applicants for credit, IMA Journal of Management Mathematics, vol.8, issue.2, pp.143-155, 1997.
DOI : 10.1093/imaman/8.2.143

A. Hassairi and S. Lajmi, Riesz exponential families on symmetric cones, Journal of Theoretical Probability, vol.14, issue.4, pp.927-948, 2001.
DOI : 10.1023/A:1012592618872

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2009.

K. M. Irvine and A. I. Gitelman, Graphical spatial models: a new view on interpreting spatial pattern, Environmental and Ecological Statistics, vol.3, issue.4, pp.447-469, 2011.
DOI : 10.2307/2389612

H. Ishi, Homogeneous cones and their applications to statistics, Modern methods of multivariate statistics, pp.135-154, 2014.

C. R. Johnson, Matrix completion problems: a survey, Matrix theory and applications, pp.171-198, 1990.
DOI : 10.1090/psapm/040/1059486

M. I. Jordan, Z. Ghahramani, T. S. Jaakkola, and L. K. Saul, An Introduction to Variational Methods for Graphical Models, Machine learning, vol.37, issue.2, pp.183-233, 1999.
DOI : 10.1007/978-94-011-5014-9_5
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.106.3844

K. Khare and B. Rajaratnam, Wishart distributions for decomposable covariance graph models, The Annals of Statistics, pp.514-555, 2011.

Y. Konno, Estimation of normal covariance matrices parametrized by irreducible symmetric cones under Stein's loss, Journal of Multivariate Analysis, vol.98, issue.2, pp.295-316, 2007.
DOI : 10.1016/j.jmva.2006.06.006

Y. Konno, Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss, Journal of Multivariate Analysis, vol.100, issue.10, pp.2237-2253, 2009.
DOI : 10.1016/j.jmva.2009.05.002

S. Kuriki and Y. Numata, Graph presentations for moments of noncentral Wishart distributions and their applications, Annals of the Institute of Statistical Mathematics, vol.42, issue.4, pp.645-672, 2010.
DOI : 10.1093/biomet/20A.1-2.32

M. Laurent, A tour d???horizon on positive semidefinite and Euclidean distance matrix completion problems, Topics in Semidefinite and Interior-Point Methods, pp.51-76, 1998.
DOI : 10.1090/fic/018/05

S. L. Lauritzen, The EM algorithm for graphical association models with missing data, Computational Statistics & Data Analysis, vol.19, issue.2, pp.191-201, 1995.
DOI : 10.1016/0167-9473(93)E0056-A

S. L. Lauritzen and N. A. Sheehan, Graphical Models for Genetic Analyses, Graphical models for genetic analyses, pp.489-514, 2003.
DOI : 10.1214/ss/1081443232
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.126.4353

S. L. Lauritzen and D. J. Spiegelhalter, Local computations with probabilities on graphical structures and their application to expert systems, Journal of the Royal Statistical Society. Series B, pp.157-224, 1988.

S. L. Lauritzen and N. Wermuth, Graphical models for associations between variables , some of which are qualitative and some quantitative, The Annals of Statistics, pp.31-57, 1989.

E. Lehmann and G. Casella, Theory of point estimation, 1998.

E. Lehmann and J. Romano, Testing Statistical Hypotheses, 2005.

G. Letac, A characterization of the Wishart exponential families by an invariance property, Journal of Theoretical Probability, vol.8, issue.1, pp.71-86, 1989.
DOI : 10.1007/BF01048270

G. Letac, Lectures on natural exponential families and their variance functions, 1992.

G. Letac, Decomposable graphs, in Modern methods of multivariate statistics, pp.155-196, 2014.

G. Letac and H. Massam, Wishart distributions for decomposable graphs, The Annals of Statistics, vol.35, issue.3, pp.1278-1323, 2007.
DOI : 10.1214/009053606000001235
URL : https://hal.archives-ouvertes.fr/hal-00635771

G. Letac and H. Massam, The noncentral Wishart as an exponential family, and its moments, Journal of Multivariate Analysis, vol.99, issue.7, 2008.
DOI : 10.1016/j.jmva.2008.04.006
URL : https://hal.archives-ouvertes.fr/hal-00635425

G. Letac and H. Massam, Existence and non-existence of the noncentral Wishart distributions, arXiv preprint, 2011.

W. N. Mohamed, I. Diamond, and P. W. Smith, The determinants of infant mortality in Malaysia: a graphical chain modelling approach, Journal of the Royal Statistical Society: Series A (Statistics in Society), vol.161, issue.3, pp.349-366, 1998.
DOI : 10.1111/1467-985X.00113

K. Murphy, A. Torralba, and W. Freeman, Using the forest to see the trees: a graphical model relating features, objects and scenes, Advances in neural information processing systems, pp.1499-1506, 2003.

N. Oliver and A. P. Pentland, Graphical models for driver behavior recognition in a SmartCar, Proceedings of the IEEE Intelligent Vehicles Symposium 2000 (Cat. No.00TH8511), pp.7-12, 2000.
DOI : 10.1109/IVS.2000.898310

V. I. Paulsen, S. C. Power, and R. R. Smith, Schur products and matrix completions, Schur products and matrix completions, pp.151-178, 1989.
DOI : 10.1016/0022-1236(89)90050-5
URL : http://doi.org/10.1016/0022-1236(89)90050-5

A. Philipov and M. Glickman, Multivariate Stochastic Volatility via Wishart Processes, Journal of Business & Economic Statistics, vol.24, issue.3, pp.313-328, 2006.
DOI : 10.1198/073500105000000306

V. R. Ramirez, P. Q. Hernandez, S. H. Castro, and U. M. Diwekar, Fisher information as a novel tool for process control applications, 20th European Symposium on Computer Aided Process Engineering -ESCAPE20 S. Pierucci and G. Buzzi Ferraris, p.2010, 2010.

A. Roverato, Cholesky decomposition of a hyper inverse Wishart matrix, Biometrika, vol.87, issue.1, pp.99-112, 2000.
DOI : 10.1093/biomet/87.1.99

P. Sewart and J. Whittaker, Graphical models in credit scoring, IMA Journal of Management Mathematics, vol.9, issue.3, pp.241-266, 1998.
DOI : 10.1093/imaman/9.3.241

P. W. Smith, A. Berrington, and P. Sturgis, A comparison of graphical models and structural equation models for the analysis of longitudinal survey data, Methodology of Longitudinal Surveys, pp.381-392, 2009.

T. Speed and H. Kiiveri, Gaussian Markov distributions over finite graphs, The Annals of Statistics, pp.138-150, 1986.

N. Sugiura and Y. Konno, Entropy loss and risk of improved estimators for the generalized variance and precision, Annals of the Institute of Statistical Mathematics, vol.6, issue.2, pp.329-341, 1988.
DOI : 10.1007/BF00052348

H. Tsukuma and Y. Konno, On improved estimation of normal precision matrix and discriminant coefficients, Journal of Multivariate Analysis, vol.97, issue.7, pp.1477-1500, 2006.
DOI : 10.1016/j.jmva.2005.11.006

N. Wermuth, Analogies between Multiplicative Models in Contingency Tables and Covariance Selection, Biometrics, vol.32, issue.1, pp.95-108, 1976.
DOI : 10.2307/2529341

J. Wishart, The generalised product moment distribution in samples from a normal multivariate population, Biometrika, pp.32-52, 1928.

H. Wold, Causality and Econometrics, Econometrica, vol.22, issue.2, pp.162-177, 1954.
DOI : 10.2307/1907540

S. Wright, Correlation and causation, Journal of agricultural research, vol.20, issue.7, pp.557-585, 1921.

S. Wright, The Method of Path Coefficients, The Annals of Mathematical Statistics, vol.5, issue.3, pp.161-215, 1934.
DOI : 10.1214/aoms/1177732676