S. Arnborg and A. Proskurowski, Linear time algorithms for NP-hard problems restricted to partial k-trees, Discrete Applied Mathematics, vol.23, issue.1, pp.11-24, 1989.
DOI : 10.1016/0166-218X(89)90031-0

A. Becker and D. Geiger, A sufficiently fast algorithm for finding close to optimal clique trees, Artificial Intelligence, vol.125, issue.1-2, pp.3-17, 2001.
DOI : 10.1016/S0004-3702(00)00075-8

D. Bellot and P. Bessière, Approximate discrete probability distribution representation using a multi-resolution binary tree, Proceedings. 15th IEEE International Conference on Tools with Artificial Intelligence, 2003.
DOI : 10.1109/TAI.2003.1250231
URL : https://hal.archives-ouvertes.fr/hal-00068631

G. E. Box and M. E. Muller, A Note on the Generation of Random Normal Deviates, The Annals of Mathematical Statistics, vol.29, issue.2, pp.610-611, 1958.
DOI : 10.1214/aoms/1177706645

G. Cooper, The computational complexity of probabilistic inference using bayesian belief networks, Artificial Intelligence, vol.42, issue.2-3, pp.393-405, 1990.
DOI : 10.1016/0004-3702(90)90060-D

A. Corana, C. Martini, and S. Ridella, Minimizing multimodal functions of continuous variables with the ???simulated annealing??? algorithm, ACM Transactions on Mathematical Software, vol.13, issue.3, pp.262-280, 1987.
DOI : 10.1145/29380.29864

D. 'ambrosio, B. Shachter, R. D. Delfavero, and B. A. , Symbolic probabilistic inference in belief networks, Proc. of AAAI'90, pp.126-131, 1990.

A. Darwiche and G. Provan, Query DAGs: A Practical Paradigm for Implementing Belief Network Inference, J. Artif. Intellig. Res. (JAIR), vol.6, pp.147-176, 1997.

R. Dechter, Bucket Elimination: A Unifying Framework for Probabilistic Inference, Proc. of the Twelveth Conf. on Uncertainty in Artificial Intelligence, pp.211-219, 1996.
DOI : 10.1007/978-94-011-5014-9_4

R. Dechter, Bucket Elimination: A Unifying Framework for Probabilistic Inference, Artificial Intelligence, vol.113, issue.12, pp.41-85, 1999.
DOI : 10.1007/978-94-011-5014-9_4

F. Dellaert, D. Fox, W. Burgard, and S. Thrun, Monte Carlo localization for mobile robots, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C), 1999.
DOI : 10.1109/ROBOT.1999.772544

A. Eyal, Efficient approximation for triangulation of minimum treewidth, Proc. of Uncertainty in Artificial Intelligence (UAI'17), pp.7-15, 2001.

W. Feller, An introduction to Probability Theory and its applications. Third Edition, 1968.

J. A. Fill, Eigenvalue Bounds on Convergence to Stationarity for Nonreversible Markov Chains, with an Application to the Exclusion Process, The Annals of Applied Probability, vol.1, issue.1, pp.62-87, 1991.
DOI : 10.1214/aoap/1177005981

D. Fox, W. Burgard, F. Dellaert, and S. Thrun, Monte carlo localization: Efficient position estimation for mobile robots, Proc. of the Sixteenth National Conference on Artificial Intelligence (AAAI'99), 1999.

S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions and the bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.6, pp.721-741, 1984.

J. Geweke, Monte Carlo simulation and numerical integration, Handbook of Computational Economics, pp.731-800, 1996.

J. J. Grefenstette, Credit assignment in rule discovery systems based on genetic algorithms, Machine Learning, pp.225-245, 1988.
DOI : 10.1007/BF00113898

J. H. Holland, Adaptation in Natural and Artificial Systems, 1975.

T. S. Jaakkola and M. I. Jordan, Variational probabilistic inference and the QMR-DT network, J. Artif. Intellig. Res. (JAIR), vol.10, pp.291-322, 1999.

F. Jensen, An Introduction to Bayesian Networks, 1996.

F. Jensen, Bayesian Networks and Decision Graphs, Statistics for Engineering and Information Science, 2001.
DOI : 10.1007/978-0-387-68282-2

M. Jordan, Z. Ghahramani, T. S. Jaakkola, and L. K. Saul, An Introduction to Variational Methods for Graphical Models, Machine Learning, 1999.
DOI : 10.1007/978-94-011-5014-9_5

M. Jordan and Y. Weiss, Graphical Models, Statistical Science, vol.19, issue.1, 2002.
DOI : 10.1214/088342304000000026

A. Keller, The fast calculation of form factors using low discrepancy point sequence, Proc. of the 12th Spring Conf. on Computer Graphics, pp.195-204, 1996.

U. Kjaerulff, Triangulation of graphs -algorithms giving small total state space, 1990.

S. L. Lauritzen and D. J. Spiegelhalter, Local computations with probabilities on graphical structures and their applications to expert systems, Proc. of the Royal Statistical Society, pp.154-227, 1988.

Z. Li and B. Ambrosio, Efficient inference in Bayes networks as a combinatorial optimization problem, International Journal of Approximate Reasoning, vol.11, issue.1, pp.55-81, 1994.
DOI : 10.1016/0888-613X(94)90019-1

D. G. Mackay, Introduction to Monte Carlo Methods, Proc. of an Erice summer school, 1996.
DOI : 10.1007/978-94-011-5014-9_7

A. L. Madsen and F. V. Jensen, Lazy propagation in junction trees, Proc. of the Fourteenth Conference on Uncertainty in Artificial Intelligence, pp.362-369, 1998.

E. Mazer, J. M. Ahuactzin, and P. Bessière, The Ariadne's Clew algorithm, J. Artif. Intellig. Res. (JAIR), vol.9, pp.295-316, 1998.

K. Mekhnacha, P. Bessière, and E. Mazer, A Bayesian framework for geometric uncertainties handling, AIP Conference Proceedings, 2000.
DOI : 10.1063/1.1381919
URL : https://hal.archives-ouvertes.fr/hal-00019367

K. Mekhnacha, E. Mazer, and P. Bessière, A robotic CAD system using a Bayesian framework, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113), pp.1597-1604, 2000.
DOI : 10.1109/IROS.2000.895201
URL : https://hal.archives-ouvertes.fr/hal-00004990

K. Mekhnacha, E. Mazer, and P. Bessière, The design and implementation of a Bayesian CAD modeler for robotic applications, Advanced Robotics, vol.9, issue.4, pp.45-70, 2001.
DOI : 10.1163/156855301750095578
URL : https://hal.archives-ouvertes.fr/hal-00019182

N. Metropolis, A. W. Rosenblusth, M. N. Rosenblusth, A. Teller, and E. Teller, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, vol.21, issue.6, pp.1087-1092, 1953.
DOI : 10.1063/1.1699114

R. M. Neal, Probabilistic inference using Markov Chain Monte Carlo methods, 1993.

J. Pearl, Reverand bayes on inference engines: A distributed hierarchical approach, Proc. of the AAAI National Conference on AI, pp.133-136, 1982.

J. Pearl, Uncertainty in Artificial Intelligence, chap. A constraint-propagation approach to probabilistic reasoning, pp.371-382, 1986.

J. Pearl, Probabilistic reasoning in intelligent systems: networks of plausible inference, 1988.

B. A. Reed, Finding approximate separators and computing tree width quicly, Proc. of the 24th Annual ACM Symposium on the Theory of Computing, pp.221-229, 1992.

N. Robertson and P. D. Seymour, Graph Minors .XIII. The Disjoint Paths Problem, Journal of Combinatorial Theory, Series B, vol.63, issue.1, pp.65-110, 1995.
DOI : 10.1006/jctb.1995.1006
URL : http://doi.org/10.1006/jctb.1999.1919

D. J. Rose, Triangulated graphs and the elimination process, Journal of Mathematical Analysis and Applications, vol.32, issue.3, pp.597-609, 1970.
DOI : 10.1016/0022-247X(70)90282-9

R. Y. Rubinstein, Simulation and the Monte Carlo method, 1981.

P. Shenoy and G. Shafer, Uncertainty in AI, Axioms for Probability and Belief-Function Propagation. R. Shachter et al, 1990.

K. Shokhet and D. Geiger, A practical algorithm for finding optimal triangulations, Proc. of AAAI'97, pp.187-190, 1997.

L. Smail, Algorithmique pour les Réseaux Bayésiens et leurs Extensions, Thèse de doctorat, 2004.

A. F. Smith and G. O. Roberts, Bayesian computation via the Gibbs sampler and related monte carlo methods, Journal of the Royal Statistical Society B, vol.55, pp.3-23, 1993.

N. L. Zhang and D. Poole, A simple approach to bayesian network computations, Proc. of the Tenth Canadian Conference on Artificial Intelligence, pp.171-178, 1994.

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