P. J. Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, vol.82, issue.4, pp.711-732, 1995.
DOI : 10.1093/biomet/82.4.711

C. Andrieu and A. Doucet, Joint Bayesian model selection and estimation of noisy sinusoids via reversible jump MCMC, IEEE Transactions on Signal Processing, vol.47, issue.10, pp.2667-2676, 1999.
DOI : 10.1109/78.790649

M. Davy, S. J. Godsill, and J. Idier, Bayesian analysis of polyphonic western tonal music, The Journal of the Acoustical Society of America, vol.119, issue.4, pp.2498-2517, 2006.
DOI : 10.1121/1.2168548

URL : https://hal.archives-ouvertes.fr/inria-00120240

J. R. Larocque and J. P. Reilly, Reversible jump MCMC for joint detection and estimation of sources in colored noise, IEEE Transactions on Signal Processing, vol.50, issue.2, pp.231-240, 2000.
DOI : 10.1109/78.978379

S. Gulam-razul, W. Fitzgerald, and C. Andrieu, Bayesian model selection and parameter estimation of nuclear emission spectra using RJMCMC, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.497, issue.2-3, pp.492-510, 2003.
DOI : 10.1016/S0168-9002(02)01807-7

A. Zellner, On assessing prior distributions and Bayesian regression analysis with g-prior distributions Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, pp.233-243, 1986.

F. Liang, R. Paulo, G. Molina, M. Clyde, and J. Berger, Priors for Bayesian Variable Selection, Journal of the American Statistical Association, vol.103, issue.481, pp.410-423, 2008.
DOI : 10.1198/016214507000001337

C. Fernández, E. Ley, and M. Steel, Benchmark priors for Bayesian model averaging, Journal of Econometrics, vol.100, issue.2, pp.381-427, 2001.
DOI : 10.1016/S0304-4076(00)00076-2

E. I. George and D. P. Foster, Calibration and empirical Bayes variable selection, Biometrika, vol.87, issue.4, pp.731-747, 2000.
DOI : 10.1093/biomet/87.4.731

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.3731

J. Jannink and R. Fernando, On the Metropolis-Hastings Acceptance Probability to Add or Drop a Quantitative Trait Locus in Markov Chain Monte Carlo-Based Bayesian Analyses, Genetics, vol.166, issue.1, pp.641-643, 2004.
DOI : 10.1534/genetics.166.1.641

S. Richardson and P. J. Green, On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion), Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.59, issue.4, pp.731-792, 1997.
DOI : 10.1111/1467-9868.00095

W. Cui and E. I. George, Empirical Bayes vs. fully Bayes variable selection, Journal of Statistical Planning and Inference, vol.138, issue.4, pp.888-900, 2008.
DOI : 10.1016/j.jspi.2007.02.011

R. A. Levine and G. Casella, Implementations of the Monte Carlo EM Algorithm, Journal of Computational and Graphical Statistics, vol.10, issue.3, pp.422-439, 2001.
DOI : 10.1198/106186001317115045

J. Besag, P. Green, D. Higdon, and K. Mengersen, Bayesian Computation and Stochastic Systems, Statistical Science, vol.10, issue.1, pp.3-41, 1995.
DOI : 10.1214/ss/1177010123

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.8854

C. Andrieu and A. Doucet, Joint Bayesian model selection and estimation of noisy sinusoids via reversible jump MCMC, IEEE Transactions on Signal Processing, vol.47, issue.10, pp.2667-2676, 1999.
DOI : 10.1109/78.790649

W. Cui and E. I. George, Empirical Bayes vs. fully Bayes variable selection, Journal of Statistical Planning and Inference, vol.138, issue.4, pp.888-900, 2008.
DOI : 10.1016/j.jspi.2007.02.011

M. Davy, S. J. Godsill, and J. Idier, Bayesian analysis of polyphonic western tonal music, The Journal of the Acoustical Society of America, vol.119, issue.4, pp.2498-2517, 2006.
DOI : 10.1121/1.2168548

URL : https://hal.archives-ouvertes.fr/inria-00120240

C. Fernández, E. Ley, and M. Steel, Benchmark priors for Bayesian model averaging, Journal of Econometrics, vol.100, issue.2, pp.381-427, 2001.
DOI : 10.1016/S0304-4076(00)00076-2

E. I. George and D. P. Foster, Calibration and empirical Bayes variable selection, Biometrika, vol.87, issue.4, pp.731-747, 2000.
DOI : 10.1093/biomet/87.4.731

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.3731

R. Gramacy, R. Samworth, and R. King, Importance tempering, Statistics and Computing, vol.95, issue.449, pp.1-7, 2010.
DOI : 10.1007/s11222-008-9108-5

P. J. Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, vol.82, issue.4, pp.711-732, 1995.
DOI : 10.1093/biomet/82.4.711

P. J. Green, Trans-dimensional Markov chain Monte Carlo, Highly Structured Stochastic Systems, pp.179-198, 2003.

S. Gulam-razul, W. Fitzgerald, and C. Andrieu, Bayesian model selection and parameter estimation of nuclear emission spectra using RJMCMC, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.497, issue.2-3, pp.492-510, 2003.
DOI : 10.1016/S0168-9002(02)01807-7

J. Jannink and R. Fernando, On the Metropolis-Hastings Acceptance Probability to Add or Drop a Quantitative Trait Locus in Markov Chain Monte Carlo-Based Bayesian Analyses, Genetics, vol.166, issue.1, pp.641-643, 2004.
DOI : 10.1534/genetics.166.1.641

J. R. Larocque and J. P. Reilly, Reversible jump MCMC for joint detection and estimation of sources in colored noise, IEEE Transactions on Signal Processing, vol.50, issue.2, pp.231-240, 2000.
DOI : 10.1109/78.978379

R. A. Levine, G. Casella, F. Liang, R. Paulo, G. Molina et al., Implementations of the Monte Carlo EM algorithm Mixtures of g-priors for Bayesian variable selection, J. Comput. Graph. Stat. J. Am. Stat. Assoc, vol.103, issue.481, pp.422-439410, 2001.

F. Quintana, J. Liu, and G. Pino, Monte Carlo EM with importance reweighting and its applications in random effects models, Computational Statistics & Data Analysis, vol.29, issue.4, pp.429-444, 1999.
DOI : 10.1016/S0167-9473(98)00075-9

S. Richardson and P. J. Green, On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion), Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.59, issue.4, pp.731-792, 1997.
DOI : 10.1111/1467-9868.00095

C. Robert and G. Casella, Monte Carlo Statistical Methods (second edition), 2004.

C. P. Robert, The Bayesian Choice, 2007.
DOI : 10.1007/978-1-4757-4314-2

A. Roodaki, J. Bect, and G. Fleury, On the Joint Bayesian model selection and estimation of noisy sinusoids via reversible jump MCMC in Low SNR Situations, Proc. 10 th Int. Conf. on Information Science , Signal Processing and their Application (ISSPA), Kuala lumpur, Malaysia, pp.5-8, 2010.

G. C. Wei and M. A. Tanner, A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms, Journal of the American Statistical Association, vol.51, issue.411, pp.699-704, 1990.
DOI : 10.1214/aos/1176346060

A. Zellner, On assessing prior distributions and bayesian regression analysis with g-prior distributions, Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, pp.233-243, 1986.

C. References, A. Andrieu, and . Doucet, Joint Bayesian model selection and estimation of noisy sinusoids via reversible jump MCMC, IEEE Transactions on Signal Processing, issue.10, pp.47-2667, 1999.

C. Andrieu and É. Moulines, On the ergodicity properties of some adaptive MCMC algorithms, The Annals of Applied Probability, vol.16, issue.3, pp.1462-1505, 2006.
DOI : 10.1214/105051606000000286

C. Andrieu, A. Doucet, W. J. Fitzgerald, and J. M. Pérez, Bayesian computational approaches to model selection. Nonlinear and Nonstationary Signal Processing, pp.1-41, 1998.

C. Andrieu, N. D. Freitas, and A. Doucet, Reversible jump MCMC Simulated annealing for neural networks, Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence, pp.11-18, 2000.

C. Andrieu, N. D. Freitas, and A. Doucet, Robust Full Bayesian Learning for Radial Basis Networks, Neural Computation, vol.12, issue.261, pp.2359-2407, 2001.
DOI : 10.1162/neco.1997.9.2.461

C. Andrieu, P. M. Djuri?, and A. Doucet, Model selection by MCMC computation, Signal Processing, vol.81, issue.1, pp.19-37, 2001.
DOI : 10.1016/S0165-1684(00)00188-2

C. Andrieu, E. Barat, and A. Doucet, Bayesian deconvolution of noisy filtered point processes, IEEE Transactions on Signal Processing, vol.49, issue.1, pp.134-146, 2002.
DOI : 10.1109/78.890355

S. Asmussen, K. Binswanger, and B. Højgaard, Rare Events Simulation for Heavy-Tailed Distributions, Bernoulli, vol.6, issue.2, pp.303-322, 2000.
DOI : 10.2307/3318578

Y. F. Atchadé and J. S. Rosenthal, On adaptive Markov chain Monte Carlo algorithms, Bernoulli, vol.11, issue.5, pp.815-828, 2005.
DOI : 10.3150/bj/1130077595

A. Collaboration, The Pierre Auger Project Design Report, 1997.

A. Collaboration, Properties and performance of the prototype instrument for the Pierre Auger Observatory. Nuclear Instruments and Methods in Physics Research A, pp.50-95, 2004.

Y. Bai, R. V. Craiu, and A. F. Di-narzo, Divide and Conquer: A Mixture-Based Approach to Regional Adaptation for MCMC, Journal of Computational and Graphical Statistics, vol.20, issue.1, pp.63-79, 2011.
DOI : 10.1198/jcgs.2010.09035

E. Barat and T. Dautremer, Nonparametric Bayesian estimation of x/?-ray spectra using a hierarchical polya tree-dirichlet mixture model, AIP CONFERENCE PROCEED- INGS, p.477, 2006.

M. M. Barbieri and J. O. Berger, Optimal predictive model selection. The Annals of Statistics, pp.870-897, 2004.

R. Bardenet, B. Kégl, and D. Veberic, Single muon response: The signal model, 2010.

R. Bardenet, O. Cappé, G. Fort, and B. Kégl, An adaptive Metropolis algorithm with online relabeling, the proceeding of the 15 th International Conference on Artificial Intelligence and Statistics (AISTATS), 2012.

A. Basu, I. R. Harris, N. L. Hjort, and M. C. Jones, Robust and efficient estimation by minimising a density power divergence, Biometrika, vol.85, issue.3, p.549, 1998.
DOI : 10.1093/biomet/85.3.549

J. O. Berger, Robust Bayesian analysis: sensitivity to the prior, Journal of Statistical Planning and Inference, vol.25, issue.3, pp.303-328, 1990.
DOI : 10.1016/0378-3758(90)90079-A

J. O. Berger, V. D. Oliveira, and B. Sansó, Objective Bayesian Analysis of Spatially Correlated Data, Journal of the American Statistical Association, vol.96, issue.456, pp.1361-1374, 2001.
DOI : 10.1198/016214501753382282

J. O. Berger, J. M. Bernardo, and D. Sun, The formal definition of reference priors. The Annals of Statistics, pp.905-938, 2009.

J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. Smith, On the development of reference priors, Bayesian Statistics, vol.4, pp.35-60, 1992.

L. References, A. Bornn, R. Doucet, and . Gottardo, An efficient computational approach for prior sensitivity analysis and cross-validation, Canadian Journal of Statistics, vol.38, issue.1, pp.47-64, 2010.

G. L. Bretthorst, Bayesian Spectrum Analysis and Parameter Estimation, 1988.
DOI : 10.1007/978-1-4684-9399-3

M. Broniatowski and A. Keziou, Parametric estimation and tests through divergences and the duality technique, Journal of Multivariate Analysis, vol.100, issue.1, pp.16-36, 2009.
DOI : 10.1016/j.jmva.2008.03.011

M. Broniatowski, G. Celeux, and J. Diebolt, Reconnaissance de mélanges de densités par un algorithme d'apprentissage probabiliste. Data analysis and informatics, pp.359-373, 1983.

S. P. Brooks, P. Giudici, and G. O. Roberts, Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.28, issue.1, pp.3-39, 2003.
DOI : 10.1016/S0165-1684(00)00192-4

K. P. Burnham and D. R. Anderson, Model selection and multimodel inference: a practical information-theoretic approach, 2002.
DOI : 10.1007/b97636

E. Candes and T. Tao, The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics, pp.2313-2351, 2007.

O. Cappé, A. Doucet, M. Lavielle, and E. Moulines, Simulation-based methods for blind maximum-likelihood filter identification, Signal Processing, vol.73, issue.1-2, pp.3-25, 1999.
DOI : 10.1016/S0165-1684(98)00182-0

O. Cappé, C. P. Robert, and T. Rydén, Reversible jump, birth-and-death and more general continuous time Markov chain Monte Carlo samplers, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.28, issue.3, pp.679-700, 2003.
DOI : 10.1111/1467-9868.00219

G. Casella and E. I. George, Explaining the Gibbs sampler, American Statistician, pp.167-174, 1992.

G. Celeux, Bayesian Inference for Mixture: The Label Switching Problem, pp.227-232, 1998.
DOI : 10.1007/978-3-662-01131-7_26

G. Celeux and J. Diebolt, The SEM algorithm : a probabilistic teacher algorithm derived from the EM algorithm for the mixture problem, Computational Statistics Quaterly, vol.2, pp.73-82, 1985.

G. Celeux and J. Diebolt, A stochastic approximation type EM algorithm for the mixture problem, Stochastics An International Journal of Probability and Stochastic Processes, vol.41, issue.1, pp.119-134, 1992.
DOI : 10.1080/17442509208833797

URL : https://hal.archives-ouvertes.fr/inria-00075178

G. Celeux, M. Hurn, and C. P. Robert, Computational and Inferential Difficulties with Mixture Posterior Distributions, Journal of the American Statistical Association, vol.60, issue.451, pp.957-970, 2000.
DOI : 10.1080/01621459.1995.10476589

URL : https://hal.archives-ouvertes.fr/inria-00073049

G. Celeux, M. E. Anbari, J. M. Marin, and C. P. Robert, Regularization in Regression: Comparing Bayesian and Frequentist Methods in a Poorly Informative Situation, Bayesian Analysis, vol.7, issue.2, pp.1-26, 2012.
DOI : 10.1214/12-BA716

URL : https://hal.archives-ouvertes.fr/hal-00943727

S. S. Chen, D. L. Donoho, and M. A. Saunders, Atomic Decomposition by Basis Pursuit, SIAM Journal on Scientific Computing, vol.20, issue.1, pp.33-61, 1999.
DOI : 10.1137/S1064827596304010

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.113.7694

H. Chipman, E. I. George, R. E. Mcculloch, M. Clyde, D. P. Foster et al., The Practical Implementation of Bayesian Model Selection, Lecture Notes-Monograph Series, pp.65-134, 2001.
DOI : 10.1214/lnms/1215540964

N. Chopin, A sequential particle filter method for static models, Biometrika, vol.89, issue.3, p.539, 2002.
DOI : 10.1093/biomet/89.3.539

M. A. Clyde and E. I. George, Model uncertainty, Statistical Science, vol.19, issue.1, pp.81-94, 2004.

P. Congdon, Bayesian Statistical Modeling, 2006.

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, pp.883-904, 1996.
DOI : 10.1080/01621459.1996.10476956

I. Csiszár, Information-type measures of difference of probability distributions and indirect observations, Studia scientiarum mathematicarum Hungarica, vol.2, pp.299-318, 1967.

W. Cui and E. I. George, Empirical Bayes vs. fully Bayes variable selection, Journal of Statistical Planning and Inference, vol.138, issue.4, pp.888-900, 2008.
DOI : 10.1016/j.jspi.2007.02.011

R. N. Davé and R. Krishnapuram, Robust clustering methods: a unified view, IEEE Transactions on Fuzzy Systems, vol.5, issue.2, pp.270-293, 1997.
DOI : 10.1109/91.580801

M. Davy, S. J. Godsill, and J. Idier, Bayesian analysis of polyphonic western tonal music, The Journal of the Acoustical Society of America, vol.119, issue.4, pp.2498-2517, 2006.
DOI : 10.1121/1.2168548

URL : https://hal.archives-ouvertes.fr/inria-00120240

P. , D. Moral, A. Doucet, and A. Jasra, Sequential Monte Carlo samplers, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.68, issue.3, pp.411-436, 2006.

A. P. Dempster, N. B. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 1977.

X. Descombes, R. Van-lieshout, J. Stoica, and . Zerubia, Parameter estimation by a Markov chain Monte Carlo technique for the Candy model, Proceedings of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing (Cat. No.01TH8563), 2001.
DOI : 10.1109/SSP.2001.955212

X. Descombes, F. Kruggel, G. Wollny, and H. J. Gertz, An Object-Based Approach for Detecting Small Brain Lesions: Application to Virchow-Robin Spaces, IEEE Transactions on Medical Imaging, vol.23, issue.2, pp.246-255, 2004.
DOI : 10.1109/TMI.2003.823061

P. Diaconis, S. Holmes, and R. M. Neal, Analysis of a nonreversible Markov chain sampler, The Annals of Applied Probability, vol.10, issue.3, pp.726-752, 2000.
DOI : 10.1214/aoap/1019487508

J. Diebolt and G. Celeux, Asymptotic properties of a stochastic EM algorithm for estimating mixing proportions. Stochastic Models, pp.599-613, 1993.
URL : https://hal.archives-ouvertes.fr/inria-00074969

J. Diebolt and C. P. Robert, Estimation of finite mixture distributions through Bayesian sampling, Journal of the Royal Statistical Society. Series B (Statistical Methodology), pp.363-375, 1994.

P. M. Djuri?, A model selection rule for sinusoids in white Gaussian noise, IEEE Transactions on Signal Processing, vol.44, issue.7, pp.1744-1751, 1996.
DOI : 10.1109/78.510621

N. Dobigeon, A. O. Hero, and J. Y. Tourneret, Hierarchical Bayesian Sparse Image Reconstruction With Application to MRFM, IEEE Transactions on Image Processing, vol.18, issue.9, pp.2059-2070, 2009.
DOI : 10.1109/TIP.2009.2024067

URL : https://hal.archives-ouvertes.fr/hal-00324075

L. Dou and R. J. Hodgson, Bayesian inference and Gibbs sampling in spectral analysis and parameter estimation. I. Inverse problems, p.1069, 1995.

L. Dou and R. J. Hodgson, Bayesian inference and Gibbs sampling in spectral analysis and parameter estimation: II, Inverse Problems, vol.12, issue.2, p.121, 1996.
DOI : 10.1088/0266-5611/12/2/002

A. Doucet, S. G. Godsill, and C. Andrieu, On sequential Monte Carlo sampling methods for Bayesian filtering, Statistics and Computing, vol.10, issue.3, pp.197-208, 2000.
DOI : 10.1023/A:1008935410038

A. Doucet, N. D. Freitas, and N. Gordon, Sequential Monte Carlo Methods in Practice, 2001.
DOI : 10.1007/978-1-4757-3437-9

N. R. Draper and H. Smith, Applied Regression Analysis (Wiley Series in Probability and Statistics), 1981.

M. Elad and M. Aharon, Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries, IEEE Transactions on Image Processing, vol.15, issue.12, pp.3736-3745, 2006.
DOI : 10.1109/TIP.2006.881969

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.6477

Y. Fan, G. W. Peters, and S. A. Sisson, Automating and evaluating reversible jump MCMC proposal distributions, Statistics and Computing, vol.25, issue.6, pp.409-421, 2009.
DOI : 10.1007/s11222-008-9101-z

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.9295

C. Fernández, E. Ley, and M. F. Steel, Benchmark priors for Bayesian model averaging, Journal of Econometrics, vol.100, issue.2, pp.381-427, 2001.
DOI : 10.1016/S0304-4076(00)00076-2

C. Fevotte and S. J. , Sparse linear regression in unions of bases via Bayesian variable selection, IEEE Signal Processing Letters, vol.13, issue.7, pp.441-444, 2006.
DOI : 10.1109/LSP.2006.873139

D. H. Fremlin, Measure Theory, Broad Foundations. Torres Fremlin, vol.2, 2001.

S. Frühwirth-schnatter, Finite Mixture and Markov Switching Models, 2006.

H. Fujisawa and S. Eguchi, Robust estimation in the normal mixture model, Journal of Statistical Planning and Inference, vol.136, issue.11, pp.3989-4011, 2006.
DOI : 10.1016/j.jspi.2005.03.008

A. E. Gelfand and A. F. Smith, Sampling-Based Approaches to Calculating Marginal Densities, Journal of the American Statistical Association, vol.4, issue.410, pp.398-409, 1990.
DOI : 10.1080/01621459.1986.10478240

A. Gelman, G. O. Roberts, and W. Gilks, Efficient Metropolis jumping rules, Bayesian Statistics, vol.5, pp.599-608, 1996.

A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin, Bayesian Data Analysis, 2004.

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.

E. I. George and D. P. Foster, Calibration and empirical Bayes variable selection, Biometrika, vol.87, issue.4, pp.731-747, 2000.
DOI : 10.1093/biomet/87.4.731

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.3731

C. J. Geyer and J. Møller, Simulation procedures and likelihood inference for spatial point processes, Scandinavian Journal of Statistics, vol.21, issue.4, pp.359-373, 1994.

W. R. Gilks and C. Berzuini, Following a moving target-Monte Carlo inference for dynamic Bayesian models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.63, issue.1, pp.127-146, 2001.
DOI : 10.1111/1467-9868.00280

W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Markov Chain Monte Carlo in Practice, 1996.

N. J. Gordon, D. J. Salmond, and A. F. Smith, Novel approach to nonlinear/non-Gaussian Bayesian state estimation, IEE Proceedings F Radar and Signal Processing, vol.140, issue.2, pp.107-113, 1993.
DOI : 10.1049/ip-f-2.1993.0015

P. J. Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, vol.82, issue.4, pp.711-732, 1995.
DOI : 10.1093/biomet/82.4.711

P. J. Green, Trans-dimensional Markov chain Monte Carlo, Highly Structured Stochastic Systems, pp.179-198, 2003.

B. Grün and F. Leisch, Dealing with label switching in mixture models under genuine multimodality, Journal of Multivariate Analysis, vol.100, issue.5, pp.851-861, 2009.
DOI : 10.1016/j.jmva.2008.09.006

H. Haario, E. Saksman, and J. Tamminen, An Adaptive Metropolis Algorithm, Bernoulli, vol.7, issue.2, pp.223-242, 2001.
DOI : 10.2307/3318737

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.8948

C. Han and B. P. Carlin, Markov Chain Monte Carlo Methods for Computing Bayes Factors, Journal of the American Statistical Association, vol.96, issue.455, pp.1122-1132, 2001.
DOI : 10.1198/016214501753208780

D. Hastie, Towards automatic reversible jump Markov chain Monte Carlo, 2005.
DOI : 10.1111/j.1467-9574.2012.00516.x

URL : https://opus.lib.uts.edu.au/bitstream/10453/32396/1/2013007521OK.pdf

D. I. Hastie and P. J. Green, Model choice using reversible jump Markov chain Monte Carlo, Statistica Neerlandica, vol.69, issue.3, 2011.
DOI : 10.1111/j.1467-9574.2012.00516.x

URL : https://opus.lib.uts.edu.au/bitstream/10453/32396/1/2013007521OK.pdf

W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, vol.57, issue.1, pp.97-109, 1970.
DOI : 10.1093/biomet/57.1.97

A. Hero and I. , Timing estimation for a filtered Poisson process in Gaussian noise, IEEE Transactions on Information Theory, vol.37, issue.1, pp.92-106, 1991.
DOI : 10.1109/18.61107

J. A. Hoeting, D. Madigan, A. E. Raftery, and C. T. Volinsky, Bayesian model averaging: a tutorial, Statistical Science, pp.382-401, 1999.

M. Hong, M. F. Bugallo, and P. M. Djuri?, Joint Model Selection and Parameter Estimation by Population Monte Carlo Simulation, IEEE Journal of Selected Topics in Signal Processing, vol.4, issue.3, pp.526-539, 2010.
DOI : 10.1109/JSTSP.2010.2048385

M. Hurn and H. Rue, High level image priors in confocal microscopy applications. The Art and Science of Bayesian Image Analysis, pp.36-43, 1997.

J. Jannink and R. L. Fernando, On the Metropolis-Hastings Acceptance Probability to Add or Drop a Quantitative Trait Locus in Markov Chain Monte Carlo-Based Bayesian Analyses, Genetics, vol.166, issue.1, pp.641-643, 2004.
DOI : 10.1534/genetics.166.1.641

A. Jasra, Bayesian inference for mixture models via Monte Carlo computation, 2005.

A. Jasra, C. C. Holmes, and D. A. Stephens, Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling, Statistical Science, vol.20, issue.1, pp.50-67, 2005.
DOI : 10.1214/088342305000000016

E. T. Jaynes, Bayesian spectrum and chirp analysis. Maximum Entropy and Bayesian Spectral Analysis and Estimation Problems, 1987.
DOI : 10.1007/978-94-009-3961-5_1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.7022

M. C. Jones, N. L. Hjort, I. R. Harris, and A. Basu, A comparison of related density-based minimum divergence estimators, Biometrika, vol.88, issue.3, p.865, 2001.
DOI : 10.1093/biomet/88.3.865

R. E. Kass and A. E. Raftery, Bayes Factors, Journal of the American Statistical Association, vol.2, issue.430, pp.773-795, 1995.
DOI : 10.1080/01621459.1995.10476572

R. E. Kass and L. Wasserman, The Selection of Prior Distributions by Formal Rules, Journal of the American Statistical Association, vol.36, issue.435, pp.1343-1370, 1996.
DOI : 10.1080/01621459.1996.10477003

B. Kégl and D. Veberic, Single muon response: Tracklength, 2009.

S. Kullback and R. A. Leibler, On Information and Sufficiency, The Annals of Mathematical Statistics, vol.22, issue.1, pp.79-86, 1951.
DOI : 10.1214/aoms/1177729694

C. Lacoste, X. Descombes, and J. Zerubia, Point processes for unsupervised line network extraction in remote sensing, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.27, issue.10, pp.1568-1579, 2005.
DOI : 10.1109/TPAMI.2005.206

P. Lahiri, Model selection, Lecture Notes?Monograph Series, vol.38, 2001.

J. R. Larocque and J. P. Reilly, Reversible jump MCMC for joint detection and estimation of sources in colored noise, IEEE Transactions on Signal Processing, vol.50, issue.2, pp.231-240, 2002.
DOI : 10.1109/78.978379

J. R. Larocque, J. P. Reilly, and W. Ng, Particle filters for tracking an unknown number of sources, IEEE Transactions on Signal Processing, vol.50, issue.12, pp.2926-2937, 2002.
DOI : 10.1109/TSP.2002.805251

R. A. Levine and G. Casella, Implementations of the Monte Carlo EM Algorithm, Journal of Computational and Graphical Statistics, vol.10, issue.3, pp.422-439, 2001.
DOI : 10.1198/106186001317115045

M. S. Lewicki and T. J. Sejnowski, Learning Overcomplete Representations, Neural Computation, vol.33, issue.2, pp.337-365, 2000.
DOI : 10.1109/18.119725

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.164.7690

F. Liang, R. Paulo, G. Molina, M. A. Clyde, and J. O. Berger, Priors for Bayesian Variable Selection, Journal of the American Statistical Association, vol.103, issue.481, pp.410-423, 2008.
DOI : 10.1198/016214507000001337

J. S. Liu, Monte Carlo Strategies in Scientific Computing, 2001.
DOI : 10.1007/978-0-387-76371-2

J. S. Liu and R. Chen, Sequential Monte Carlo Methods for Dynamic Systems, Journal of the American Statistical Association, vol.24, issue.443, pp.1032-1044, 1998.
DOI : 10.1073/pnas.94.26.14220

S. G. Mallat and Z. Zhang, Matching pursuits with time-frequency dictionaries, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.3397-3415, 1993.
DOI : 10.1109/78.258082

S. G. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way, 2009.

J. M. Marin, K. L. Mengersen, and C. P. Robert, Bayesian Modelling and Inference on Mixtures of Distributions, Bayesian Thinking, Modeling and Computation, vol.25, 2005.
DOI : 10.1016/S0169-7161(05)25016-2

R. A. Maronna, R. D. Martin, and V. J. Yohai, Robust Statistics: Theory and Methods, 2006.
DOI : 10.1002/0470010940

G. J. Mclachlan and T. Krishnan, The EM Algorithm and Extensions, 2008.

G. J. Mclachlan and D. Peel, Finite Mixture Models, 2000.
DOI : 10.1002/0471721182

L. Melie-garcía, E. J. Canales-rodríguez, Y. Alemán-gómez, C. P. Lin, Y. Iturria-medina et al., Valdés-Hernández. A Bayesian framework to identify principal intravoxel diffusion profiles based on diffusion-weighted MR imaging, Neuroimage, issue.2, pp.42750-770, 2008.

V. Melnykov and I. Melnykov, Initializing the EM algorithm in Gaussian mixture models with an unknown number of components, Computational Statistics & Data Analysis, vol.56, issue.6, 2011.
DOI : 10.1016/j.csda.2011.11.002

K. L. Mengersen and C. P. Robert, MCMC convergence diagnostics: a reviewww, Bayesian statistics 6: proceedings of the Sixth Valencia International Meeting, p.415, 1999.

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of state calculations by fast computing machines. The journal of chemical physics, p.1087, 1953.

S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, 1993.

M. Mihoko and S. Eguchi, Robust Blind Source Separation by Beta Divergence, Neural Computation, vol.2, issue.8, pp.1859-1886, 2002.
DOI : 10.1109/78.599941

A. J. Miller, Subset Selection in Regression, 2002.

Y. Mishchencko, J. T. Vogelstein, and L. Paninski, A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data, The Annals of Applied Statistics, vol.5, issue.2B, pp.1229-1261, 2011.
DOI : 10.1214/09-AOAS303

M. Miyamura and Y. Kano, Robust Gaussian graphical modeling, Journal of Multivariate Analysis, vol.97, issue.7, pp.1525-1550, 2006.
DOI : 10.1016/j.jmva.2006.02.006

URL : http://doi.org/10.1016/j.jmva.2006.02.006

W. Ng, J. P. Reilly, T. Kirubarajan, and J. R. Larocque, Wideband array signal processing using MCMC methods, IEEE Transactions on Signal Processing, vol.53, issue.2, pp.411-426, 2005.
DOI : 10.1109/TSP.2004.838934

W. Ng, T. Chan, H. C. So, and K. C. Ho, On particle filters for landmine detection using impulse ground penetrating radar, 2008 5th IEEE Sensor Array and Multichannel Signal Processing Workshop, pp.225-228, 2008.
DOI : 10.1109/SAM.2008.4606860

G. K. Nicholls, Bayesian image analysis with Markov chain Monte Carlo and coloured continuum triangulation models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.60, issue.3, pp.643-659, 1998.
DOI : 10.1111/1467-9868.00145

S. F. Nielsen, The Stochastic EM Algorithm: Estimation and Asymptotic Results, Bernoulli, vol.6, issue.3, pp.457-489, 2000.
DOI : 10.2307/3318671

S. F. Nielsen, On simulated EM algorithms, Journal of Econometrics, vol.96, issue.2, pp.267-292, 2000.
DOI : 10.1016/S0304-4076(99)00060-3

J. Nocedal and S. J. Wright, Numerical Optimization, 1999.
DOI : 10.1007/b98874

P. Papastamoulis and G. Iliopoulos, An Artificial Allocations Based Solution to the Label Switching Problem in Bayesian Analysis of Mixtures of Distributions, Journal of Computational and Graphical Statistics, vol.19, issue.2, pp.313-331, 2010.
DOI : 10.1198/jcgs.2010.09008

L. Parclo, Statistical Inference Based on Divergence Measures, CRC, 2005.

A. Pievatolo and P. J. Green, Boundary detection through dynamic polygons, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.60, issue.3, pp.609-635, 1998.
DOI : 10.1111/1467-9868.00143

E. Punskaya, C. Andrieu, A. Doucet, and W. J. Fitzgerald, Bayesian curve fitting using MCMC with applications to signal segmentation, IEEE Transactions on Signal Processing, vol.50, issue.3, pp.747-758, 2002.
DOI : 10.1109/78.984776

F. A. Quintana, J. S. Liu, and G. E. Pino, Monte Carlo EM with importance reweighting and its applications in random effects models, Computational Statistics & Data Analysis, vol.29, issue.4, pp.429-444, 1999.
DOI : 10.1016/S0167-9473(98)00075-9

S. Richardson and P. J. Green, On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion), Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.59, issue.4, pp.731-792, 1997.
DOI : 10.1111/1467-9868.00095

S. Richardson and P. J. Green, Corrigendum: On Bayesian analysis of mixtures with an unknown number of components, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.60, issue.3, p.661, 1998.
DOI : 10.1111/1467-9868.00146

C. P. Robert, S. Richardson, and P. J. Green, Discussion of On Bayesian analysis of mixtures with an unknown number of components, Journal of the Royal Statistical Society. Series B (Statistical Methodology), vol.59, issue.4, pp.758-764, 1997.

C. P. Robert, The Bayesian Choice, 2007.
DOI : 10.1007/978-1-4757-4314-2

G. O. Roberts and J. S. Rosenthal, Optimal scaling for various Metropolis-Hastings algorithms, Statistical Science, vol.16, issue.4, pp.351-367, 2001.
DOI : 10.1214/ss/1015346320

G. O. Roberts and J. S. Rosenthal, General state space Markov chains and MCMC algorithms, Probability Surveys, vol.1, issue.0, pp.20-71, 2004.
DOI : 10.1214/154957804100000024

G. O. Roberts and J. S. Rosenthal, Harris recurrence of Metropolis-within-Gibbs and trans-dimensional Markov chains. The Annals of Applied Probability, pp.2123-2139, 2006.

G. O. Roberts and J. S. Rosenthal, Examples of Adaptive MCMC, Journal of Computational and Graphical Statistics, vol.18, issue.2, pp.349-367, 2009.
DOI : 10.1198/jcgs.2009.06134

O. Rosec, J. M. Boucher, B. Nsiri, and T. Chonavel, Blind marine seismic deconvolution using statistical MCMC methods, IEEE Journal of Oceanic Engineering, vol.28, issue.3, pp.502-512, 2003.
DOI : 10.1109/JOE.2003.816683

D. V. Rubtsov and J. L. Griffin, Time-domain Bayesian detection and estimation of noisy damped sinusoidal signals applied to NMR spectroscopy, Journal of Magnetic Resonance, vol.188, issue.2, pp.367-379, 2007.
DOI : 10.1016/j.jmr.2007.08.008

H. Rue and M. A. Hurn, Bayesian object identification, Biometrika, vol.86, issue.3, pp.649-660, 1999.
DOI : 10.1093/biomet/86.3.649

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.2451

M. N. Schmidt and M. Mørup, Infinite non-negative matrix factorization, 18 th European Signal Processing Conference (EUSIPCO), 2010.

A. Schuster, On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena, Journal of Geophysical Research, vol.91, issue.1, pp.13-41, 1898.
DOI : 10.1029/TM003i001p00013

Z. G. Shi, J. X. Zhou, H. Z. Zhao, and Q. Fu, Study on joint Bayesian model selection and parameter estimation method of GTD model, Science in China Series F: Information Sciences, pp.261-272, 2007.
DOI : 10.1007/s11432-007-0019-4

M. J. Sillanpaa, D. Gasbarra, and E. Arjas, Comment on "On the Metropolis-Hastings Acceptance Probability to Add or Drop a Quantitative Trait Locus in Markov Chain Monte Carlo-Based Bayesian Analyses", Genetics, vol.167, issue.2, p.1037, 2004.
DOI : 10.1534/genetics.103.025320

S. A. Sisson, Transdimensional Markov Chains, Journal of the American Statistical Association, vol.100, issue.471, pp.1077-1090, 2005.
DOI : 10.1198/016214505000000664

M. Sperrin, T. Jaki, and E. Wit, Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models, Statistics and Computing, vol.62, issue.2, pp.357-366, 2010.
DOI : 10.1007/s11222-009-9129-8

M. Stephens, S. Richardson, and P. J. Green, Discussion of On Bayesian analysis of mixtures with an unknown number of components, Journal of the Royal Statistical Society. Series B (Statistical Methodology), vol.59, issue.4, pp.768-769, 1997.

M. Stephens, Bayesian methods for mixture of normal distributions, 1997.

M. Stephens, Dealing with label switching in mixture models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.62, issue.4, pp.795-809, 2000.
DOI : 10.1111/1467-9868.00265

P. Stoica and Y. Selen, Model-order selection, IEEE Signal Processing Magazine, vol.21, issue.4, pp.36-47, 2004.
DOI : 10.1109/MSP.2004.1311138

P. Stoica, R. L. Moses, B. Friedlander, and T. Soderstrom, Maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.37, issue.3, pp.378-392, 1989.
DOI : 10.1109/29.21705

R. Stoica, X. Descombes, and J. Zerubia, A Gibbs Point Process for Road Extraction from Remotely Sensed Images, International Journal of Computer Vision, vol.57, issue.2, pp.121-136, 2004.
DOI : 10.1023/B:VISI.0000013086.45688.5d

M. A. Tanner and W. H. Wong, The Calculation of Posterior Distributions by Data Augmentation, Journal of the American Statistical Association, vol.56, issue.398, pp.528-540, 1987.
DOI : 10.1016/0304-4076(84)90007-1

M. B. Thompson, Graphical comparison of MCMC performance, 2010.

R. Tibshirani, Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B (Statistical Methodology), pp.267-288, 1996.

L. Tierney, Markov chains for exploring posterior distributions. The Annals of Statistics, pp.1701-1728, 1994.

L. Tierney, A note on Metropolis-Hastings kernels for general state spaces, The Annals of Applied Probability, vol.8, issue.1, pp.1-9, 1998.
DOI : 10.1214/aoap/1027961031

D. A. Van-dyk and T. Park, Partially Collapsed Gibbs Samplers, Journal of the American Statistical Association, vol.103, issue.482, pp.790-796, 2008.
DOI : 10.1198/016214508000000409

M. Van-lieshout, Markov Point Processes and their Applications, 2000.
DOI : 10.1142/p060

G. C. Wei and M. A. Tanner, A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms, Journal of the American Statistical Association, vol.51, issue.411, pp.699-704, 1990.
DOI : 10.1214/aos/1176346060

M. West, Approximating posterior distributions by mixture, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.55, issue.2, pp.409-422, 1993.

P. J. Wolfe, S. J. Godsill, and W. J. Ng, Bayesian variable selection and regularization for time-frequency surface estimation, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.45, issue.3, pp.575-589, 2004.
DOI : 10.1162/15324430152748236

W. Yao, Model based labeling for mixture models, Statistics and Computing, vol.104, issue.2, pp.1-11, 2011.
DOI : 10.1007/s11222-010-9226-8

A. Zellner, On assessing prior distributions and Bayesian regression analysis with gprior distributions, Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, pp.233-243, 1986.