N. Akakpo, F. Balabdaoui, and C. Durot, Testing monotonicity via local least concave majorants, Bernoulli, vol.20, issue.2, pp.514-544, 2014.
DOI : 10.3150/12-BEJ496SUPP
URL : https://hal.archives-ouvertes.fr/hal-01575154

Y. Baraud, S. Huet, L. , and B. , Adaptive tests of qualitative hypotheses, ESAIM: Probability and Statistics, vol.7, pp.147-159, 2003.
DOI : 10.1051/ps:2003006

J. O. Berger, B. Boukai, W. , and Y. , Unified frequentist and Bayesian testing of a precise hypothesis, Statist. Sci, vol.12, issue.3, pp.133-160, 1997.

J. O. Berger and M. Delampady, Testing Precise Hypotheses, Statistical Science, vol.2, issue.3, pp.317-352, 1987.
DOI : 10.1214/ss/1177013238

J. O. Berger and T. Sellke, Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence, Journal of the American Statistical Association, vol.82, issue.397, pp.112-139, 1987.
DOI : 10.2307/2289131

J. Bernardo, A Bayesian analysis of classical hypothesis testing, Trabajos de Estadistica Y de Investigacion Operativa, pp.605-647, 1980.
DOI : 10.1002/j.1538-7305.1948.tb01338.x

M. Bogdan, A. Chakrabarti, F. Frommlet, and J. K. Ghosh, Asymptotic Bayes-optimality under sparsity of some multiple testing procedures, The Annals of Statistics, vol.39, issue.3, pp.1551-1579, 2011.
DOI : 10.1214/10-AOS869SUPP

A. Bowman, M. Jones, and I. Gijbels, Testing monotonicity of regression, Journal of computational and Graphical Statistics, vol.7, issue.4, pp.489-500, 1998.

C. M. Carvalho, N. G. Polson, and J. G. Scott, The horseshoe estimator for sparse signals, Biometrika, vol.97, issue.2, pp.465-480, 2010.
DOI : 10.1093/biomet/asq017

I. Castillo and J. Rousseau, A General Bernstein?von Mises Theorem in semiparametric models The Annals of Statistics, 2015.

S. C. Dass and J. Lee, A note on the consistency of Bayes factors for testing point null versus non-parametric alternatives, Journal of Statistical Planning and Inference, vol.119, issue.1, pp.143-152, 2004.
DOI : 10.1016/S0378-3758(02)00413-5

J. Datta and J. K. Ghosh, Asymptotic Properties of Bayes Risk for the Horseshoe Prior, Bayesian Analysis, vol.8, issue.1, pp.111-131, 2013.
DOI : 10.1214/13-BA805

R. De-jonge and H. Van-zanten, Semiparametric Bernstein???von Mises for the error standard deviation, Electronic Journal of Statistics, vol.7, issue.0, pp.217-24313, 2013.
DOI : 10.1214/13-EJS768

D. B. Dunson and S. D. Peddada, Bayesian nonparametric inference on stochastic ordering, Biometrika, vol.95, issue.4, pp.859-874, 2008.
DOI : 10.1093/biomet/asn043

T. V. Erven, P. Grünwald, and S. De-rooij, Catching up faster by switching sooner: a predictive approach to adaptive estimation with an application to the AIC-BIC dilemma, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.23, issue.3, pp.74-361, 2012.
DOI : 10.1111/j.1751-5823.2001.tb00457.x

A. Gelman, Objections to Bayesian statistics, Bayesian Analysis, vol.3, issue.3, pp.445-449, 2008.
DOI : 10.1214/08-BA318
URL : http://doi.org/10.1214/08-ba318

S. Ghosal, J. K. Ghosh, . Van-der, and A. W. Vaart, Convergence rates of posterior distributions, The Annals of Statistics, vol.28, issue.2, pp.500-531, 2000.
DOI : 10.1214/aos/1016218228

S. Ghosal, A. Sen, and A. W. Van-der-vaart, Testing monotonicity of regression, The Annals of Statistics, vol.28, issue.4, pp.1054-1082, 2000.

S. Ghosal and A. Van-der-vaart, Convergence rates of posterior distributions for noniid observations, The Annals of Statistics, vol.35, issue.1, pp.192-223, 2007.
DOI : 10.1214/009053606000001172

C. Holmes and N. Heard, Generalized monotonic regression using random change points, Statistics in Medicine, vol.82, issue.4, pp.623-638, 2003.
DOI : 10.1002/9780470316870

Y. I. Ingster, Asymptotically minimax testing of nonparametric hypotheses, Probability theory and mathematical statistics, pp.553-574, 1985.

Y. I. Ingster and I. A. Suslina, Nonparametric goodness-of-fit testing under Gaussian models, Lecture Notes in Statistics, vol.169, 2003.
DOI : 10.1007/978-0-387-21580-8

H. Jeffreys, Theory of Probability, 1939.

V. E. Johnson, Uniformly most powerful Bayesian tests, The Annals of Statistics, vol.41, issue.4, pp.1716-1741, 2013.
DOI : 10.1214/13-AOS1123
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3960084

V. E. Johnson and D. Rossell, On the use of non-local prior densities in Bayesian hypothesis tests, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.63, issue.2, pp.143-170, 2010.
DOI : 10.1016/j.crma.2005.05.001

A. Juditsky and A. Nemirovski, On nonparametric tests of positivity/monotonicity/convexity, The Annals of Statistics, vol.30, issue.2, pp.498-527, 2002.
DOI : 10.1214/aos/1021379863

O. Lepski and A. B. Tsybakov, Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point, Probability Theory and Related Fields, pp.17-48, 2000.
DOI : 10.1007/s004400050265

O. V. Lepski and C. F. Pouet, Hypothesis Testing under Composite Functions Alternative, Topics in stochastic analysis and nonparametric estimation, pp.123-150, 2008.
DOI : 10.1007/978-0-387-75111-5_7
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.504.8130

O. V. Lepski and V. G. Spokoiny, Minimax Nonparametric Hypothesis Testing: The Case of an Inhomogeneous Alternative, Bernoulli, vol.5, issue.2, pp.333-358, 1999.
DOI : 10.2307/3318439

C. P. Robert, The Bayesian choice. Springer Texts in Statistics, 2007.

D. Rossell and D. Telesca, Non-Local Priors for High-Dimensional Estimation, Journal of the American Statistical Association, issue.ja, pp.0-1, 2016.
DOI : 10.1080/01621459.2015.1130634
URL : http://arxiv.org/pdf/1402.5107

J. Rousseau, Approximating interval hypothesis: p-values and Bayes factors, Bayesian statistics 8, pp.417-452, 2007.

J. Rousseau and C. Robert, On moment priors for Bayesian model choice: a discussion, Bayesian Statistics, vol.9, pp.1-2, 2010.

J. G. Scott, T. S. Shively, and S. G. Walker, Nonparametric Bayesian testing for monotonicity, Biometrika, vol.102, issue.3, pp.617-630, 2015.
DOI : 10.1093/biomet/asv023
URL : http://arxiv.org/abs/1304.3378

S. T. Tokdar, A. Chakrabarti, and J. K. Ghosh, Bayesian nonparametric goodness of fit tests Frontiers of Statistical Decision Making and Bayesian Analysis, 2010.

I. Verdinelli and L. Wasserman, Bayesian goodness-of-fit testing using infinitedimensional exponential families, The Annals of Statistics, vol.26, issue.4, pp.1215-1241, 1998.

L. Wang and D. B. Dunson, Bayesian isotonic density regression, Biometrika, vol.98, issue.3, pp.537-551, 2011.
DOI : 10.1093/biomet/asr025
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3384359