The Bernstein–von Mises theorem and nonregular models

@article{Bochkina2014TheBM,
  title={The Bernstein–von Mises theorem and nonregular models},
  author={Natalia Bochkina and Peter J. Green},
  journal={Annals of Statistics},
  year={2014},
  volume={42},
  pages={1850-1878}
}
We study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the “true” solution occurs on the boundary of the parameter space. We show that in this case the Bayesian inference is consistent, and that the posterior distribution has not only Gaussian components as in the case of regular models (the Bernstein–von Mises theorem) but also has Gamma distribution components that depend on the behaviour of the prior distribution on the boundary and have… Expand

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