references.bib

@Preamble{ " \newcommand{\noop}[1]{} " }

@article{Allassonniere2010,
  title = {Construction of bayesian deformable models via a stochastic approximation algorithm: a convergence study},
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  year = {2010},
  journal = {Bernoulli},
  volume = {16},
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}


@article{Andrieu2005,
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}

@article{baey2019asymptotic,
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}

@book{bickel2015mathematical,
  title = {Mathematical statistics: basic ideas and selected topics, volumes I-II package},
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}

@book{billingsley2013convergence,
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}

@misc{cappe2005,
  title = {Inference in Hidden Markov Models},
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@article{charkhi2018asymptotic,
  author = {{Charkhi A.} and {Claeskens G.}},
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}


@article{Delyon1999,
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}


@article{efron1978assessing,
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  title = {Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information},
  journal = {Biometrika}, 
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}

@book{feller1968,
  author = {{Feller W.}},
  description = {An Introduction to Probability Theory and Its Applications},
  publisher = {Wiley},
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@book{fisher1925,
  author = {{Fisher R.A.}},
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  title = {Statistical methods for research workers}, 
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}


@article{Fort2015,
  title={Convergence of the Wang-Landau algorithm},
  author={{Fort G.} and {Jourdain B.} and {Kuhn E.} and {Leli{\`e}vre, T.} and {Stoltz, G.}},
  journal={Mathematics of Computation},
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  number={295},
  pages={2297--2327},
  year={2015}
}


@article{Gloaguen2014,
  author = {{Gloaguen P.} and {Mah\'evas S.} and {Rivot E.} and {Woillez M.} and {Guitton J.} and {Vermard Y.} and {Etienne M.-P.}},
  year = {2014},
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}


@article{jarner2000,
  title = {Geometric ergodicity of Metropolis algorithms},
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}


@article{Kuhn2004,
  author = {{Kuhn E.} and {Lavielle M.}},
  year = {2004},
  title = {Coupling a stochastic approximation version of EM with an MCMC procedure},
  journal = {ESAIM P\&S}, 
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  pages = {115--131},
  doi = {10.1051/ps:2004007}
}


@article{kuhn2020,
  title = {Properties of the stochastic approximation EM algorithm with mini-batch sampling},
  author = {{Kuhn E.} and {Matias C.} and {Rebafka T.}},
  journal = {Statistics and Computing},
  volume = {30},
  number = {6},
  pages = {1725--1739},
  year = {2020},
  publisher = {Springer},
  doi = {10.1007/s11222-020-09968-0}
}


@inproceedings{kunstner2019limitations,
  author = {{Kunstner F.} and {Hennig P.} and {Balles L.}},
  year = {2019},
  title = {Limitations of the empirical fisher approximation for natural gradient descent},
  booktitle = {Advances in neural information processing systems}, 
  volume = {32}
}
 
@article{le2021fisher,
  author = {{Le Brigant A.} and {Preston S. C.} and {Puechmorel S.}},
  year = {2021},
  title = {Fisher-Rao geometry of Dirichlet distributions},
  journal = {Differential Geometry and its Applications}, 
  volume = {74}, 
  doi = {10.1016/j.difgeo.2020.101702}
} 

@book{lehmann2006theory,
  title = {Theory of point estimation},
  author = {{Lehmann E. L.} and {Casella G.}},
  year = {2006},
  publisher = {Springer Science \& Business Media},
  doi = {10.1007/b98854}
}


@article{Louis1982,
  author = {{Louis T. A.}},
  year = {1982},
  title = {Finding the Observed Information Matrix when Using the EM Algorithm},
  journal = {Journal of the Royal Statistical Society. Series B (Methodological)},
  volume = {44},
  issue = {2}, 
  pages = {226--233},
  doi = {10.1111/j.2517-6161.1982.tb01203.x}
}

@book{McLachlan2008,
  author = {{McLachlan G.-J.} and {Krishnan T.}},
  year = {2008},
  title = {The EM algorithm and extensions}, 
  series = {Wiley series in probability and statistics}, 
  publisher = {Wiley},
  doi = {10.1002/9780470191613}
}


@article{Meng1991,
  author = {{Meng X.-L.} and {Rubin D. B.}},
  year = {1991},
  title = {Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm},
  journal = {Journal of the American Statistical Association}, 
  volume = {86},
  issue = {416}, 
  pages = {899--909},
  doi = {10.1080/01621459.1991.10475130}
}

@inproceedings{Meng2017,
  author = {{Meng L.} and {Spall J. C.}},
  year = {2017},
  title = {Efficient computation of the Fisher information matrix in the EM algorithm},
  booktitle = {Annual Conference on Information Sciences and Systems (CISS)},
  doi = {10.1109/CISS.2017.7926126}
}


@article{Oakes1999,
  author = {{Oakes D.}},
  year = {1999},
  title = {Direct calculation of the information matrix via  the EM algorithm},
  journal = {Journal of the Royal Statistical Society. Series B (Methodological)},
  volume = {61},
  issue = {2}, 
  pages = {479--482},
  doi = {10.1111/1467-9868.00188}
}

@inproceedings{Woodbury1972,
  author = {{Orchard T.} and {Woodbury M. A.}},
  year = {1972},
  title = {A missing information principle: theory and applications},
  booktitle = {Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability}
}


@article{Picard2007,
  author = {{Picard F.} and {Robin S.} and {Lebarbier E.} and {Daudin J.-J.}},
  year = {2007},
  title = {A Segmentation/Clustering Model for the Analysis of Array CGH Data},
  journal = {Biometrics}, 
  volume = {63}, 
  pages = {758--766},
  doi = {10.1111/j.1541-0420.2006.00729.x}
}


@Manual{mixfim2018,
  author = {{Riviere-Jourdan M.-K.} and {Mentre F.}},
  year = {2018},
  title = {MIXFIM: Evaluation of the FIM in NLMEMs using MCMC}, 
  note = {R package version 1.1},
  url = {https://CRAN.R-project.org/package=MIXFIM}
}


@article{Scott2002,
  author = {{Scott W.-A.}},
  year = {2002},
  title = {Maximum likelihood estimation using the empirical fisher information matrix},
  journal = {Journal of Statistical Computation and Simulation}, 
  volume = {72},
  issue = {8}, 
  pages = {599--611},
  doi = {10.1080/00949650213744}
}

@article{Technow2015,
  author = {{Technow F.} and {Messina C. D.} and {Totir L. R.} and {Cooper M.}},
  year = {2015},
  title = {Integrating crop growth models with whole genome prediction through approximate   Bayesian computation},
  journal = {PloS one},
  volume = {10},
  issue = {6},
  doi ={10.1371/journal.pone.0130855}
}

@book{VanderVaart2000,
  author = {{Van der Vaart A. W.}}, 
  year = {2000},
  title = {Asymptotic Statistics}, 
  series = {Cambridge Series in Statistical and Probabilistic Mathematics}, 
  publisher = {Cambridge University Press},
  doi = {10.1017/CBO9780511802256}
}