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The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance.
Graphical Models, Exponential Families, and Variational Inference
Martin J. Wainwright and Michael I. Jordan · 1935
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Convex Analysis
Ralph Tyrell Rockafellar · 1970
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Statistical Estimation: Asymptotic Theory
I. A. Ibragimov and R. Z. Has’minskii · 1981
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Diffusions hypercontractives
Dominique Bakry and Michel Émery · 1985
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Memoir on the Probability of the Causes of Events
Pierre Simon Laplace · 1986
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Logarithmic Sobolev inequalities and stochastic Ising models
R. Holley and D. Stroock · 1987
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Asymptotic statistics
A.W. van der Vaart · 1998
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An MCMC approach to classical estimation
Victor Chernozhukov and Han Hong · 2003
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Bayesian Nonparametrics
J. K. Ghosh and R. V. Ramamoorthi · 2003
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Pattern Recognition and Machine Learning
Christopher M. Bishop · 2006
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Concentration inequalities and model selection
Pascal Massart · 2007
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A characterization of dimension free concentration in terms of transportation inequalities
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Optimal Transport Old and New
Cédric Villani · 2009
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The Bernstein-Von-Mises theorem under misspecification
B.J.K. Kleijn and A.W. van der Vaart · 2012
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Fast estimation of expected information gains for Bayesian experimental designs based on Laplace approximations
Quan Long, Marco Scavino, Raúl Tempone, and Suojin Wang · 2013
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Inconsistency of Pitman-Yor Process Mixtures for the Number of Components
Jeffrey W. Miller and Matthew T. Harrison · 2014
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Laplace approximation for logistic Gaussian process density estimation and regression
Jaakko Riihimäki and Aki Vehtari · 2014
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Log-concavity and strong log-concavity: A review
Adrien Saumard and Jon A. Wellner · 2014
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Measuring Sample Quality with Stein’s Method
Jackson Gorham and Lester Mackey · 2015
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Finite Sample Bernstein – von Mises Theorem for Semiparametric Problems
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Analysis and Geometry of Markov Diffusion Operators
Dominique Bakry, Ivan Gentil, and Michel Ledoux · 2016
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Laplace Approximation in High-Dimensional Bayesian Regression
Rina Foygel Barber, Mathias Drton, and Kean Ming Tan · 2016
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A general framework for updating belief distributions
P. G. Bissiri, C. C. Holmes, and S. G. Walker · 2016
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A Kernel Test of Goodness of Fit
Kacper Chwialkowski, Heiko Strathmann, and Arthur Gretton · 2016
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Riemannian metrics on convex sets with applications to Poincaré and log-Sobolev inequalities
A.V. Kolesnikov and E. Milman · 2016
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A Kernelized Stein Discrepancy for Goodness-of-fit Tests
Qiang Liu, Jason Lee, and Michael Jordan · 2016
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Variational Inference: A Review for Statisticians
David M. Blei, Alp Kucukelbir, and Jon D. McAuliffe · 2017
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On frequentist coverage errors of Bayesian credible sets in moderately high dimensions
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Laplace Redux - Effortless Bayesian Deep Learning
Erik Daxberger, Agustinus Kristiadi, Alexander Immer, Runa Eschenhagen, Matthias Bauer, and Philipp Hennig · 2021
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Measurements of the Hubble constant: tensions in perspective
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Spatial models using Laplace approximation methods
Virgilio Gomez-Rubio, Roger S Bivand, and Håvard Rue · 2021
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Estimating infectiousness throughout SARS-CoV-2 infection course
Terry C Jones, Guido Biele, Barbara Mühlemann, Talitha Veith, Julia Schneider, Jörn Beheim-Schwarzbach, Tobias Bleicker, Julia Tesch, Marie Luisa Schmidt, Leif Erik Sander, et al · 2021
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Asymptotic Normality, Concentration, and Coverage of Generalized Posteriors
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Control functionals for Monte Carlo integration
Chris J. Oates, Mark Girolami, and Nicolas Chopin · 2017
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Validation of ecological state space models using the Laplace approximation
Uffe Høgsbro Thygesen, Christoffer Moesgaard Albertsen, Casper Willestofte Berg, Kasper Kristensen, and Anders Nielsen · 2017
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Practical Bounds on the Error of Bayesian Posterior Approximations: a Nonasymptotic Approach
Jonathan H. Huggins, Mikołaj Kasprzak, Trevor Campbell, and Tamara Broderick · 2018
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Online structured Laplace approximations for overcoming catastrophic forgetting
Hippolyt Ritter, Aleksandar Botev, and David Barber · 2018
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High-Dimensional Probability: An Introduction with Applications in Data Science
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Convergence of Langevin Monte Carlo in Chi-Squared and Rényi Divergence
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Wasserstein convergence rates of increasingly concentrating probability measures
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Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems
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Probabilistic Machine Learning: An introduction
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Dimension free non-asymptotic bounds on the accuracy of high dimensional Laplace approximation
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