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The vast majority of the literature on learning dynamical systems or stochastic processes from time series has focused on stable or ergodic systems, for both Bayesian and frequentist inference procedures.
The activated complex in chemical reactions
Henry Eyring · 1935
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Brownian motion in a field of force and the diffusion model of chemical reactions
Hendrik Anthony Kramers · 1940
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Application of the theory of martingales
J.L. Doob · 1948
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Kinds of Probability
Irving J. Good · 1959
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Locally asymptotically normal families of distributions
Lucien LeCam · 1960
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Some limit theorems for stationary processes
Ildar A. Ibragimov · 1962
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On Bayes procedures
Lorraine Schwartz · 1965
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Bayes estimates for the linear model
D.V. Lindley and A.F.M. Smith · 1972
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On the asymptotic behavior of the greatesteig envalue of a second order elliptlic differential operator with a small parameter in the higher derivatives
Alexander D. Ventcel · 1972
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The asymptotic behavior of the first real eigenvalue of a second order elliptic operator with a small parameter in the highest derivatives
Avner Friedman and Mark Kac · 1973
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The asymptotic behavior of the first real eigenvalue of second order elliptic operators with a small parameter in the highest derivatives, II
Allen Devinatz, Richard Ellis, and Avner Friedman · 1974
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On the asymptotic behavior of the first eigenvalue of a second-order differential operator with small parameter in higher derivatives
Alexander D. Vent-Tsel’ · 1976
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Asymptotic theory for non-linear least squares estimator for diffusion processes
Bhagavatula L.S. Prakasa Rao · 1983
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On the consistency of Bayes estimates
Persi Diaconis and David Freedman · 1986
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The Dynamic Linear Model
Mike West and Jeff Harrison · 1989
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On the uniform consistency of Bayes estimates for multinomial probabilities
Persi Diaconis and David Freedman · 1990
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Estimation for diffusion processes from discrete observation
Nakahiro Yoshida · 1992
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On convergence of posterior distributions
Subhashis Ghosal, Jayanta K. Ghosh, and Tapas Samanta · 1995
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Spectra, exit times and long time asymptotics in the zero-white-noise limit
Pierre Mathieu · 1995
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Random perturbations
Mark I Freidlin and Alexander D Wentzell · 1998
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Nucleation and relaxation from meta-stability in spatial ecological models
Amar Gandhi, Simon Levin, and Steven Orszag · 1999
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Beneath the noise, chaos
Steven P. Lalley · 1999
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Convergence rates of posterior distributions
Subhashis Ghosal, Jayanta K. Ghosh, and Aad W. Van Der Vaart · 2000
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Asymptotic statistics
Aad W. Van der Vaart · 2000
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Metastability in reversible diffusion processes. I. Sharp asymptotics for capacities and exit times
Anton Bovier, Michael Eckhoff, Véronique Gayrard, and Markus Klein · 2004
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Making complexity simpler: Multivariability and metastability in the brain
Andrew A. Fingelkurts and Alexander A. Fingelkurts · 2004
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Metastability in reversible diffusion processes II: Precise asymptotics for small eigenvalues
Véronique Gayrard, Anton Bovier, and Markus Klein · 2005
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Data Analysis Using Regression and Multilevel/Hierarchical Models
Andrew Gelman and Jennifer Hill · 2006
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Denoising deterministic time series
Steven P. Lalley and Andrew B. Nobel · 2006
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Distinct metastable atmospheric regimes despite nearly Gaussian statistics: A paradigm model
Andrew J. Majda, Christian L. Franzke, Alexander Fischer, and Daniel T. Crommelin · 2006
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Models for Ecological Data: An Introduction
James S. Clark · 2007
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Convergence rates of posterior distributions for non-IID observations
Subhashis Ghosal and Aad W. Van Der Vaart · 2007
Cited alongside, same era.
Metastable decomposition of high-dimensional meteorological data with gaps
Illia Horenko, Stamen I. Dolaptchiev, Alexey V. Eliseev, Igor I. Mokhov, and Rupert Klein · 2008
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Rates of contraction of posterior distributions based on Gaussian process priors
Aad W. van der Vaart and J. Harry van Zanten · 2008
Cited alongside, same era.
Reproducing kernel Hilbert spaces of Gaussian priors
Aad W. van der Vaart, J. Harry van Zanten, et al · 2008
Cited alongside, same era.
Trends to equilibrium in total variation distance
Patrick Cattiaux and Arnaud Guillin · 2009
Cited alongside, same era.
Variational analysis of inference from dynamical systems
Kevin McGoff and Andrew B. Nobel · 2016
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On maximal agreement couplings
Florian Völlering · 2016
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Fundamentals of nonparametric Bayesian inference
Subhashis Ghosal and Aad W. Van der Vaart · 2017
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A Bernstein-type inequality for some mixing processes and dynamical systems with an application to learning
Hanyuan Hang and Ingo Steinwart · 2017
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Coupling and decoupling to bound an approximating Markov chain
James E. Johndrow and Jonathan C. Mattingly · 2017
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Bayesian inverse problems for functions and applications
S.L. Cotter, M. Dashti, J.C. Robinson, and A.M. Stuart · 2009
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Large deviations techniques and applications
Amir Dembo and Ofer Zeitouni · 2009
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Nonparametric Bayesian inference for ergodic diffusions
Laura Panzar and Harry van Zanten · 2009
Cited alongside, same era.
Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise
Ingo Steinwart and Marian Anghel · 2009
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Inverse problems: A Bayesian perspective
Andrew M Stuart · 2010
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Applied Bayesian Forecasting and Time Series Analysis, Second Edition
Andy Pole, Mike West, and Jeff Harrison · 2011
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Bayesian estimation of discretely observed multi-dimensional diffusion processes using guided proposals
Frank van der Meulen and Moritz Schauer · 2017
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Parameterizations for ensemble Kalman inversion
Neil K. Chada, Marco Iglesias, Lassi Roininen, and Andrew M. Stuart · 2018
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Kernel density estimation for dynamical systems
Hanyuan Hang, Ingo Steinwart, Yunlong Feng, and Johan A.K. Suykens · 2018
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Aggregation-diffusion equations: dynamics, asymptotics, and singular limits
José A. Carrillo, Katy Craig, and Yao Yao · 2019
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Metastability as a coexistence mechanism in a model for dryland vegetation patterns
Lukas Eigentler and Jonathan A Sherratt · 2019
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MEXIT: Maximal un-coupling times for stocastic processes
Philip A. Ernst, Wilfrid S. Kendall, Gareth O. Roberts, and Jeffrey S. Rosenthal · 2019
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Modelling microbiome recovery after antibiotics using a stability landscape framework
Liam P. Shaw, Hassan Bassam, Chris P. Barnes, A. Sarah Walker, Nigel Klein, and Francois Balloux · 2019
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Dynamic linear models guide design and analysis of microbiota studies within artificial human guts
Alex D. Washburne, Justin D. Silverman, James T. Morton, Daniel J. Becker, Daniel Crowley, Sayan Mukherjee, Lawrence A. David, and Raina K. Plowright · 2019
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Topological analysis reveals state transitions in human gut and marine bacterial communities
William K. Chang, David VanInsberghe, and Libusha Kelly · 2020
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Metastable atrial state underlies the primary genetic substrate for MYL4 mutation-associated atrial fibrillation
Zaniar Ghazizadeh, Tuomas Kiviniemi, Sigurast Olafsson, David Plotnick, Manu E. Beerens, Kun Zhang, Leah Gillon, Michael J. Steinbaugh, Victor Barrera, Shannan Ho Sui, et al · 2020
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Empirical risk minimization and complexity of dynamical models
Kevin McGoff, Andrew B. Nobel, et al · 2020
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Naught all zeros in sequence count data are the same
Justin D. Silverman, Kimberly Roche, Sayan Mukherjee, and Lawrence A. David · 2020
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On the definition of likelihood function, 2021
Flávio B. Gonçalves and Pedro Franklin · 2021
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A large deviation approach to posterior consistency in dynamical systems
Langxuan Su and Sayan Mukherjee · 2021
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Nonparametric Bayesian inference for reversible multidimensional diffusions
Matteo Giordano and Kolyan Ray · 2022
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Gibbs posterior convergence and the thermodynamic formalism
Kevin McGoff, Sayan Mukherjee, and Andrew B. Nobel · 2022
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Bayesian multinomial logistic normal models through marginally latent matrix-T processes
Justin D. Silverman, Kimberly Roche, Zachary C. Holmes, Lawrence A. David, and Sayan Mukherjee · 2022
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Generalized Bayes approach to inverse problems with model misspecification
Youngsoo Baek, Wilkins Aquino, and Sayan Mukherjee · 2023
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Local asymptotic normality of general conditionally heteroskedastic and score-driven time-series models
Christian Francq and Jean-Michel Zakoian · 2023
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Besov-Laplace priors in density estimation: Optimal posterior contraction rates and adaptation
Matteo Giordano · 2023
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Phase reduction of waves, patterns, and oscillations subject to spatially extended noise
James MacLaurin · 2023
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Understanding microbiome dynamics via interpretable graph representation learning
Kateryna Melnyk, Kuba Weimann, and Tim O.F. Conrad · 2023
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Local asymptotic normality for ergodic jump-diffusion processes via transition density approximation
Teppei Ogihara and Yuma Uehara · 2023
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Quasi-ergodicity of transient patterns in stochastic reaction-diffusion equations
Zachary P. Adams · 2024
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Noncommutative orbital stability of stochastic patterns in Banach spaces
Joris van Winden · 2024
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