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Annals of Statistics, ISSN 0090-5364, 06/2019, Volume 47, Issue 3, pp. 1268 - 1287
Nonreversible Markov chain Monte Carlo schemes based on piecewise deterministic Markov processes have been recently introduced in applied probability,... 
Geometric ergodicity | Central limit theorem | Change of variable | Piecewise deterministic Markov process | Markov chain Monte Carlo | DISTRIBUTIONS | central limit theorem | LIMIT-THEOREMS | STABILITY | HASTINGS | DETERMINISTIC MARKOV-PROCESSES | STATISTICS & PROBABILITY | geometric ergodicity | change of variable
Journal Article
Annals of Mathematics, ISSN 0003-486X, 1/2010, Volume 171, Issue 1, pp. 451 - 489
Pugh and Shub have conjectured that essential accessibility implies ergodicity for a C 2 , partially hyperbolic, volume-preserving diffeomorphism. We prove... 
Ergodic theory | Tangents | Leaves | Riemann manifold | Geometric shapes | Density | Dynamical systems | Continuous functions | Jacobians | DIFFEOMORPHISMS | MATHEMATICS | FOLIATIONS | STABLE ERGODICITY
Journal Article
Bernoulli, ISSN 1350-7265, 05/2018, Volume 24, Issue 2, pp. 842 - 872
We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and... 
Geometric ergodicity | Iterated conditional sequential Monte Carlo | Metropolis-within-Gibbs | Uniform ergodicity | Particle Gibbs | uniform ergodicity | iterated conditional sequential Monte Carlo | MARKOV-CHAINS | HASTINGS | CONVERGENCE | STATISTICS & PROBABILITY | geometric ergodicity | particle Gibbs | CHAIN MONTE-CARLO
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 02/2019, Volume 145, pp. 43 - 49
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 01/2014, Volume 84, Issue 1, pp. 192 - 197
Markov Chain Monte Carlo is repeatedly used to analyze the properties of intractable distributions in a convenient way. In this paper we derive conditions for... 
Irreducibility | Geometric ergodicity | Markov switching | Asymmetric stochastic volatility | Mixture models | STOCHASTIC VOLATILITY MODEL | STATISTICS & PROBABILITY | Markov processes | Monte Carlo method | Models | Analysis
Journal Article
Comptes rendus - Mathématique, ISSN 1631-073X, 09/2016, Volume 354, Issue 9, pp. 907 - 911
A new proof is given of Quantum Ergodicity for Eisenstein Series for cusped hyperbolic surfaces. This result is also extended to higher dimensional examples,... 
MATHEMATICS | SPECTRAL GEOMETRY | MANIFOLDS | SERIES | HYPERBOLIC SURFACES | EIGENFUNCTIONS | Mathematics | Spectral Theory
Journal Article
Nonlinearity, ISSN 0951-7715, 01/2016, Volume 29, Issue 2, pp. 657 - 691
The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are data assimilation methods used to combine high dimensional, nonlinear dynamical... 
filter stability | geometric ergodicity | catastrophic filter divergence | ensemble Kalman filter | Lyapunov function | MATHEMATICS, APPLIED | DISCRETE | PHYSICS, MATHEMATICAL | Lyapunov functions | Energy dissipation | Dissipation | Nonlinearity | Controllability | Kalman filters | Invariants | Ergodic processes | Mathematics - Probability
Journal Article
NONLINEARITY, ISSN 0951-7715, 02/2019, Volume 32, Issue 2, pp. 445 - 463
In this paper we obtain two criteria of stable ergodicity outside the partially hyperbolic scenario. In both criteria, we use a weak form of hyperbolicity... 
CENTRAL DIRECTION | weak partial hyperbolicity | SRB MEASURES | MATHEMATICS, APPLIED | stable ergodicity | dominated splitting | PARTIALLY HYPERBOLIC SYSTEMS | PHYSICS, MATHEMATICAL
Journal Article
BERNOULLI, ISSN 1350-7265, 11/2019, Volume 25, Issue 4A, pp. 3109 - 3138
We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We... 
SAMPLING METHODS | hybrid Monte Carlo | HASTINGS | MCMC | Markov chains | STATISTICS & PROBABILITY | Hamiltonian dynamics | stochastic simulation | MARKOV-CHAIN | geometric ergodicity | Hamiltonian Monte Carlo | LANGEVIN | BOUNDS | Markov chain Monte Carlo | CONVERGENCE
Journal Article
Journal of Applied Probability, ISSN 0021-9002, 06/2017, Volume 54, Issue 2, pp. 638 - 654
We describe the ergodic properties of some Metropolis-Hastings algorithms for heavy-tailed target distributions. The results of these algorithms are usually... 
Markov chain | Monte Carlo | ergodicity | regular variation | HASTINGS | MCMC | STATISTICS & PROBABILITY | METROPOLIS ALGORITHMS | KERNELS | LIMIT-THEOREMS | POLYNOMIAL ERGODICITY | CONVERGENCE | GEOMETRIC ERGODICITY | SUBGEOMETRIC RATES | Markov chains | Algorithms | Markov analysis | Monte Carlo simulation | Ergodic processes
Journal Article
Communications in Mathematical Sciences, ISSN 1539-6746, 2017, Volume 15, Issue 7, pp. 1987 - 2025
We establish ergodicity of the Langevin dynamics for a simple two-particle system involving a Lennard-Jones type potential. Moreover, we show that the dynamics... 
Geometric ergodicity | Langevin dynamics | Stochastic averaging | Lennard-Jones potential | Lyapunov function | MATHEMATICS, APPLIED | DYNAMICS | stochastic averaging | HYPOCOERCIVITY | geometric ergodicity
Journal Article
Biometrika, ISSN 0006-3444, 2014, Volume 101, Issue 3, pp. 655 - 671
Approximate Bayesian computation has emerged as a standard computational tool when dealing with intractable likelihood functions in Bayesian inference. We show... 
Geometric ergodicity | Variance bounding | Approximate Bayesian computation | Local adaptation | Markov chain Monte Carlo | Markov chain Monte | TIMES | HASTINGS | POPULATION-GROWTH | STATISTICS & PROBABILITY | Carlo | WIDTH OUTPUT ANALYSIS | PARAMETERS | SIMULATION | INFERENCE | RATES | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | CONVERGENCE
Journal Article
Electronic Journal of Statistics, ISSN 1935-7524, 2014, Volume 8, Issue 1, pp. 604 - 645
in recent years, a large variety of continuous shrinkage priors have been developed for a Bayesian analysis of the standard linear regression model in high... 
Geometric ergodicity | Bayesian shrinkage | Bessel functions | Markov chain Monte Carlo | REGRESSION | HASTINGS | MCMC | STATISTICS & PROBABILITY | ALGORITHMS | geometric ergodicity | DISTRIBUTIONS | GIBBS SAMPLER | BOUNDS | CONVERGENCE-RATES
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 10/2014, Volume 124, Issue 10, pp. 3362 - 3391
The paper deals with non asymptotic computable bounds for the geometric convergence rate of homogeneous ergodic Markov processes. Some sufficient conditions... 
Coupling renewal processes | Renewal theory | Ergodic diffusion processes | Convergence rate | Geometric ergodicity | Homogeneous Markov chain | Lyapunov function | Non asymptotic exponential upper bound | STATISTICS & PROBABILITY | CONVERGENCE-RATES | Markov processes | Analysis
Journal Article
Electronic Journal of Statistics, ISSN 1935-7524, 2017, Volume 11, Issue 2, pp. 4033 - 4064
We consider three Bayesian penalized regression models and show that the respective deterministic scan Gibbs samplers are geometrically ergodic regardless of... 
Starting values | Geometric ergodicity | Markov chains | Bayesian lassos | DISTRIBUTIONS | STANDARD ERRORS | ESTIMATORS | GROUP LASSO | STATISTICS & PROBABILITY | geometric ergodicity | starting values | VARIABLE SELECTION | CHAIN MONTE-CARLO
Journal Article
Communications in Statistics - Theory and Methods, ISSN 0361-0926, 08/2015, Volume 44, Issue 15, pp. 3125 - 3145
In Markov chain Monte Carlo analysis, rapid convergence of the chain to its target distribution is crucial. A chain that converges geometrically quickly is... 
Gibbs sampler | 60J05; 60J22; 65C40 | Geometric ergodicity | Convergence rates | Markov chain Monte Carlo | DISTRIBUTIONS | RANDOM EFFECTS MODEL | UNIFORM | ESTIMATORS | STATISTICS & PROBABILITY | VARIANCE | CHAIN MONTE-CARLO | Bayesian analysis | Monte Carlo simulation | Markov analysis | Samplers | Scanning | Chains | Strategy | Evolution | Statistics | Ergodic processes | Convergence
Journal Article
Electronic Journal of Statistics, ISSN 1935-7524, 2018, Volume 12, Issue 2, pp. 3295 - 3311
The logistic regression model is the most popular model for analyzing binary data. In the absence of any prior information, an improper flat prior is often... 
Markov chain | Data augmentation | Posterior propriety | Central limit theorem | Geometric rate | Drift condition | drift condition | geometric rate | data augmentation | MODELS | BINARY | CONVERGENCE | STATISTICS & PROBABILITY | posterior propriety
Journal Article
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