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For affine processes on finite-dimensional cones, we give criteria for geometric ergodicity - that is exponentially fast convergence to a unique stationary distribution. Ergodic results include both the existence of exponential moments of…

Probability · Mathematics 2021-01-12 Eberhard Mayerhofer , Robert Stelzer , Johanna Vestweber

One main limitation of the existing optimal scaling results for Metropolis--Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis…

Computation · Statistics 2020-05-05 Jun Yang , Gareth O. Roberts , Jeffrey S. Rosenthal

In this paper, we investigate the exponential ergodicity in a Wasserstein-type distance for a damping Hamiltonian dynamics with state-dependent and non-local collisions, which indeed is a special case of piecewise deterministic Markov…

Probability · Mathematics 2022-04-05 Jianhai Bao , Jian Wang

Uncertainty estimation is a key issue when considering the application of deep neural network methods in science and engineering. In this work, we introduce a novel algorithm that quantifies epistemic uncertainty via Monte Carlo sampling…

Machine Learning · Statistics 2024-12-06 Sebastian Bieringer , Gregor Kasieczka , Maximilian F. Steffen , Mathias Trabs

Drifts of asset returns are notoriously difficult to model accurately and, yet, trading strategies obtained from portfolio optimization are very sensitive to them. To mitigate this well-known phenomenon we study robust growth-optimization…

Mathematical Finance · Quantitative Finance 2026-01-01 Balint Binkert , David Itkin , Paul Mangers Bastian , Josef Teichmann

Markov Chain Monte Carlo methods are widely used in signal processing and communications for statistical inference and stochastic optimization. In this work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw samples…

Computation · Statistics 2016-03-17 David Luengo , Luca Martino

From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…

Mathematical Physics · Physics 2019-09-25 Bastien Fernandez

Given a target distribution $\mu \propto e^{-\mathcal{H}}$ to sample from with Hamiltonian $\mathcal{H}$, in this paper we propose and analyze new Metropolis-Hastings sampling algorithms that target an alternative distribution…

Probability · Mathematics 2021-11-30 Michael C. H. Choi , Jing Zhang

In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…

Computation · Statistics 2015-10-12 Alexandros Beskos , Gareth Roberts , Alexandre Thiery , Natesh Pillai

The choice of the increment distribution is crucial for the random-walk Metropolis-Hastings (RWM) algorithm. In this paper we study the optimal choice in high-dimension setting among all possible increment distributions. The conclusion is…

Methodology · Statistics 2016-05-24 Kengo Kamatani

We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on…

Computation · Statistics 2014-12-31 Chris Sherlock , Alexandre H. Thiery , Gareth O. Roberts , Jeffrey S. Rosenthal

We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers. Our main findings are that the essential…

Probability · Mathematics 2015-04-15 Christophe Andrieu , Anthony Lee , Matti Vihola

The classical Metropolis-Hastings (MH) algorithm can be extended to generate non-reversible Markov chains. This is achieved by means of a modification of the acceptance probability, using the notion of vorticity matrix. The resulting Markov…

Probability · Mathematics 2020-09-29 Joris Bierkens

A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert…

Machine Learning · Statistics 2014-06-16 Dino Sejdinovic , Heiko Strathmann , Maria Lomeli Garcia , Christophe Andrieu , Arthur Gretton

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…

Methodology · Statistics 2017-01-06 Patrick R. Conrad , Youssef M. Marzouk , Natesh S. Pillai , Aaron Smith

We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuous probability density function. Almost all previous analysis has focused upon continuous…

Probability · Mathematics 2012-10-19 Peter Neal , Gareth Roberts , Wai Kong Yuen

This paper proposes a new sampling scheme based on Langevin dynamics that is applicable within pseudo-marginal and particle Markov chain Monte Carlo algorithms. We investigate this algorithm's theoretical properties under standard…

Methodology · Statistics 2016-05-30 Christopher Nemeth , Chris Sherlock , Paul Fearnhead

Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…

Computation · Statistics 2022-08-16 Peter A. Whalley , Daniel Paulin , Benedict Leimkuhler

The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density.…

Computation · Statistics 2019-12-04 Sebastian M. Schmon , George Deligiannidis , Arnaud Doucet , Michael K. Pitt

Convergence of Extremum Seeking (ES) algorithms has been established in the limit of small gains. Using averaging theory and contraction analysis, we propose a framework for computing explicit bounds on the departure of the ES scheme from…

Optimization and Control · Mathematics 2013-03-20 Gabriel Bousquet , Jean-Jacques Slotine