167 citations · 623 across the 43 of their papers we have counts for
48 papers
Stable Matrix Parametrizations and Structured Adjoints for Ornstein-Uhlenbeck Processes
Filippo Monti, Andrew Holbrook, Nathan E. Glatt-Holtz +1
Ornstein-Uhlenbeck processes with flexible multivariate drift matrices are powerful models for capturing coupled, asymmetric, and damped-oscillatory mean reversion. However, likeli…
On the mixing properties of some preconditioned multiproposal Markov Chain Monte Carlo algorithms
Giulia Carigi, Nathan E. Glatt-Holtz, Cecilia F. Mondaini +1
We study two recently discovered "dimension-free" Monte Carlo sampling algorithms, the multiproposal and multiple-try preconditioned Crank-Nicolson methods (mpCN and MTpCN). These…
Mad Props: Parallelism in Markov Chain Monte Carlo Through the Lens of the Infinite Proposal Limit
Nathan E. Glatt-Holtz, Andrew J. Holbrook, Justin A. Krometis +1
Multiproposal MCMC (MP-MCMC) algorithms use clouds of proposals to efficiently traverse state spaces and overcome complex target geometries. While MCMC methods are embarrassingly p…
Multiproposal Elliptical Slice Sampling
Guillermina Senn, Nathan Glatt-Holtz, Giulia Carigi +2
We introduce Multiproposal Elliptical Slice Sampling, a self-tuning multiproposal Markov chain Monte Carlo method for Bayesian inference with Gaussian priors. Our method generalize…
Bayesian Semi-Blind Deconvolution at Scale
Guillermina Senn, Håkon Tjelmeland, Nathan Glatt-Holtz +2
Blind image deconvolution refers to the problem of simultaneously estimating the blur kernel and the true image from a set of observations when both the blur kernel and the true im…
Existence and higher regularity of statistically steady states for the stochastic Coleman-Gurtin equation
Nathan E. Glatt-Holtz, Vincent R. Martinez, Hung D. Nguyen
We study a class of semi-linear differential Volterra equations with polynomial-type potentials that incorporates the effects of memory while being subjected to random perturbation…
Sacred and Profane: from the Involutive Theory of MCMC to Helpful Hamiltonian Hacks
Nathan E. Glatt-Holtz, Andrew J. Holbrook, Justin A. Krometis +2
In the first edition of this Handbook, two remarkable chapters consider seemingly distinct yet deeply connected subjects ...
On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2
Gustavo Didier, Nathan E. Glatt-Holtz, Andrew J. Holbrook +2
The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the deri…
Long-term accuracy of numerical approximations of SPDEs with the stochastic Navier-Stokes equations as a paradigm
Nathan E. Glatt-Holtz, Cecilia F. Mondaini
This work introduces a general framework for establishing the long time accuracy for approximations of Markovian dynamical systems on separable Banach spaces. Our results illuminat…
A Statistical Framework for Domain Shape Estimation in Stokes Flows
Jeff Borggaard, Nathan E. Glatt-Holtz, Justin A. Krometis
We develop and implement a Bayesian approach for the estimation of the shape of a two dimensional annular domain enclosing a Stokes flow from sparse and noisy observations of the e…
The short memory limit for long time statistics in a stochastic Coleman-Gurtin model of heat conduction
Nathan E. Glatt-Holtz, Vincent R. Martinez, Hung D. Nguyen
We consider a class of semi-linear differential Volterra equations with polynomial-type potentials that incorporates the effects of memory while being subjected to random perturbat…
Unique Ergodicity in Stochastic Electroconvection
Elie Abdo, Nathan Glatt-Holtz, Mihaela Ignatova
We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prov…
Parallel MCMC Algorithms: Theoretical Foundations, Algorithm Design, Case Studies
Nathan E. Glatt-Holtz, Andrew J. Holbrook, Justin A. Krometis +1
Parallel Markov Chain Monte Carlo (pMCMC) algorithms generate clouds of proposals at each step to efficiently resolve a target probability distribution. We build a rigorous foundat…
Embracing Uncertainty in "Small Data" Problems: Estimating Earthquakes from Historical Anecdotes
Nathan E. Glatt-Holtz, Ronald A. Harris, Andrew J. Holbrook +4
Seismic risk estimates will be vastly improved with an increased understanding of historical (and pre-historical) seismic events. However the only existing data for these events is…
On the long-time statistical behavior of smooth solutions of the weakly damped, stochastically-driven KdV equation
Nathan Glatt-Holtz, Vincent R. Martinez, Geordie H. Richards
This paper considers the damped periodic Korteweg-de Vries (KdV) equation in the presence of a white-in-time and spatially smooth stochastic source term and studies the long-time b…
On the accept-reject mechanism for Metropolis-Hastings algorithms
Nathan E. Glatt-Holtz, Justin A. Krometis, Cecilia F. Mondaini
This work develops a powerful and versatile framework for determining acceptance ratios in Metropolis-Hastings type Markov kernels widely used in statistical sampling problems. Our…
Sensitivity of steady states in a degenerately-damped stochastic Lorenz system
Juraj Foldes, Nathan E. Glatt-Holtz, David P. Herzog
We study stability of solutions for a randomly driven and degenerately damped version of the Lorenz '63 model. Specifically, we prove that when damping is absent in one of the temp…
Methodological reconstruction of historical seismic events from anecdotal accounts of destructive tsunamis: a case study for the great 1852 Banda arc mega-thrust earthquake and tsunami
Hayden Ringer, Jared P. Whitehead, Justin Krometis +14
We demonstrate the efficacy of a Bayesian statistical inversion framework for reconstructing the likely characteristics of large pre-instrumentation earthquakes from historical rec…
Mixing Rates for Hamiltonian Monte Carlo Algorithms in Finite and Infinite Dimensions
Nathan E. Glatt-Holtz, Cecilia F. Mondaini
We establish the geometric ergodicity of the preconditioned Hamiltonian Monte Carlo (HMC) algorithm defined on an infinite-dimensional Hilbert space, as developed in [Beskos et al.…
Data Assimilation in Large-Prandtl Rayleigh-Bénard Convection from Thermal Measurements
A. Farhat, N. E. Glatt-Holtz, V. R. Martinez +2
This work applies a continuous data assimilation scheme---a particular framework for reconciling sparse and potentially noisy observations to a mathematical model---to Rayleigh-Bén…
On Bayesian Consistency for Flows Observed Through a Passive Scalar
Jeff Borggaard, Nathan E. Glatt-Holtz, Justin A. Krometis
We consider the statistical inverse problem of estimating a background fluid flow field from the partial, noisy observations of the concentration of a substance pa…
GPU-Accelerated Particle Methods for Evaluation of Sparse Observations for PDE-Constrained Inverse Problems
Jeff Borggaard, Nathan E. Glatt-Holtz, Justin A. Krometis
We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of…
Affine Poisson & Non-Poisson trace principles for
Nico Lombardi, Jie Xiao
This note discovers not only an affine non-sharp-Poisson trace inequality but also its sharp-non-Poisson version for a Sobolev function with the fractional antiderivative.
On the convergence of stationary solutions in the Smoluchowski-Kramers approximation of infinite dimensional systems
Sandra Cerrai, Nathan Glatt-Holtz
We prove the convergence, in the small mass limit, of statistically invariant states for a class of semi-linear damped wave equations, perturbed by an additive Gaussian noise, both…