32 citations · 183 across the 54 of their papers we have counts for
9 papers · 1 filter
A First Course in Monte Carlo Methods
Daniel Sanz-Alonso, Omar Al-Ghattas
This is a concise mathematical introduction to Monte Carlo methods, a rich family of algorithms with far-reaching applications in science and engineering. Monte Carlo methods are a…
From Optimization to Sampling Through Gradient Flows
N. Garcia Trillos, B. Hosseini, D. Sanz-Alonso
This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, s…
Hierarchical Ensemble Kalman Methods with Sparsity-Promoting Generalized Gamma Hyperpriors
Hwanwoo Kim, Daniel Sanz-Alonso, Alexander Strang
This paper introduces a computational framework to incorporate flexible regularization techniques in ensemble Kalman methods for nonlinear inverse problems. The proposed methodolog…
Finite Element Representations of Gaussian Processes: Balancing Numerical and Statistical Accuracy
Daniel Sanz-Alonso, Ruiyi Yang
The stochastic partial differential equation approach to Gaussian processes (GPs) represents Matérn GP priors in terms of finite element basis functions and Gaussian coefficien…
Bayesian Update with Importance Sampling: Required Sample Size
Daniel Sanz-Alonso, Zijian Wang
Importance sampling is used to approximate Bayes' rule in many computational approaches to Bayesian inverse problems, data assimilation and machine learning. This paper reviews and…
Data-Driven Forward Discretizations for Bayesian Inversion
Daniele Bigoni, Yuming Chen, Nicolas Garcia Trillos +2
This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governi…
HMC: avoiding rejections by not using leapfrog and some results on the acceptance rate
M. P. Calvo, D. Sanz-Alonso, J. M. Sanz-Serna
The leapfrog integrator is routinely used within the Hamiltonian Monte Carlo method and its variants. We give strong numerical evidence that alternative, easy to implement algorith…
Importance Sampling and Necessary Sample Size: an Information Theory Approach
Daniel Sanz-Alonso
Importance sampling approximates expectations with respect to a target measure by using samples from a proposal measure. The performance of the method over large classes of test fu…
Importance Sampling: Intrinsic Dimension and Computational Cost
S. Agapiou, O. Papaspiliopoulos, D. Sanz-Alonso +1
The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to unde…