Related papers: Ensemble-based implicit sampling for Bayesian inve…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
In Bayesian inverse problems, the posterior distribution is used to quantify uncertainty about the reconstructed solution. In practice, Markov chain Monte Carlo algorithms often are used to draw samples from the posterior distribution.…
Many parameter estimation problems arising in applications are best cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also for the quantification of uncertainties in the estimates.…
Recent developments in generative modeling have utilized score-based methods coupled with stochastic differential equations to sample from complex probability distributions. However, these and other performant sampling methods generally…
A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In…
Due to their uncertainty quantification, Bayesian solutions to inverse problems are the framework of choice in applications that are risk averse. These benefits come at the cost of computations that are in general, intractable. New advances…
Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al.,…
Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assign to base models a set of deterministic, constant model weights that (1) do not fully account for individual models' varying accuracy…
Sampling from a multimodal distribution is a fundamental and challenging problem in computational science and statistics. Among various approaches proposed for this task, one popular method is Annealed Importance Sampling (AIS). In this…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…
The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
This work proposes ensemble Kalman randomized maximum likelihood estimation, a new derivative-free method for performing randomized maximum likelihood estimation, which is a method that can be used to generate approximate samples from…
We propose an approach based on function evaluations and Bayesian inference to extract higher-order differential information of objective functions {from a given ensemble of particles}. Pointwise evaluation $\{V(x^i)\}_i$ of some potential…
This work proposes a novel method through which local information about the target density can be used to construct an efficient importance sampler. The backbone of the proposed method is the Incremental Mixture Importance Sampling (IMIS)…
Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…