Related papers: Bayesian one- and two-sided inference on the local…
This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows…
The practical implementation of Bayesian inference requires numerical approximation when closed-form expressions are not available. What types of accuracy (convergence) of the numerical approximations guarantee robustness and what types do…
We consider the Cauchy problem with smooth data for compressible Euler equations in many dimensions and concentrate on two cases: solutions with finite mass and energy and solutions corresponding to a compact perturbation of a nontrivial…
We consider Bayesian optimization of an expensive-to-evaluate black-box objective function, where we also have access to cheaper approximations of the objective. In general, such approximations arise in applications such as reinforcement…
Bayesian optimal experimental design (OED) seeks to conduct the most informative experiment under budget constraints to update the prior knowledge of a system to its posterior from the experimental data in a Bayesian framework. Such…
Inverse optimization (IO) is used to estimate unknown parameters of an optimization model from observed decisions. In the data-driven context, the estimated parameters are inherently uncertain, yet quantifying this uncertainty has received…
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…
We study the sample complexity of Bayesian recovery for solving inverse problems with general prior, forward operator and noise distributions. We consider posterior sampling according to an approximate prior $\mathcal{P}$, and establish…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…
We study the support recovery problem for a high-dimensional signal observed with additive noise. With suitable parametrization of the signal sparsity and magnitude of its non-zero components, we characterize a phase-transition phenomenon…
We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…
In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…
We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate. The…
In the noisy population recovery problem of Dvir et al., the goal is to learn an unknown distribution $f$ on binary strings of length $n$ from noisy samples. For some parameter $\mu \in [0,1]$, a noisy sample is generated by flipping each…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
We consider an isotropic elastic medium occupying a bounded domain D whose density and Lam\'e parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave…
The recent availability of huge, many-dimensional data sets, like those arising from genome-wide association studies (GWAS), provides many opportunities for strengthening causal inference. One popular approach is to utilize these…
We introduce a high-performance implementation of a loosely coherent statistic sensitive to signals spanning a finite-dimensional manifold in parameter space. Results from full scale simulations on Gaussian noise are discussed, as well as…
Spatial regression of random fields based on potentially biased sensing information is proposed in this paper. One major concern in such applications is that since it is not known a-priori what the accuracy of the collected data from each…