Related papers: Anisotropic multidimensional smoothing using Bayes…

The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that…

P-spline models have achieved great popularity both in statistical and in applied research. A possible drawback of P-spline is that they assume a smooth transition of the covariate effect across its whole domain. In some practical…

The paper motivates high dimensional smoothing with penalized splines and its numerical calculation in an efficient way. If smoothing is carried out over three or more covariates the classical tensor product spline bases explode in their…

Multidimensional scaling (MDS) is widely used to reconstruct a low-dimensional representation of high-dimensional data while preserving pairwise distances. However, Bayesian MDS approaches based on Markov chain Monte Carlo (MCMC) face…

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…

We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…

A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable…

We propose two new Bayesian smoothing methods for general state-space models with unknown parameters. The first approach is based on the particle learning and smoothing algorithm, but with an adjustment in the backward resampling weights.…

Large samples have been generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyze such large samples due to expensive computational costs. In particular,…

The Markov chain Monte Carlo (MCMC) method is the computational workhorse for Bayesian inverse problems. However, MCMC struggles in high-dimensional parameter spaces, since its iterates must sequentially explore the high-dimensional space.…

The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…

High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…

Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…

In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also establish a strong error estimate for PDPs as well as a weak…

In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…

Many scientific and engineering problems require to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary…

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…

Monte Carlo methods, such as Markov chain Monte Carlo (MCMC), remain the most regularly-used approach for implementing Bayesian inference. However, the computational cost of these approaches usually scales worse than linearly with the…

This article introduces two absolutely continuous global-local shrinkage priors to enable stochastic variable selection in the context of high-dimensional matrix exponential spatial specifications. Existing approaches as a means to dealing…

We address the numerical solution of infinite-dimensional inverse problems in the framework of Bayesian inference. In the Part I companion to this paper (arXiv.org:1308.1313), we considered the linearized infinite-dimensional inverse…