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In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…
Bayes linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article we connect these ideas by demonstrating that regression-adjustment ABC algorithms…
We develop a fast variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. Our approach enables uncertainty in covariance function…
We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step…
This paper introduces a quasi-Bayesian method that integrates frequentist nonparametric estimation with Bayesian inference in a two-stage process. Applied to an endogenous discrete choice model, the approach first uses kernel or sieve…
Deep Gaussian processes have recently been proposed as natural objects to fit, similarly to deep neural networks, possibly complex features present in modern data samples, such as compositional structures. Adopting a Bayesian nonparametric…
We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…
This paper introduces a hierarchical framework to incorporate Hellinger distance methods into Bayesian analysis. We propose to modify a prior over non-parametric densities with the exponential of twice the Hellinger distance between a…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…
Nonresponse weighting adjustment using the response propensity score is a popular tool for handling unit nonresponse. Statistical inference after the nonresponse weighting adjustment is complicated because the effect of estimating the…
In this work, we developed a new Bayesian method for variable selection in function-on-scalar regression (FOSR). Our method uses a hierarchical Bayesian structure and latent variables to enable an adaptive covariate selection process for…
Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference…
There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…
Approximate Bayesian Computation (ABC) methods are applicable to statistical models specified by generative processes with analytically intractable likelihoods. These methods try to approximate the posterior density of a model parameter by…
Additive nonparametric regression models provide an attractive tool for variable selection in high dimensions when the relationship between the response and predictors is complex. They offer greater flexibility compared to parametric…
We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…
Hierarchical Bayesian Poisson regression models (HBPRMs) provide a flexible modeling approach of the relationship between predictors and count response variables. The applications of HBPRMs to large-scale datasets require efficient…