Related papers: Skew-Normal Posterior Approximations
Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is…
Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…
Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…
Skew-Gaussian processes (SkewGPs) extend the multivariate Unified Skew-Normal distributions over finite dimensional vectors to distribution over functions. SkewGPs are more general and flexible than Gaussian processes, as SkewGPs may also…
The skew-normal and the skew-$t$ distributions are parametric families which are currently under intense investigation since they provide a more flexible formulation compared to the classical normal and $t$ distributions by introducing a…
Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…
We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make these computations cheaper in high-dimensional settings is…
Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…
We recently proposed a general algorithm for approximating nonstandard Bayesian posterior distributions by minimization of their Kullback-Leibler divergence with respect to a more convenient approximating distribution. In this note we offer…
Bayesian neural networks often approximate the weight-posterior with a Gaussian distribution. However, practical posteriors are often, even locally, highly non-Gaussian, and empirical performance deteriorates. We propose a simple parametric…
Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…
We propose a general framework using spike-and-slab prior distributions to aid with the development of high-dimensional Bayesian inference. Our framework allows inference with a general quasi-likelihood function. We show that highly…
It is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting…
In the sparse normal means model, convergence of the Bayesian posterior distribution associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…
Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…
Frequentist and likelihood methods of inference based on the multivariate skew-normal model encounter several technical difficulties with this model. In spite of the popularity of this class of densities, there are no broadly satisfactory…
In recent years, inconsistency in Bayesian deep learning has attracted significant attention. Tempered or generalized posterior distributions are frequently employed as direct and effective solutions. Nonetheless, the underlying mechanisms…
Bayesian neural network posterior distributions have a great number of modes that correspond to the same network function. The abundance of such modes can make it difficult for approximate inference methods to do their job. Recent work has…