Related papers: Bayesian Ultrahigh-Dimensional Screening Via MCMC
Computer vision tasks are difficult because of the large variability in the data that is induced by changes in light, background, partial occlusion as well as the varying pose, texture, and shape of objects. Generative approaches to…
Power and sample size analysis comprises a critical component of clinical trial study design. There is an extensive collection of methods addressing this problem from diverse perspectives. The Bayesian paradigm, in particular, has attracted…
Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…
We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
Bayesian methods hold significant promise for improving the uncertainty quantification ability and robustness of deep neural network models. Recent research has seen the investigation of a number of approximate Bayesian inference methods…
Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…
In this article, we investigate large sample properties of model selection procedures in a general Bayesian framework when a closed form expression of the marginal likelihood function is not available or a local asymptotic quadratic…
This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un-…
Background: Continuous traits evolution of a group of taxa that are correlated through a phylogenetic tree is commonly modelled using parametric stochastic differential equations to represent deterministic change of trait through time,…
Bayesian formulations of inverse problems are attractive for their ability to incorporate prior knowledge and update probabilistic models as new data become available. Markov chain Monte Carlo (MCMC) methods sample posterior probability…
The problem of selecting the most useful features from a great many (eg, thousands) of candidates arises in many areas of modern sciences. An interesting problem from genomic research is that, from thousands of genes that are active…
Bayesian methods are commonly applied to solve image analysis problems such as noise-reduction, feature enhancement and object detection. A primary limitation of these approaches is the computational complexity due to the interdependence of…
Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…
We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior…
Bayesian low-rank matrix factorization techniques have become an essential tool for relational data analysis and matrix completion. A standard approach is to assign zero-mean Gaussian priors on the columns or rows of factor matrices to…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
Advances in digital sensors, digital data storage and communications have resulted in systems being capable of accumulating large collections of data. In the light of dealing with the challenges that massive data present, this work proposes…
When performing Bayesian data analysis using a general linear mixed model, the resulting posterior density is almost always analytically intractable. However, if proper conditionally conjugate priors are used, there is a simple two-block…
Bayesian model selection is a tool to decide whether the introduction of a new parameter is warranted by data. I argue that the usual sampling statistic significance tests for a null hypothesis can be misleading, since they do not take into…