Related papers: Variational Bayesian Approximation of Inverse Prob…

There are several challenges associated with inverse problems in which we seek to reconstruct a piecewise constant field, and which we model using multiple level sets. Adopting a Bayesian viewpoint, we impose prior distributions on both the…

Variational inference has been widely used in machine learning literature to fit various Bayesian models. In network analysis, this method has been successfully applied to solve the community detection problems. Although these results are…

In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…

Radial velocity (RV) planet searches are increasingly finding planets with small velocity amplitudes, with long orbital periods, or in multiple planet systems. Bayesian inference has the potential to improve the interpretation of existing…

The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…

As a statistical tool to assist formative assessments in educational settings, diagnostic classification models (DCMs) have been increasingly used to provide diagnostic information regarding examinees' attributes. DCMs often adopt a…

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a…

Bayesian inference is useful to obtain a predictive distribution with a small generalization error. However, since posterior distributions are rarely evaluated analytically, we employ the variational Bayesian inference or sampling method to…

Geoscientists use observed data to estimate properties of the Earth's interior. This often requires non-linear inverse problems to be solved and uncertainties to be estimated. Bayesian inference solves inverse problems under a probabilistic…

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…

Uncertainty of decisions in safety-critical engineering applications can be estimated on the basis of the Bayesian Markov Chain Monte Carlo (MCMC) technique of averaging over decision models. The use of decision tree (DT) models assists…

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…

Variational Bayes (VB) is a popular tool for Bayesian inference in statistical modeling. Recently, some VB algorithms are proposed to handle intractable likelihoods with applications such as approximate Bayesian computation. In this paper,…

A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…

Markov chain Monte Carlo (MCMC) methods remain the mainstay of Bayesian estimation of structural equation models (SEM), though they often incur a high computational cost. We present a bespoke approximate Bayesian approach to SEM, drawing on…

The digital telecommunications receiver is an important context for inference methodology, the key objective being to minimize the expected loss function in recovering the transmitted information. For that criterion, the optimal decision is…

Brute force cross-validation (CV) is a method for predictive assessment and model selection that is general and applicable to a wide range of Bayesian models. Naive or `brute force' CV approaches are often too computationally costly for…

In order to predict future performance of subsurface fluid reservoirs under possible operating scenarios, a dynamic, porous-medium flow simulation model must be tuned to include representative properties of the reservoir. Estimating…

Markov chain Monte Carlo (MCMC) methods form one of the algorithmic foundations of Bayesian inverse problems. The recent development of likelihood-informed subspace (LIS) methods offers a viable route to designing efficient MCMC methods for…

Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…