Related papers: Multi-core parallel tempering Bayeslands for basin…
This paper addresses the problem of fault diagnosis in multistation assembly systems. Fault diagnosis is to identify process faults that cause the excessive dimensional variation of the product using dimensional measurements. For such…
A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and non-linear, therefore computationally expensive. An emulator-based methodology is…
In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…
Metadynamics, a member of the `flat histogram' class of advanced sampling algorithms, has been widely used in molecular simulations to drive the exploration of states separated by high free energy barriers and promote comprehensive sampling…
Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time…
In this chapter, we address the challenge of exploring the posterior distributions of Bayesian inverse problems with computationally intensive forward models. We consider various multivariate proposal distributions, and compare them with…
Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement,…
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…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
Recognizing traversable terrain from 3D point cloud data is critical, as it directly impacts the performance of autonomous navigation in off-road environments. However, existing segmentation algorithms often struggle with challenges related…
Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This…
Hierarchical models in Bayesian inverse problems are characterized by an assumed prior probability distribution for the unknown state and measurement error precision, and hyper-priors for the prior parameters. Combining these probability…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
The effectiveness of a new algorithm, parallel tempering, is studied for numerical simulations of biological molecules. These molecules suffer from a rough energy landscape. The resulting slowing down in numerical simulations is overcome by…
Probabilistic modeling of multidimensional spatiotemporal data is critical to many real-world applications. As real-world spatiotemporal data often exhibits complex dependencies that are nonstationary and nonseparable, developing effective…
We advocate for a new paradigm of cosmological likelihood-based inference, leveraging recent developments in machine learning and its underlying technology, to accelerate Bayesian inference in high-dimensional settings. Specifically, we…
Bayesian inference requires determining the posterior distribution, a task that becomes particularly challenging when the dimension of the parameter space is large and unknown. This limitation arises in many physics problems, such as…
In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced…
Bayesian curve fitting plays an important role in inverse problems, and is often addressed using the Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm. However, this algorithm can be computationally inefficient without…