Related papers: A Bayesian inference and model selection algorithm…
In this paper we address the problem of performing Bayesian inference for the parameters of a nonlinear multi-output model and the covariance matrix of the different output signals. We propose an adaptive importance sampling (AIS) scheme…
Bayesian neural networks (BNNs) have received an increased interest in the last years. In BNNs, a complete posterior distribution of the unknown weight and bias parameters of the network is produced during the training stage. This…
Many contemporary machine learning models require extensive tuning of hyperparameters to perform well. A variety of methods, such as Bayesian optimization, have been developed to automate and expedite this process. However, tuning remains…
Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on the class of Layered Adaptive Importance Sampling…
We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the…
Bayesian inference promises to ground and improve the performance of deep neural networks. It promises to be robust to overfitting, to simplify the training procedure and the space of hyperparameters, and to provide a calibrated measure of…
We introduce a new class of adaptive importance samplers leveraging adaptive optimisation tools, which we term AdaOAIS. We build on Optimised Adaptive Importance Samplers (OAIS), a class of techniques that adapt proposals to improve the…
One of the main problems of importance sampling in Bayesian networks is representation of the importance function, which should ideally be as close as possible to the posterior joint distribution. Typically, we represent an importance…
Markov chain Monte Carlo methods are a powerful and commonly used family of numerical methods for sampling from complex probability distributions. As applications of these methods increase in size and complexity, the need for efficient…
Importance sampling (IS) is a powerful Monte Carlo (MC) methodology for approximating integrals, for instance in the context of Bayesian inference. In IS, the samples are simulated from the so-called proposal distribution, and the choice of…
In many applications, Bayesian inverse problems can give rise to probability distributions which contain complexities due to the Hessian varying greatly across parameter space. This complexity often manifests itself as lower dimensional…
Stochastic sampling algorithms, while an attractive alternative to exact algorithms in very large Bayesian network models, have been observed to perform poorly in evidential reasoning with extremely unlikely evidence. To address this…
Estimating rare events in complex systems is a key challenge in reliability analysis. The challenge grows in multimodal problems, where traditional methods often rely on a small set of design points and risk overlooking critical failure…
We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…
Increased access to computing resources has led to the development of algorithms that can run efficiently on multi-core processing units or in distributed computing environments. In the context of Bayesian inference, many parallel computing…
Adaptive importance samplers are adaptive Monte Carlo algorithms to estimate expectations with respect to some target distribution which \textit{adapt} themselves to obtain better estimators over a sequence of iterations. Although it is…
This paper surveys some well-established approaches on the approximation of Bayes factors used in Bayesian model choice, mostly as covered in Chen et al. (2000). Our focus here is on methods that are based on importance sampling strategies…
Importance sampling is used to approximate Bayes' rule in many computational approaches to Bayesian inverse problems, data assimilation and machine learning. This paper reviews and further investigates the required sample size for…
Bayesian inference often faces a trade-off between computational speed and sampling accuracy. We propose an adaptive workflow that integrates rapid amortized inference with gold-standard MCMC techniques to achieve a favorable combination of…
Bayesian inference under a set of priors, called robust Bayesian analysis, allows for estimation of parameters within a model and quantification of epistemic uncertainty in quantities of interest by bounded (or imprecise) probability.…