Related papers: Adaptive quadrature schemes for Bayesian inference…
Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…
We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
Simulation models of critical systems often have parameters that need to be calibrated using observed data. For expensive simulation models, calibration is done using an emulator of the simulation model built on simulation output at…
Many fields of science and engineering rely on running simulations with complex and computationally expensive models to understand the involved processes in the system of interest. Nevertheless, the high cost involved hamper reliable and…
We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for…
Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
This work proposes an adaptive sequential Monte Carlo sampling algorithm to solve Bayesian inverse problems in scenarios where likelihood evaluations are costly but can be approximated using a surrogate model built from previous evaluations…
I describe a framework for adaptive scientific exploration based on iterating an Observation--Inference--Design cycle that allows adjustment of hypotheses and observing protocols in response to the results of observation on-the-fly, as data…
Simulation-based inference has been popular for amortized Bayesian computation. It is typical to have more than one posterior approximation, from different inference algorithms, different architectures, or simply the randomness of…
In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model…
Our article is concerned with adaptive sampling schemes for Bayesian inference that update the proposal densities using previous iterates. We introduce a copula based proposal density which is made more efficient by combining it with…
Variational Bayes methods approximate the posterior density by a family of tractable distributions whose parameters are estimated by optimisation. Variational approximation is useful when exact inference is intractable or very costly. Our…
We study the performance of the adaptive construction scheme for a Bayesian inference on the Quadratic GARCH model which introduces the asymmetry in time series dynamics. In the adaptive construction scheme a proposal density in the…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…
Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…
We propose a novel adaptive empirical Bayesian method for sparse deep learning, where the sparsity is ensured via a class of self-adaptive spike-and-slab priors. The proposed method works by alternatively sampling from an adaptive…
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…