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Many scientifically well-motivated statistical models in natural, engineering and environmental sciences are specified through a generative process, but in some cases it may not be possible to write down a likelihood for these models…
In this paper, we address the challenge of Markov Chain Monte Carlo (MCMC) algorithms within the approximate Bayesian Computation (ABC) framework, which often get trapped in local optima due to their inherent local exploration mechanism. We…
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…
Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte…
The power of fuzz testing lies in its random, often brute-force, generation and execution of inputs to trigger unexpected behaviors and vulnerabilities in software applications. However, given the reality of infinite possible input…
There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the…
We are living in the big data era, as current technologies and networks allow for the easy and routine collection of data sets in different disciplines. Bayesian Statistics offers a flexible modeling approach which is attractive for…
Sequential Monte Carlo (SMC) samplers are powerful tools for Bayesian inference but suffer from high computational costs due to their reliance on large particle ensembles for accurate estimates. We introduce persistent sampling (PS), an…
A computationally simple approach to inference in state space models is proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation of an intractable likelihood by matching summary statistics for the observed data with…
Monte Carlo (MC) integration is the de facto method for approximating the predictive distribution of Bayesian neural networks (BNNs). But, even with many MC samples, Gaussian-based BNNs could still yield bad predictive performance due to…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems.…
Due to the importance of uncertainty quantification (UQ), Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. However, traditional Bayesian inference methods based on Markov…
Approximate Bayesian computation (ABC) methods are used to approximate posterior distributions using simulation rather than likelihood calculations. We introduce Gaussian process (GP) accelerated ABC, which we show can significantly reduce…
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…
This work introduces a new method designed for Bayesian deep learning called scalable Bayesian Monte Carlo (SBMC). The method is comprised of a model and an algorithm. The model interpolates between a point estimator and the posterior. The…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
We describe a simple method for making inference on a functional of a multivariate distribution. The method is based on a copula representation of the multivariate distribution and it is based on the properties of an Approximate Bayesian…
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…
Hierarchical Bayesian Poisson regression models (HBPRMs) provide a flexible modeling approach of the relationship between predictors and count response variables. The applications of HBPRMs to large-scale datasets require efficient…