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Likelihood-free (a.k.a. simulation-based) inference problems are inverse problems with expensive, or intractable, forward models. ODE inverse problems are commonly treated as likelihood-free, as their forward map has to be numerically…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
Approximate Bayesian computation (ABC) is computationally intensive for complex model simulators. To exploit expensive simulations, data-resampling via bootstrapping can be employed to obtain many artificial datasets at little cost.…
Bayesian inference without the likelihood evaluation, or likelihood-free inference, has been a key research topic in simulation studies for gaining quantitatively validated simulation models on real-world datasets. As the likelihood…
Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating families, often taken to be Gaussian. This choice…
In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian…
State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
Bayesian Likelihood-Free Inference methods yield posterior approximations for simulator models with intractable likelihood. Recently, many works trained neural networks to approximate either the intractable likelihood or the posterior…
Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits…
Approximate Bayesian computation (ABC) methods, which are applicable when the likelihood is difficult or impossible to calculate, are an active topic of current research. Most current ABC algorithms directly approximate the posterior…
Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility…
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…
Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…
Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference…
We investigate the use of the Metropolis-Hastings algorithm to sample posterior distribution in a Bayesian inverse problem, where the likelihood function is random. Concretely, we consider the case where one has full field observations of a…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…