Related papers: Bayesian Computing with INLA: A Review
This paper provides a review of Approximate Bayesian Computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional…
Bayesian methods have shown success in deep learning applications. For example, in predictive tasks, Bayesian neural networks leverage Bayesian reasoning of model uncertainty to improve the reliability and uncertainty awareness of deep…
In a non supervised Bayesian estimation approach for inverse problems in imaging systems, one tries to estimate jointly the unknown image pixels $f$ and the hyperparameters $\theta$ given the observed data $g$ and a model $M$ linking these…
We study approximations to the Moreau envelope -- and infimal convolutions more broadly -- based on Laplace's method, a classical tool in analysis which ties certain integrals to suprema of their integrands. We believe the connection…
This paper studies computationally and theoretically attractive estimators called the Laplace type estimators (LTE), which include means and quantiles of Quasi-posterior distributions defined as transformations of general…
We present a scalable and robust Bayesian inference method for linear state space models. The method is applied to demand forecasting in the context of a large e-commerce platform, paying special attention to intermittent and bursty target…
Bayesian inference is a popular method to build learning algorithms but it is hampered by the fact that its key object, the posterior probability distribution, is often uncomputable. Expectation Propagation (EP) (Minka (2001)) is a popular…
Under the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai…
Variable selection in high-dimensional spaces is a pervasive challenge in contemporary scientific exploration and decision-making. However, existing approaches that are known to enjoy strong statistical guarantees often struggle to cope…
Double hierarchical generalized linear models (DHGLM) are a family of models that are flexible enough as to model hierarchically the mean and scale parameters. In a Bayesian framework, fitting highly parameterized hierarchical models is…
Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…
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…
Although the Laplace approximation offers a simple route to uncertainty quantification in deep neural networks, its reliance on inverting large Hessian matrices has motivated a range of computationally feasible low-dimensional or sparse…
We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…
This paper proposes a two-stage estimation approach for a spatial misalignment scenario that is motivated by the epidemiological problem of linking pollutant exposures and health outcomes. We use the integrated nested Laplace approximation…
Joint models for longitudinal and time-to-event data are increasingly used in health research to characterize the association between biomarker trajectories and the risk of clinical events. However, these models usually assume a linear…
Uncertainty quantification for deep neural networks has recently evolved through many techniques. In this work, we revisit Laplace approximation, a classical approach for posterior approximation that is computationally attractive. However,…
Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state…
Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…
Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods…