Related papers: Improved Laplace Approximation for Marginal Likeli…
There is a growing demand for performing larger-scale Bayesian inference tasks, arising from greater data availability and higher-dimensional model parameter spaces. In this work we present parallelization strategies for the methodology of…
This paper uses the Modified Projection Method to examine the errors in solving the boundary integral equation from Laplace equation. The analysis uses weighted norms, and parallel algorithms help solve the independent linear systems. By…
The Integrated Nested Laplace Approximation (INLA) is a convenient way to obtain approximations to the posterior marginals for parameters in Bayesian hierarchical models when the latent effects can be expressed as a Gaussian Markov Random…
Inference by means of mathematical modeling from a collection of observations remains a crucial tool for scientific discovery and is ubiquitous in application areas such as signal compression, imaging restoration, and supervised machine…
The Laplace approximation provides a scalable and efficient means of quantifying weight-space uncertainty in deep neural networks, enabling the application of Bayesian tools such as predictive uncertainty and model selection via Occam's…
The Integrated Nested Laplace Approximation (INLA) has established itself as a widely used method for approximate inference on Bayesian hierarchical models which can be represented as a latent Gaussian model (LGM). INLA is based on…
Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…
In this paper we obtain an approximation for the multivariate Laplace's integral with a large parameter and estimate error term for two cases, when the maximum of the exponent is in the interior of the domain and on the boundary. We are…
This letter gives approximations to an integral appearing in the formula for downlink coverage probability of a typical user in Poisson point process (PPP) based stochastic geometry frameworks of the form $\int_0^\infty \exp\{ - (Ax + B…
It is common practice to use Laplace approximations to compute marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to…
Complex models used to describe biological processes in epidemiology and ecology often have computationally intractable or expensive likelihoods. This poses significant challenges in terms of Bayesian inference but more significantly in the…
Bayesian inference requires approximation methods to become computable, but for most of them it is impossible to quantify how close the approximation is to the true posterior. In this work, we present a theorem upper-bounding the KL…
Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…
The integrated nested Laplace approximations (INLA) method has become a widely utilized tool for researchers and practitioners seeking to perform approximate Bayesian inference across various fields of application. To address the growing…
Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood and Laplace approximation. In…
Exact MLE for generalized linear mixed models (GLMMs) is a long-standing problem unsolved until today. The proposed research solves the problem. In this problem, the main difficulty is caused by intractable integrals in the likelihood…