Related papers: Estimating the marginal likelihood with Integrated…
Recently, it has been shown that approximations to marginal posterior distributions obtained using a low discrepancy sequence (LDS) can outperform standard grid-based methods with respect to both accuracy and computational efficiency. This…
In this paper, we present a novel approach to fitting mixture models based on estimating first the posterior distribution of the auxiliary variables that assign each observation to a group in the mixture. The posterior distributions of the…
Robust time series analysis is an important subject in statistical modeling. Models based on Gaussian distribution are sensitive to outliers, which may imply in a significant degradation in estimation performance as well as in prediction…
The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies.…
Nested Sampling is a method for computing the Bayesian evidence, also called the marginal likelihood, which is the integral of the likelihood with respect to the prior. More generally, it is a numerical probabilistic quadrature rule. The…
Approximate Bayesian inference typically revolves around computing the posterior parameter distribution. In practice, however, the main object of interest is often a model's predictions rather than its parameters. In this work, we propose…
The hierarchical prior used in Latent Gaussian models (LGMs) induces a posterior geometry prone to frustrate inference algorithms. Marginalizing out the latent Gaussian variable using an integrated Laplace approximation removes the…
The Linearized Laplace Approximation (LLA) has been recently used to perform uncertainty estimation on the predictions of pre-trained deep neural networks (DNNs). However, its widespread application is hindered by significant computational…
Many models require integrals of high-dimensional functions: for instance, to obtain marginal likelihoods. Such integrals may be intractable, or too expensive to compute numerically. Instead, we can use the Laplace approximation (LA). The…
Recent advances in Markov chain Monte Carlo (MCMC) extend the scope of Bayesian inference to models for which the likelihood function is intractable. Although these developments allow us to estimate model parameters, other basic problems…
Generalized linear mixed models are useful in studying hierarchical data with possibly non-Gaussian responses. However, the intractability of likelihood functions poses challenges for estimation. We develop a new method suitable for this…
Laplace's method, a family of asymptotic methods used to approximate integrals, is presented as a potential candidate for the tool box of techniques used for knowledge acquisition and probabilistic inference in belief networks with…
Measurement error (ME) and missing values in covariates are often unavoidable in disciplines that deal with data, and both problems have separately received considerable attention during the past decades. However, while most researchers are…
We present and implement two algorithms for analytic asymptotic evaluation of the marginal likelihood of data given a Bayesian network with hidden nodes. As shown by previous work, this evaluation is particularly hard for latent Bayesian…
This paper develops methodology that provides a toolbox for routinely fitting complex models to realistic spatial point pattern data. We consider models that are based on log-Gaussian Cox processes and include local interaction in these by…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
By providing a framework of accounting for the shared ancestry inherent to all life, phylogenetics is becoming the statistical foundation of biology. The importance of model choice continues to grow as phylogenetic models continue to…
We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…