On the convergence of the Laplace approximation and noise-level-robustness of Laplace-based Monte Carlo methods for Bayesian inverse problems
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DOI: 10.1007/s00211-020-01131-1
Abstract: The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. We are interested in designing numerical methods which are robust w.r.t. the size… read more here.
Keywords: laplace approximation; monte carlo; laplace;
Markov chain Monte Carlo with the Integrated Nested Laplace Approximation
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DOI: 10.1007/s11222-017-9778-y
Abstract: 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… read more here.
Keywords: laplace approximation; approximation; nested laplace; integrated nested ... See more keywords
Laplace approximation, penalized quasi-likelihood, and adaptive Gauss–Hermite quadrature for generalized linear mixed models: towards meta-analysis of binary outcome with sparse data
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DOI: 10.1186/s12874-020-01035-6
Abstract: Background In meta-analyses of a binary outcome, double zero events in some studies cause a critical methodology problem. The generalized linear mixed model (GLMM) has been proposed as a valid statistical tool for pooling such… read more here.
Keywords: laplace approximation; methodology; penalized quasi; quasi likelihood ... See more keywords