Results 1  10
of
88,184
Choice of Basis for Laplace Approximation
 Machine Learning
, 1998
"... Maximum a posterJori optimization of parameters and the Laplace approximation for the marginal likelihood are both basisdependent methods. This note compares two choices of basis for models parameterized by probabilities, showing that it is possible to improve on the traditional choice, the prob ..."
Abstract

Cited by 35 (1 self)
 Add to MetaCart
Maximum a posterJori optimization of parameters and the Laplace approximation for the marginal likelihood are both basisdependent methods. This note compares two choices of basis for models parameterized by probabilities, showing that it is possible to improve on the traditional choice
Integrated Nested Laplace Approximations
"... Volatility in financial time series is mainly analysed through two classes of models; the Generalised Autoregressive Conditional Heteroscedasticity (GARCH) models and the Stochastic Volatility (SV) ones. GARCH models are straightforward to estimate using maximum likelihood techniques, while SV mode ..."
Abstract
 Add to MetaCart
by applying a new inferential tool, Integrated Nested Laplace Approximations (INLA), which substitutes MCMC simulations with accurate deterministic approximations, making a full Bayesian analysis of many kinds of SV models extremely fast and accurate. Our hope is that the use of INLA will help SV models
Asymptotic expansions for the Laplace approximations for Itô functionals of Brownian rough paths
 J. Funct. Anal
"... for the Laplace approximations ..."
Coxme and the Laplace Approximation
, 2011
"... The coxme function fits the following mixed effects Cox model λ(t) = λ0(t)e Xβ+Zb b ∼ G(0, Σ(θ)) where λ0 is an unspecified baseline hazard function, X and Z are the design matrices for the fixed and random effects, respectively, β is the vector of fixedeffects coefficients and b is the vector of ..."
Abstract
 Add to MetaCart
The coxme function fits the following mixed effects Cox model λ(t) = λ0(t)e Xβ+Zb b ∼ G(0, Σ(θ)) where λ0 is an unspecified baseline hazard function, X and Z are the design matrices for the fixed and random effects, respectively, β is the vector of fixedeffects coefficients and b is the vector of random effects coefficients. The random effects distribution G is modeled as Gaussian with mean zero and a variance matrix Σ, which in turn depends a vector of parameters θ. The MLE for the variance of the random effects is based on an integrated partial likelihood IP L(β, θ) = 1
Integrated Nested Laplace Approximation for Bayesian
"... The goal of phylodynamics, an area on the intersection of phylogenetics and population genetics, is to reconstruct population size dynamics from genetic data. Recently, a series of nonparametric Bayesian methods have been proposed for such demographic reconstructions. These methods rely on prior spe ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
specifications based on Gaussian processes and proceed by approximating the posterior distribution of population size trajectories via Markov chain Monte Carlo (MCMC) methods. In this paper, we adapt an integrated nested Laplace approximation (INLA), a recently proposed approximate Bayesian inference for latent
Introducing the Laplace approximation in particle filtering
"... Abstract—The situations where particle filtering fails (socalled weight degeneracy) can be detected with the asymptotic variance of the particle approximation. However, this asymptotic variance is in general intractable, and in the case of weight degeneracy, computing it by Monte Carlo sampling is ..."
Abstract
 Add to MetaCart
is inefficient. We propose to compute the asymptotic variance of the particle approximation via the Laplace method for multidimensional integrals. We present this method, and illustrate how it can be used to improve particle filtering robustness.
Implementing approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations: A manual for the inlaprogram
, 2008
"... Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemp ..."
Abstract

Cited by 293 (20 self)
 Add to MetaCart
applications, the extent of these problems is such that Markov chain Monte Carlo is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals
Bayesian random fields: The BetheLaplace approximation
 In ICML
, 2006
"... While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text modelling (e.g. conditional random fields). But where Bayes ..."
Abstract

Cited by 14 (5 self)
 Add to MetaCart
Bayesian approaches for directed models have been very successful, a proper Bayesian treatment of undirected models in still in its infant stages. We propose a new method for approximating the posterior of the parameters given data based on the Laplace approximation. This approximation requires
Animal models and Integrated Nested Laplace Approximations
, 2011
"... Animal models are generalized linear mixed model (GLMM) used in evolutionary biology and animal breeding to identify the genetic part of traits. Integrated Nested Laplace Approximation (INLA) is a methodology for making fast nonsampling based Bayesian inference for hierarchical Gaussian Markov mode ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Animal models are generalized linear mixed model (GLMM) used in evolutionary biology and animal breeding to identify the genetic part of traits. Integrated Nested Laplace Approximation (INLA) is a methodology for making fast nonsampling based Bayesian inference for hierarchical Gaussian Markov
Results 1  10
of
88,184