• Corpus ID: 231857215

Implementing Approximate Bayesian Inference using Adaptive Quadrature: the aghq Package

@inproceedings{Stringer2021ImplementingAB,
  title={Implementing Approximate Bayesian Inference using Adaptive Quadrature: the aghq Package},
  author={Alex Stringer},
  year={2021}
}
The aghq package for implementing approximate Bayesian inference using adaptive quadrature is introduced. The method and software are described, and use of the package in making approximate Bayesian inferences in several challenging lowand highdimensional models is illustrated. Examples include an infectious disease model; an astrostatistical model for estimating the mass of the Milky Way; two examples in nonGaussian model-based geostatistics including one incorporating zero-inflation which is… 

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References

SHOWING 1-10 OF 45 REFERENCES
Stochastic Convergence Rates and Applications of Adaptive Quadrature in Bayesian Inference
TLDR
The first stochastic convergence rates for a family of adaptive quadrature rules used to normalize the posterior distribution in Bayesian models are provided, guaranteeing fast asymptotic convergence of approximate summary statistics used in practice.
No-U-turn sampling for fast Bayesian inference in ADMB and TMB: Introducing the adnuts and tmbstan R packages
TLDR
The R packages adnuts and tmbstan are introduced, which provide NUTS sampling in parallel and interactive diagnostics with ShinyStan, and adnuts provides a new method for estimating hierarchical ADMB models which previously were infeasible.
Fast, Scalable Approximations to Posterior Distributions in Extended Latent Gaussian Models
TLDR
A novel class of additive models called Extended Latent Gaussian Models is defined and a fast, scalable approximate Bayesian inference methodology for this class is developed, which is better suited to large samples than existing approaches.
Fitting Linear Mixed-Effects Models Using lme4
Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most
TMB: Automatic Differentiation and Laplace Approximation
TLDR
TMB is an open source R package that enables quick implementation of complex nonlinear random effect (latent variable) models in a manner similar to the established AD Model Builder package, and is designed to be fast for problems with many random effects and parameters.
Asymptotic properties of adaptive maximum likelihood estimators in latent variable models
TLDR
This paper formally investigate the properties of maximum likelihood estimators based on adaptive quadratures used to perform inference in generalized linear latent variable models.
A note on the accuracy of adaptive Gauss–Hermite quadrature
SummaryNumerical quadrature methods are needed for many models in order to approximate integrals in the likelihood function. In this note, we correct the error rate given by Liu & Pierce (1994) for
Model-Based Geostatistics the Easy Way
  • P. Brown
  • Environmental Science, Geology
  • 2015
This paper briefly describes geostatistical models for Gaussian and non-Gaussian data and demonstrates the geostatsp and dieasemapping packages for performing inference using these models. Making use
Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors
TLDR
A new concept for constructing prior distributions that is invariant to reparameterisations, have a natural connection to Jeffreys’ priors, seem to have excellent robustness properties, and allow this approach to define default prior distributions.
Model-Based Geostatistics for Prevalence Mapping in Low-Resource Settings
TLDR
This article reviews statistical methods and software associated with this standard model, then considers several methodological extensions whose development has been motivated by the requirements of specific applications, including methods for combining randomized survey data with data from nonrandomized, and therefore potentially biased, surveys; spatio-temporal extensions; and spatially structured zero-inflation.
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