TMB: Automatic differentiation and laplace approximation

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Abstract

TMB is an open source R package that enables quick implementation of complex nonlinear random effects (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, http://admb-project.org/; Fournier et al. 2011). In addition, it offers easy access to parallel computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (approximate to 10(6)) and parameters (approximate to 10(3)). Computation times using ADMB and TMB are compared on a suite of examples ranging from simple models to large spatial models where the random effects are a Gaussian random field. Speedups ranging from 1.5 to about 100 are obtained with increasing gains for large problems
Original languageEnglish
JournalJournal of Statistical Software
Volume70
Issue number5
Pages (from-to)1-21
ISSN1548-7660
Publication statusPublished - 2016

Cite this

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title = "TMB: Automatic differentiation and laplace approximation",
abstract = "TMB is an open source R package that enables quick implementation of complex nonlinear random effects (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, http://admb-project.org/; Fournier et al. 2011). In addition, it offers easy access to parallel computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (approximate to 10(6)) and parameters (approximate to 10(3)). Computation times using ADMB and TMB are compared on a suite of examples ranging from simple models to large spatial models where the random effects are a Gaussian random field. Speedups ranging from 1.5 to about 100 are obtained with increasing gains for large problems",
author = "Kasper Kristensen and Anders Nielsen and Berg, {Casper Willestofte} and Skaug, {Hans J.} and Brad Bell",
year = "2016",
language = "English",
volume = "70",
pages = "1--21",
journal = "Journal of Statistical Software",
issn = "1548-7660",
publisher = "The Foundation for Open Access Statistics",
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TMB: Automatic differentiation and laplace approximation. / Kristensen, Kasper; Nielsen, Anders; Berg, Casper Willestofte; Skaug, Hans J.; Bell, Brad.

In: Journal of Statistical Software, Vol. 70, No. 5, 2016, p. 1-21.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - TMB: Automatic differentiation and laplace approximation

AU - Kristensen, Kasper

AU - Nielsen, Anders

AU - Berg, Casper Willestofte

AU - Skaug, Hans J.

AU - Bell, Brad

PY - 2016

Y1 - 2016

N2 - TMB is an open source R package that enables quick implementation of complex nonlinear random effects (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, http://admb-project.org/; Fournier et al. 2011). In addition, it offers easy access to parallel computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (approximate to 10(6)) and parameters (approximate to 10(3)). Computation times using ADMB and TMB are compared on a suite of examples ranging from simple models to large spatial models where the random effects are a Gaussian random field. Speedups ranging from 1.5 to about 100 are obtained with increasing gains for large problems

AB - TMB is an open source R package that enables quick implementation of complex nonlinear random effects (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, http://admb-project.org/; Fournier et al. 2011). In addition, it offers easy access to parallel computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (approximate to 10(6)) and parameters (approximate to 10(3)). Computation times using ADMB and TMB are compared on a suite of examples ranging from simple models to large spatial models where the random effects are a Gaussian random field. Speedups ranging from 1.5 to about 100 are obtained with increasing gains for large problems

M3 - Journal article

VL - 70

SP - 1

EP - 21

JO - Journal of Statistical Software

JF - Journal of Statistical Software

SN - 1548-7660

IS - 5

ER -