TMB: Automatic Differentiation and Laplace Approximation

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Authors Kasper Kristensen, Anders Nielsen, Casper Willestofte Berg, Hans Julius Skaug, Brad Bell
Journal/Conference Name Journal of Statistical Software
Paper Category
Paper 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,; 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 (≈ 106 ) and parameters (≈ 103 ). 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. The package and examples are available at
Date of publication 2016
Code Programming Language R

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