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TMB: Automatic Differentiation and Laplace Approximation

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  • Kristensen, Kasper
  • Nielsen, Anders
  • Berg, Casper W.
  • Skaug, Hans
  • Bell, Bradley M.

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 (≈ 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 http://tmb-project.org/.

Suggested Citation

  • Kristensen, Kasper & Nielsen, Anders & Berg, Casper W. & Skaug, Hans & Bell, Bradley M., 2016. "TMB: Automatic Differentiation and Laplace Approximation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i05).
    • Handle: RePEc:jss:jstsof:v:070:i05
    DOI: http://hdl.handle.net/10.18637/jss.v070.i05
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    References listed on IDEAS

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    1. Wang, Guiming, 2007. "On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models," Ecological Modelling, Elsevier, vol. 200(3), pages 521-528.
    2. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    3. J. Andrew Royle, 2004. "N-Mixture Models for Estimating Population Size from Spatially Replicated Counts," Biometrics, The International Biometric Society, vol. 60(1), pages 108-115, March.
    4. Skaug, Hans J. & Fournier, David A., 2006. "Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 699-709, November.
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