An Introduction to AD Model Builder

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An Introduction to AD Model Builder
http//admb-project.org/
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Instructors

• Anders Nielsen (Technical University of Denmark,
  DTU-Aqua)
• Johnoel Ancheta (Pelagic Fisheries Research
  Program, PFRP)
• Mark Maunder (Inter-American Tropical Tuna
  Commission, IATTC)

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Introduce yourself

• Name
• Organization
• Main research

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Questionnaire

• What do you know
• Remember to ask Participants about WinBUGs.

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What is AD Model Builder

• Tool for developing nonlinear models
• Efficient estimation of model parameters
• C libraries
• Template

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Simplifying the development of models

• Removes the need to manage the interface between
  the model parameters and function minimizer.
• The template makes it easy to input and output
  data from the model, set up the parameters to
  estimate, and set up objective function to
  optimize (minimize).
• Adding additional estimable parameters or
  converting fixed parameters into estimable
  parameters is a simple process.
• ADMB is very flexible as model code is in C
• Experienced C programmers to create their own
  libraries

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Efficient and stable function minimizer

• Analytical derivatives
• Adjoint code
• Chain rule
• More efficient and stable than other packages
  that use finite difference approximation.
• Stepwise process to sequentially estimate the
  parameters
• Bounds on all estimated parameters that restrict
  the range of possible parameter values.

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MCMC algorithm for Bayesian integration

• Starts at the mode of the posterior reduces the
  burn-in time.
• Jumping rules based on the variance-covariance
  estimates at the mode of the posterior
  distribution

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Automated likelihood profiles

• Normal approximation of confidence intervals
  based on the Hessian matrix and derived
  quantities using the delta method
• Automatically calculate likelihood profiles for
  model parameters and derived quantities producing
  asymmetrical confidence intervals

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Random effects parameters

• Random effects parameters implemented using
  Laplaces approximation (and importance sampling)
• Automatic analytical second derivatives.
• Use for process error or meta analysis

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Matrix algebra

• Matrix algebra with associated precompiled
  adjoint code for derivative calculations
• Can greatly reduce computation time and memory
  usage compared to loops

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Other features

• non-linear programming solver
• numerical integration routine
• random number generation
• high dimensional and ragged arrays
• estimation of the variance-covariance matrix
• dynamic link libraries with other software
  products (e.g. s-plus, Excel, Visual Basic)
• safe mode compiling for bounds checking
• ability to make ADMB C libraries.
• Parallel processing

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What its good for Highly parameterize nonlinear
models

• Thousands of parameters
• Combining many data sets or analyses
• General Models
• Stock Synthesis (Rick Methot NMFS)

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What its good for Nonlinear models with large
data sets

• Integrating GLMs into nonlinear models

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What its good for Numerous optimizations of the
objective function

• Simulation analysis
• Likelihood profiles
• Bootstrap/cross validation
• Model testing/sensitivity analysis
• Management strategy evaluation
• Numerical integration/simulated likelihood

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What its good for Nonlinear mixed effects models

• Crossed random effects
• Nonlinear state-space models.

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The ADMB project

• Make ADMB Free
• Make ADMB open source
• Develop ADMB
• Facilitate the use of ADMB
• Promote ADMB

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Outline

• Introduction
• Installation
• First example
• Likelihood based inference
• What happens internally
• Parameter setup
• Data input and outputting results
• Simulation
• Estimating uncertainty
• Random effects
• Summary