Skip to content

Latest commit

 

History

History
52 lines (36 loc) · 3.85 KB

index.md

File metadata and controls

52 lines (36 loc) · 3.85 KB
Raw

GpABC

GpABC provides algorithms for likelihood - free [parameter inference](@ref abc-overview) and [model selection](@ref ms-overview) using Approximate Bayesian Computation (ABC). Two sets of algorithms are available:

  • Simulation based - full simulations of the model(s) is done on each step of ABC.
  • Emulation based - a small number of simulations can be used to train a regression model (the emulator), which is then used to approximate model simulation results during ABC.

GpABC offers [Gaussian Process Regression](@ref gp-overview) (GPR) as an emulator, but custom emulators can also be used. GPR can also be used standalone, for any regression task.

Stochastic models, that don't conform to Gaussian Process Prior assumption, are supported via [Linear Noise Approximation](@ref lna-overview) (LNA).

Installation

GpABC can be installed using the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run

pkg> add GpABC

Notation

In parts of this manual that deal with Gaussian Processes and kernels, we denote the number of training points as $n$, and the number of test points as $m$. The number of dimensions is denoted as $d$.

In the context of ABC, vectors in parameter space (\theta) are referred to as particles. Particles that are used for training the emulator (training_x) are called design points. To generate the distances for training the emulator (training_y), the model must be simulated for the design points.

Examples

Dependencies

  • Optim - for training Gaussian Process hyperparameters.
  • Distributions - probability distributions.
  • Distances - distance functions
  • OrdinaryDiffEq - for solving ODEs for LNA, and also used throughout the examples for model simulation (ODEs and SDEs)
  • ForwardDiff - automatic differentiation is also used by LNA

References

  • Toni, T., Welch, D., Strelkowa, N., Ipsen, A., & Stumpf, M. P. H. (2009). Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. Interface, (July 2008), 187–202. https://doi.org/10.1098/rsif.2008.0172
  • Filippi, S., Barnes, C. P., Cornebise, J., & Stumpf, M. P. H. (2013). On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo. Statistical Applications in Genetics and Molecular Biology, 12(1), 87–107. https://doi.org/10.1515/sagmb-2012-0069
  • Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian Processes for Machine Learning. MIT Press. ISBN 0-262-18253-X. http://www.gaussianprocess.org/gpml
  • Schnoerr, D., Sanguinetti, G., & Grima, R. (2017). Approximation and inference methods for stochastic biochemical kinetics—a tutorial review. Journal of Physics A: Mathematical and Theoretical, 50(9), 093001. https://doi.org/10.1088/1751-8121/aa54d9
  • Karlebach, G., & Shamir, R. (2008). Modelling and analysis of gene regulatory networks. Nature Reviews Molecular Cell Biology, 9(10), 770–780. https://doi.org/10.1038/nrm2503