Z-estimation via correlation matching for partially observed branching processes and stochastic compartmental models
This package includes functions to forward-simulate from a general class of stochastic compartmental models using the Gillespie algorithm [1], as well as capabilities to produce discretely observed datasets and partially observed datasets given a sampling distribution. The software is developed with a focus on compartmental models of hematopoiesis [2,3]. In addition to simulation, routines for parameter inference are implemented based on the method of moments or z-estimation [4]. These functions use numerical optimization to match observed correlations in the data to their corresponding model-based expressions, which depend on rate parameters. Inferring these parameters therefore amounts to a nonlinear least squares problem, seeking the parameters which minimize the residuals between empirical and analytical correlations.
The package can be installed directly from github using the devtools package, which can easily be installed using the command install.packages("devtools").
See https://github.com/hadley/devtools for more details.
To install branchCorr, run the following:
library(devtools)
install_github("jasonxu90/branchCorr")By default, the vignette is not compiled during the installation. We provide a vignette, ``branchCorr: simulation and inference for partially observed stochastic compartmental models'', that walks through simulation and inference functions necessary to recreate all simulation studies in [2]. Examples are smaller-scale, but still require quite some computing time. Users are encouraged to run all functions in the vignette locally by reducing the number of simulations, initial restarts, etc when necessary.
The source .Rnw file, as well as a .pdf of the vignette compiled using knitr, are included in the repository. To automatically compile the vignette upon package installation, instead install using the line
install_github("jasonxu90/branchCorr", build_vignettes = TRUE). Note that this option will be significantly slower than installing the package alone.
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Gillespie DT (1977) "Exact stochastic simulation of coupled chemical reactions," Journal of Physical Chemistry, 81(25):2340-2361.
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Xu J, Koelle S, Guttorp P, Wu C, Dunbar Ce, Abkowitz JL, Minin VN (2016) "Statistical inference in partially observed stochastic compartmental models with application to cell lineage tracking of in vivo hematopoiesis," https://arxiv.org/abs/1610.07550
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Catlin, SN, Abkowitz, JL and Guttorp, P (2001) "Statistical Inference in a Two-Compartment Model for Hematopoiesis," Biometrics, 57(2):546-553.
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Pakes A and Pollard D (1989) "Simulation and the asymptotics of optimization estimators," Econometrica: Journal of the Econometric Society, 57(5):1027-1057.