pdmpsim: pdmpsim: simulate PDMPs

In CharlotteJana/pdmpsim: Simulate Piecewise Deterministic Markov Processes

Description

The core of this package is the S4 class pdmpModel that has the aim to represent piecewise deterministic markov processes (PDMPs) in R. If a PDMP is implemented as pdmpModel, it can be simulated with method sim. The package provides another class named multSim to store multiple simulations and some methods for plotting and analysing the simulation results. Additionally the generator of a PDMP can be calculated with method generator.

PDMPs

A PDMP is a stochastic process that consists of continous variables and discrete variables. Discrete variables are simulated like a usual discrete markov chain with finite state space. The jump rates for the different states are defined in slot ratefunc where as the state of the variable after a jump is generated using slot jumpfunc. The continous variables evolve according to ODEs that are defined in slot dynfunc. These ODEs usually depend on the states of the discrete variables. The number of the continous variables is however fixed and does not change during the simulation. This is one restriction compared to the more general definition of PDMPs given in [Dav84]. The other restriction concernes borders for the continous variables which are implemented in the pdmpBorder Subclass. See [Zei09] and [Ben+15] for an introduction of PDMPs with definitions that match with the implementation of this package.

Provided Methods

There is a bunch of methods that can be used to analyse the simulation results. A single simulation stored in slot out of class pdmpModel can be visualised with plot and summarized with summarise. To store multiple simulations in a conventient way, use multSim or multSimCsv. The latter is only needed for simulations generating big data that can not be loaded to the working memory anymore. Method multSimCsv stores the results in csv files and returnes a class with links to the corresponding files instead of returning the simulations themselves.

Imported Packages

The following packages are needed for package pdmpsim to work:
For solving the ODEs during the simulation, package deSolve is required. To store multiple simulations as csv files and work with them without loading them into the working memory, package LaF is needed. Package Deriv is only used in function generator. Most of the plot methods are based on ggplot2 and some additional ggplot2 packages.

References

[Dav84]	Davis, M. H. (1984). Piecewise-deterministic Markov processes: A general class of
	non-diffusion stochastic models. Journal of the Royal Statistical Society. Series B
	(Methodological), 353-388.
[Zei09]	S. Zeiser. Classical and Hybrid Modeling of Gene Regulatory Networks. 2009.
[Ben+15]	Benaïm, M., Le Borgne, S., Malrieu, F., & Zitt, P. A. (2015). Qualitative properties
	of certain piecewise deterministic Markov processes. In Annales de l'Institut Henri
	Poincaré, Probabilités et Statistiques (Vol. 51, No. 3, pp. 1040-1075). Institut
	Henri Poincaré.

CharlotteJana/pdmpsim documentation built on July 2, 2019, 5:37 a.m.