MarkovProcesses.jl

A Julia package for efficient simulation, statistical inference and verification of Continuous Time Markov Chains.

It implements:

• A core of simulation for Markov Processes.
• A simple interface for Biochemical Networks / Stochastic Petri Nets.
• Synchronized simulation with Linear Hybrid Automata.
• Approximate Bayesian Computation (a likelihood-free inference method)
• Automaton-ABC: a statistical method for verification of parametric CTMC (cite paper)

Install

This package is not yet accessible via the Julia package manager. For the install of the package:

1. Clone this git repository on your computer.

2. Add the "core" directory of this repository to your LOAD_PATH. This can be done by two different ways:

   • Add the Julia line code

   import Distributed: @everywhere
   @everywhere push!(LOAD_PATH, /path/to/markovprocesses.jl/core")

   on your Julia startup file which is often located in ~/.julia/config/startup.jl in Unix systems.

   • If you don't want to add this in your startup file, you can add these lines in your Julia script before using MarkovProcesses.

Getting started

A few notebooks are available in examples/notebooks for a quick presentation of the different features of the package.

Tests

Execution tests and statistical tests are available. It can be run by:

julia tests/run_all.jl

⚠️ The statistical tests run by tests/run_cosmos.jl needs Cosmos in your PATH environment variable.

Benchmarks

Benchmarks have been made to test the performance of the package compared to well-known efficient other packages such as DifferentialEquations.jl.

Info

This package was written during my PhD thesis. The mathematical fundations and the package archtecture are presented in it.