PSI Team
Florent Morata IDIMAG
Corine Marchand IDIMAG
Jean Marc Vincent IDIMAG
PSI Presentation
PSI (Perfect Simulator) is a simulation software of markovian models. It be able to simulate discrete and continuous time models to provide a perfect sampling of the stationary distribution or directly a sampling of functional of this distribution.
The simulation kernel is based on the CFTP algorithm, and the internal simulation of transitions on the Aliasing method.
Theorical Background
CFTP
The
Coupling From The Past algorithm, designed by Propp & Wilson (1996), gives a method to directly generate a sample acording to the stationary distribution of Markov chains.
The sheme is to consider all possible initial values and observe their trajectories. Nevertheless, to obtain an exact sample, we must run the simulation from a distant point in the past until the present. The stopping criteria is simply the coalesce of different trajectories at time 0.
Aliasing
Aliasing method, designed by Walker (1974), is a reject simulation technique for discrete distributions. This technique is different to classical reject method, because all the values are considered.
The main advantage is to fast simulate any arbitrary distributions : its needs a (pseudo) random called, one comparison, and at most two memory references.
PSI Versions
PSI 1.0 release 1 is written in C++ language, and exists in two versions :
 Unix : classical use of shell commands.
 Textual interface : utilization of user interface.

