This paper describes an online solution for visualizing the simulation of a discrete time Markov chain using an animated graph. Based on the D3.js library, the development of this solution offers the user the choice between a presentation based on the concept of a probabilistic graph oriented and a presentation of the transitions in a matrix framework. As an application the solution helps to describe the dynamics of individual policyholders in a Bonus-Malus system of automobile insurance.
The standard coupling from the past (CFTP) algorithm is an interesting tool to sample from exact Markov chain steady-state probability.
The CFTP detects, with probability one, the end of the transient phase (called burn-in period) of the chain and consequently the beginning of its stationary phase.
For large and/or stiff Markov chains, the burn-in period is expensive in time consumption.
In this work, we propose a kind of dual form for CFTP called D-CFTP that, in many situations, reduces the Monte Carlo simulation time and does not need to store the history of the used random numbers from one iteration to another.
A performance comparison of CFTP and D-CFTP will be discussed, and some numerical Monte Carlo simulations are carried out to show the smooth running of the proposed D-CFTP.
The standard Coupling From The Past (CFTP) algorithm is an interesting tool to sample from exact stationary distribution of a Markov chain. But it is very expensive in time consuming for large chains. There is a monotone version of CFTP, called MCFTP, that is less time consuming for monotone chains. In this work, we propose two techniques to get monotone chain allowing use of MCFTP: widening technique based on adding two fictitious states and clustering technique based on partitioning the state space in clusters. Usefulness and efficiency of our approaches are showed through a sample of Markov Chain Monte Carlo simulations.
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