Support for the Java 2 runtime environment. Click on the icon to download the appropriate plug-in.
Object Library > Applets > Markov Chain Experiment
This applet models a Markov chain with state space . The states are shown as colored circles in the left graphics box, with the current state colored red. At time 0, the initial state can be chosen be clicking on the desired state. As the process runs, the chain moves from state to state. The time and the sate are recorded at each update in the left table. The proportion of time that the chain is in each state is shown visually in the right graphics box and displayed numerically in the right table. In the limit, these proportions should converge to an appropriate limiting distribution.
The number of state can be varied with a scroll bar, and the transition probabilities can be specified in a dialog box that is launched by clicking on the transition probability button. Several special transition matrices can be selected from the dialog box:
This chain is a simple random walk on S with absorbing barriers.
This chain is a simple random walk on S with reflecting bariers.
This chain models a simple diffusion process. Suppose that we have two urns containing a total of n balls. At each time unit, a ball is selected at random (so that each ball is equally likely to be chosen), and then moved to the opposite urn. The state at time t is the number of balls in urn 1.
This chain models a simple diffusion process. Suppose that we have two urns, each with n balls. Of the balls, n are black and n are white. At each time unit, a ball is selected from each urn and the balls are interchanged. The state at time t is the number of black balls in urn 1.
This chain models a gene that consists of n sub-units, each of which can be normal or mutant. The state of the gene is the number of mutant sub-units. The Markov chain governs the splitting of the gene.
Support for the Java 2 runtime environment. Click on the icon to download the appropriate plug-in.
Copyright © 2001-2003, Kyle Siegrist and Dawn Duehring
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public License for more details.
If you are interested in the Java source code or the Java documentation and object model for this applet, please visit MarkovChainExperiment in the Object section of the Library.