Maximum Entropy Design by a Markov Chain Process

In this article, we study an implementation of maximum entropy (ME) design utilizing a Markov chain. This design, which is also called the conditional Poisson sampling design, is difficult to implement. We first present a new method for calculating the weights associated with conditional Poisson sampling. Then, we study a very simple method of random exchanges of units, which allows switching from one sample to another. This exchange system defines an irreducible and aperiodic Markov chain whose ME design is the stationary distribution. The design can be implemented without enumerating all possible samples. By repeating the exchange process a large number of times, it is possible to select a sample that respects the design. The process is simple to implement, and its convergence rate has been investigated theoretically and by simulation, which led to promising results.