Simulation is an effective tool for analyzing probability models as well as for facilitating understanding of concepts in probability and statistics. Unfortunately, implementing a simulation from scratch often requires users to think about programming issues that are not relevant to the simulation itself. We have developed a Python package called…

Latent transition analysis (LTA) was initially developed to provide a means of measuring change in dynamic latent variables. In this article, we illustrate the use of a cognitive diagnostic model, the DINA model, as the measurement model in a LTA, thereby demonstrating a means of analyzing change in cognitive skills over time. An example is…

For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…

When one uses Google (and many people do this!), the result of the query is a list of sites that have something to do with the item one is looking for. The specific sites are always more or less on the top, so it is not necessary to have a look on hundreds of sites to read something relevant and informative. How can Google manage this? How does…

In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M…

In the No Child Left Behind Act (NCLB), Congress called for the U.S. Department of Education (ED) to conduct a rigorous study of the conditions and practices under which educational technology is effective in increasing student academic achievement. A 2007 report presenting study findings for the 2004-2005 school year, indicated that, after one…

Considers the random sum SN+X1+X2+...+XN with a stopping rule N=min((n: SN absorbing Markov chain. (AIM)

Games are promoted as examples for classroom discussion of stationary Markov chains. In a game context Markov chain terminology and results are made concrete, interesting, and entertaining. Game length for several-player games such as "Hi Ho! Cherry-O" and "Chutes and Ladders" is investigated and new, simple formulas are given. Slight…