Suppose we want to predict the chance that it rains tomorrow using the variables available to us today. To make it simple, let’s say there are two variables that we are tracking: raining or sunny. If it is sunny today, the chance of it being sunny tomorrow are higher, and if it is raining today, the chance of it raining tomorrow are higher. This seems like a reasonable, though simplified, way to model reality. When tomorrow comes, we would just repeat the process.

Similarly, suppose we want to predict the next word that will be typed on a cell phone. We could look at every word that has ever been typed on that phone and find the most frequent one, or we could just look at the most recently typed word and see what word usually comes after it.

In both cases, we are using the most recent information available to us to predict the future and ignoring everything that came before. When the future comes, we transition and repeat the process. This way of modeling the world is known as a Markov Chain and it has some powerful applications.

Continue reading “Numeracy #17: Markov Chains”