The law of large numbers is one of the most important theorems in probability theory. It states that, as a probabilistic process is repeated a large number of times, the relative frequencies of its possible outcomes will get closer and closer to … [Continue reading]
The concepts of mean, median, and mode are fundamental to statistics, probability theory, and anything related to data analysis as a whole. Being this important, they deserve their own introduction. In statistics, these 3 concepts are examples of … [Continue reading]
"Simple explanations are better than complex explanations." — have you heard this statement before? It's the most simplified version of the principle called Occam's razor. More specifically, the principle says: A simple theory is always preferable to … [Continue reading]
What does a probability of zero mean? When people use it in everyday conversations, a statement like "the probability of something is zero" usually implies that that something isn't going to happen. Or that it is impossible to happen. Or that it will … [Continue reading]
In this post, I want to talk about conditional dependence and independence between events. This is an important concept in probability theory and a central concept for graphical models. In my two-part post on Bayesian belief networks, I introduced … [Continue reading]
In the first part of this post, I gave the basic intuition behind Bayesian belief networks (or just Bayesian networks) — what they are, what they're used for, and how information is exchanged between their nodes. In this post, I'm going to show … [Continue reading]