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 Mean, the Mode, And the Median

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 … [Continue reading]

## Occam’s Razor: A Probabilistic View

"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]

## Not All Zero Probabilities Are Created Equal

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 … [Continue reading]

## When Dependence Between Events Is Conditional

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]

## What Are Bayesian Belief Networks? (Part 2)

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]