"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 that it will … [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 the … [Continue reading]

## 2016 US Presidential Election Predictions (November 7 Update)

The moment of truth! The year-long battle for the White House is coming to its conclusion! Tomorrow, voters in all states will determine the next US president in one of the most unpredictable elections in US history. Many people will be … [Continue reading]

## What Are Bayesian Belief Networks? (Part 1)

In my introductory Bayes' theorem post, I used a "rainy day" example to show how information about one event can change the probability of another. In particular, how seeing rainy weather patterns (like dark clouds) increases the probability that it … [Continue reading]