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Not All Zero Probabilities Are Created Equal

Posted on August 20, 2017 Written by The Cthaeh 8 Comments

Im_possible

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]

Filed Under: Probability Distributions Tagged With: Probability density, Probability mass, Sample space

When Dependence Between Events Is Conditional

Posted on November 26, 2016 Written by The Cthaeh 9 Comments

A spider building a web, outdoors.

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]

Filed Under: Bayes' Theorem Tagged With: Bayesian network, Causality, Conditional probability, Sample space

What Are Bayesian Belief Networks? (Part 2)

Posted on November 20, 2016 Written by The Cthaeh 11 Comments

Droplets of different sizes (on a spider web) connected to each other - a metaphor for Bayesian belief networks

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]

Filed Under: Bayes' Theorem Tagged With: Bayesian network, Causality, Conditional probability, Sample space

What Are Bayesian Belief Networks? (Part 1)

Posted on November 3, 2016 Written by The Cthaeh 22 Comments

Droplets of different sizes connected to each other - a metaphor for Bayesian belief networks

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]

Filed Under: Bayes' Theorem Tagged With: Bayesian network, Causality, Conditional probability

Predicting the 2016 US Presidential Election

Posted on September 20, 2016 Written by The Cthaeh 6 Comments

Trump, Johnson, Clinton, and Stein with an American flag in the background.

November 7 UPDATE: click here to view our final update post where we give our latest analyses just a day before the election! Click here to go to our daily predictions page. In the first 10 posts I mostly concentrated on … [Continue reading]

Filed Under: Applications, Probability Theory & Statistics Tagged With: Politics

Frequentist and Bayesian Approaches in Statistics

Posted on June 16, 2016 Written by The Cthaeh 53 Comments

Dennis Lindley vs. Ronald Fisher

What is statistics about? Well, imagine you obtained some data from a particular collection of things. It could be the heights of individuals within a group of people, the weights of cats in a clowder, the number of petals in … [Continue reading]

Filed Under: Bayes' Theorem, Fundamental Concepts, Probability Theory & Statistics Tagged With: Confidence interval, Null hypothesis, P-value, Parameter estimation

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