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 measures of central tendency. This is a fancy way of saying that they are single values that summarize collections of values.
Let’s unpack the last sentence. What exactly do I mean by ‘values’ and ‘collections of values’?
“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 a complex theory, if the complex theory doesn’t offer a better explanation.
Does it make sense? If it’s not immediately convincing, that’s okay. There have been debates around Occam’s razor’s validity and applicability for a very long time.
In this post, I’m going to give an intuitive introduction to the principle and its justification. I’m going to show that, despite historical debates, there is a sense in which Occam’s razor is always valid. In fact, I’m going to try to convince you this principle is so true that it doesn’t even need to be stated on its own.
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 never happen.
There’s zero chance I’m passing this exam!
Is this true? Can we really say that zero probability events are impossible to occur? I’m going to show you that this is, in fact, false. You will see zero probability events are more than possible: they happen all the time.
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 an important type of graphical models. You can read Part 1 and Part 2 by following these links.
This is actually an informal continuation of the two Bayesian networks posts. Even though I initially wanted to include it at the end of Part 2, I decided it’s an important enough topic that deserves its own space.
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 math underlying everything I talked about in the previous one. It’s going to be a bit more technical, but I’m going to try to give the intuition behind the relevant equations.
If you stick to the end, I promise you’ll get a much deeper understanding of Bayesian networks. To the point of actually being able to use them for real-world calculations.
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 celebrating and many will be disappointed when the final votes are counted a little over 24 hours from now.
Donald Trump managed to achieve a miraculous recovery of his campaign just 2 weeks before election day. Currently, Hillary Clinton has about 76% chance of winning the election. Donald Trump’s chances for a direct win are about 11%. There is also a significant probability of 13-14% for a tie between the candidates, which would send the contest to the US Congress!