# Bayes' Theorem {% embed url="" %} [Bayes.com](https://bayes.com/) - "We’re excited to bring you BAYES — a creative, no-code tool for thinking and speaking with data." [Bayesian Inference](https://seeing-theory.brown.edu/bayesian-inference/index.html) [The Bayesian Trap](https://www.youtube.com/watch?v=R13BD8qKeTg\&feature=youtu.be) #video - "Bayes' theorem explained with examples and implications for life." [Bayes: How one equation changed the way I think](https://www.youtube.com/watch?v=za7RqnT7CM0) #video - "Bayes' Rule is a simple formula that tells you how to weigh evidence and change your beliefs. I don't go around plugging numbers into a formula all the time, but nevertheless, becoming familiar with Bayes has shifted the way I think in some important ways." [Bayes theorem](https://www.youtube.com/watch?v=HZGCoVF3YvM) #video - 3Blue1Brown. "Perhaps the most important formula in probability." {% embed url="" %} [Bayes' theorem](https://en.wikipedia.org/wiki/Bayes'_theorem) #article - "One of the many applications of Bayes’ theorem is [Bayesian inference](https://en.wikipedia.org/wiki/Bayesian_inference), a particular approach to [statistical inference](https://en.wikipedia.org/wiki/Statistical_inference). When applied, the probabilities involved in Bayes’ theorem may have different [probability interpretations](https://en.wikipedia.org/wiki/Probability_interpretation). With [Bayesian probability](https://en.wikipedia.org/wiki/Bayesian_probability) interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to [Bayesian statistics](https://en.wikipedia.org/wiki/Bayesian_statistics)." Crash Course * [You know I’m all about that Bayes: Crash Course Statistics #24](https://www.youtube.com/watch?v=9TDjifpGj-k\&feature=youtu.be) #video - "Today we’re going to talk about Bayes Theorem and Bayesian hypothesis testing. Bayesian methods like these are different from how we've been approaching statistics so far, because they allow us to update our beliefs as we gather new information - which is how we tend to think naturally about the world. And this can be a really powerful tool, since it allows us to incorporate both scientifically rigorous data AND our previous biases into our evolving opinions." * [Bayes in science and everyday life: Crash Course Statistics #25](https://www.youtube.com/watch?v=51bLRF02b4w\&list=PL8dPuuaLjXtNM_Y-bUAhblSAdWRnmBUcr\&index=26) #video - "Today we're going to finish up our discussion of Bayesian inference by showing you how we can it be used for continuous data sets and be applied both in science and everyday life. From A/B testing of websites and getting a better understanding of psychological disorders to helping with language translation and purchase recommendations Bayes statistics really are being used everywhere!" [How to become a Bayesian in eight easy steps: An annotated reading list](https://link.springer.com/article/10.3758/s13423-017-1317-5) #article ![https://xkcd.com/2545/](https://1225933412-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-LbgvKp60ZrcgYsadNVB%2Fuploads%2FHcmyOtMJZfX3mj23oiK3%2Fimage.png?alt=media\&token=4cc6de41-81e7-4f70-a70e-587faa1778c4) [Thinking like a Bayesian - Julia Galef (Strata + Hadoop World 2016)](https://www.youtube.com/watch?v=kpdBOUnynps) #video - "Julia Galef outlines the most important principles of thinking like a Bayesian." [A visual guide to Bayesian thinking](https://www.youtube.com/watch?v=BrK7X_XlGB8) #video - "I use pictures to illustrate the mechanics of "Bayes' rule," a mathematical theorem about how to update your beliefs as you encounter new evidence. Then I tell three stories from my life that show how I use Bayes' rule to improve my thinking." {% embed url="" %} --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://brain.nathanarthur.com/rationality/bayes-theorem.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.