Seonglae ChoBayes' rule
We use Bayes’ rule when we have a hypothesis and observed some evidence, and we want to get probability of Hypothesis given the evidence. That is a method for calculating posterior probability using prior probability and likelihood. We can induce probability of hypothesis given the evidence by filtering out possibilities fitting the evidence from all possibilities.
It's a formula expressing a Statistical Thinking, one form derived from the definitions of Conditional probability, Joint Probability, and Marginalization.
Product rule to Bayes Theorem
The car key example well illustrates Bayes' probability because it shows how the probability distribution of a model's parameters changes before and after observation. It is a formula for calculating the degree of updated belief based on prior probability and new evidence, using conditional probability to calculate the posterior probability.
We can chain is Hyperparameter used to determine prior and not is the reason that hyperparameters alpha and beta are used to determine the prior probability distribution, but they do not affect the relationship between the data D and the model parameter theta
Log form
where
Bayes Theorem Notion
Bayes theorem, the geometry of changing beliefs
Perhaps the most important formula in probability.
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The quick proof: https://youtu.be/U_85TaXbeIo
Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/
The study with Steve:
https://science.sciencemag.org/content/185/4157/1124
http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf
You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project.
Contents:
0:00 - Intro example
4:09 - Generalizing as a formula
10:13 - Making probability intuitive
13:35 - Issues with the Steve example
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Good if make prior after data instead of before — LessWrong
They say you’re supposed to choose your prior in advance. That’s why it’s called a “prior”. First, you’re supposed to say say how plausible different…
https://www.lesswrong.com/posts/JAA2cLFH7rLGNCeCo/good-if-make-prior-after-data-instead-of-before
