11–20 of 36 posts
I appreciate the lack of math notation, for many with a poor mathematics backgrounds it feels like a huge wall into getting into interesting and useful theories.
Yikes.
I appreciate the lack of math notation, for many with a poor mathematics backgrounds it feels like a huge wall into getting into interesting and useful theories.
Bayes Theorem hardly requires any math notation at all. It would literally take you less than a minute to understand conditional probability. Yikes.
change my mind: bayes in practice is just a way to regularize your model and the language of bayes makes it seem principled but really you could use literally any regularizer and it would work almost just as well. i believe this because ultimately you're always going to minimize loglikelihood anyway (and so the prior becomes the regularization term).
The difference here, is that knowing a distribution is often more useful than just knowing the mean, or the variance, or some confidence intervals. Bayesian methods tend to be useful when you want this sort of information which is often the case when you are using it for decision making (or something like game theory).
Another uses case is when you are making decisions requiring multiple pieces of information that don't neatly fit together. A simple example is cancer screening. A rational decision about the proper threshold requires you to combine information about (1) The accuracy of your test, (2) The prevalence of the cancer in the population.
I will also add that the formula presented in the article is the simple case with discrete distributions. The more general version of the formula can also handle continuous distributions.
I appreciate the lack of math notation, for many with a poor mathematics backgrounds it feels like a huge wall into getting into interesting and useful theories.
This is a far gentler introduction, and the rest of the blog is pretty good too: https://www.countbayesie.com/blog/2016/5/1/a-guide-to-bayesi... Edit: this is a different take on the subject but an enjoyable and accessible read too: http://mbmlbook.com/toc.html
change my mind: bayes in practice is just a way to regularize your model and the language of bayes makes it seem principled but really you could use literally any regularizer and it would work almost just as well. i believe this because ultimately you're always going to minimize loglikelihood anyway (and so the prior becomes the regularization term).
A standard normal prior centered at 0 and one centered at 42 can give very different results.
Earlier quoted context omitted.
Bayes Theorem hardly requires any math notation at all. It would literally take you less than a minute to understand conditional probability. Yikes.
Oh yeah, and the first actually usable form of Bayesian Theorem would be probabilistic graphical models with max-sum algorithm. Good luck mastering that quickly or at all!
Bayes Theorem is easily derived algebraically using conditional probability and the chain rule. You can also derive it easily with a Venn diagram. There is barely any notation needed at all here to understand it.
If you're struggling with things at that level, it is more likely due to your own laziness, not because the math is hard. Because it is very easy to reason about.
I appreciate the lack of math notation, for many with a poor mathematics backgrounds it feels like a huge wall into getting into interesting and useful theories.
Bayes Theorem hardly requires any math notation at all. It would literally take you less than a minute to understand conditional probability. Yikes.
change my mind: bayes in practice is just a way to regularize your model and the language of bayes makes it seem principled but really you could use literally any regularizer and it would work almost just as well. i believe this because ultimately you're always going to minimize loglikelihood anyway (and so the prior becomes the regularization term).
A bottling company is interested in determining the accuracy with which their equipment is filling bottles of water. One answer would be "95% percent of the bottles contain between 11.9 and 12.1 ounces". A different way of answering the question would be to estimate the actual distribution of water amounts. The difference here, is that knowing a distribution is often more useful than just knowing the mean, or the var…