Just finished this #book on the history of Bayes theorem and I highly recommend it.
In case you’re wondering what is it, keep reading.
(A thread on Bayes theorem)
In case you’re wondering what is it, keep reading.
(A thread on Bayes theorem)
1/ Statistics is all about calculating probabilities, and there are two camps who interpret probability differently.
Frequentists = frequency of events over multiple trials
Bayesians = subjective belief of outcome of events
Frequentists = frequency of events over multiple trials
Bayesians = subjective belief of outcome of events
2/ This philosophical divide informs what these two camps usually bother with.
Frequentists = probability of data, given a model (of how data could have been generated)
Bayesians = probability of model, given the data
Frequentists = probability of data, given a model (of how data could have been generated)
Bayesians = probability of model, given the data
3/ Most often we care about the latter question.
E.g we want to know given that the mammography test is positive, what is the probability of having breast cancer.
And not given breast cancer, probability of test being positive.
E.g we want to know given that the mammography test is positive, what is the probability of having breast cancer.
And not given breast cancer, probability of test being positive.
4/ These two questions sound similar, but have different answers.
E.g. if 80% of mammograms detect breast cancer when it’s there and ~90% come out as negative when it’s not there.
If only 1% population has breast cancer, then probability of having it given positive test is 8%
E.g. if 80% of mammograms detect breast cancer when it’s there and ~90% come out as negative when it’s not there.
If only 1% population has breast cancer, then probability of having it given positive test is 8%
5/ Read that again.
80% times the mammography test works and yet if you get a positive, your chances of having breast cancer is only 7.8%
How is it possible?
Read this simple explantion: betterexplained.com/articles/an-in…
80% times the mammography test works and yet if you get a positive, your chances of having breast cancer is only 7.8%
How is it possible?
Read this simple explantion: betterexplained.com/articles/an-in…
6/ When you understand Bayes theorem, you realise that it is nothing but arithmetic.
It’s perhaps the simplest but most powerful framework I know.
Here’s another intuitive explanation of Bayes theorem by @obonilla oscarbonilla.com/2009/05/visual…
It’s perhaps the simplest but most powerful framework I know.
Here’s another intuitive explanation of Bayes theorem by @obonilla oscarbonilla.com/2009/05/visual…
7/ The key idea behind being a Bayesian is that *everything* has a probability.
So instead of thinking in certainties (yes/no), you start thinking in chances and odds.
So instead of thinking in certainties (yes/no), you start thinking in chances and odds.
8/ Today, Bayes theorem is behind many of the apps we use daily because it helps answer questions like:
- Given an e-mail, what’s the probability of it being spam?
- Given an ad, what’s the probability of it being clicked?
- Given the DNA, is the accused the culprit?
- Given an e-mail, what’s the probability of it being spam?
- Given an ad, what’s the probability of it being clicked?
- Given the DNA, is the accused the culprit?
9/ If you’re interested in getting into the rabbit hole, go through this self study interactive guide recommended by @ESYudkowsky
arbital.com/p/bayes_rule_g…
arbital.com/p/bayes_rule_g…
10/ That’s it!
Hope you also fall in love with the Bayesian way of looking at the world.
If you have any questions, let me know. Happy to answer!
Hope you also fall in love with the Bayesian way of looking at the world.
If you have any questions, let me know. Happy to answer!
