how much more complicated this would have been without that assumption.
I'll add a footnote mentioning it.
Speaking of this, I personally would have liked a back-of-the-envelope calculation on how much of an effect the independence assumption has on your results, maybe by differentiating between "highly competent fake" and "normal fake" hypotheses and continuing to assume independence.
I'm not sure what that calculation would look like. I don't think I've ever tried conditionals before.
I would have thought more than a footnote would have been helpful. To avoid lazy other-optimizing, I've written some content below which you may use/adapt/modify as you see fit.
The odds form of Bayes' theorem is this:
P(a|b)/P(~a|b) = P(a)/P(~a) x P(b|a)/P(b|~a)
In English, the ratio of the posterior probabilities (the posterior odds of a) equals the product of the ratio of the prior probabilities and the likelihood ratio.
What we are interested in is the likelihood ratio p(e|is-real)/p(e|is-not-real), where e is all external and internal evidence we have a...
"Who wrote the Death Note script?"
If you're already familiar this particular leaked 2009 live-action script, please write down your current best guess as to how likely it is to be authentic.
This is intended to be easy to understand and essentially beginner-level for Bayes's theorem and fermi estimates, like my other Death Note essay (information theory, crypto) or my console insurance page (efficient markets, positive psychology, expected value).
Be sure to check out the controversial twist ending!
(I'm sorry to post just a link, but I briefly thought about writing it and all the math in the LW edit box and decided that cutting my wrists sounded both quicker and more enjoyable. Unfortunately, there seems to be a math problem in the Google Chrome/Chromium browser where fractions simply don't render, apparently due to not enabling Webkit's MathML code; if fractions don't render for you, well, I know the math works well in my Iceweasel and it seems to work well in other Firefoxes.)