Illustrator needed: Intuitive Bayes 2.0

by Eliezer Yudkowsky1 min read19th Jul 201113 comments


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A huge revision of The Intuitive Explanation of Bayesian Reasoning is in progress, aimed at being considerably more accessible and hence with a lot more graphics.  I need someone who can turn out versions of the illustrations that are technically accurate enough to try on beta readers, fast enough and reliably enough that I can ask for revised versions of the illustrations a day later if the beta reader says they didn't understand it.  There is a Google Doc in progress which you would be given permission to edit, containing some hand-drawn attempts on my part to indicate what the illustrations should look like, and a number of finished illustrations from an illustrator who unfortunately cannot put in any further work on this job.

For this job, technical accuracy (i.e., if a ratio is 3:4, it should not look like 1:9), understandability, and speed is much more important than beauty - the idea is to get as quickly as possible to a working version with understandable illustrations that has been verified by the beta readers.

If interested, email me at

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Not directly relevant to finding an illustrator, but relevant to designing the illustrations... did you see ? I find the Venn Diagram visualization of Bayes Theorem to be the most intuitive.

If we're plugging visualizations of Bayes, I happen to like this one. :-)

Well dang. I had some musings about how you could visualize Bayes theorem by having a grid of colored pixels and then tests would be loose-fitting circles, but I guess that works just as well.

[-][anonymous]10y 0

I was very impressed with the simplicity of the Venn diagrams. Making a more intuitive explanation of Bayes Theorem than Bonilla's won't be easy, but obviously it's a worthy cause.

A Venn Pie chart is very intuitive and shows ratios better than Venn diagrams:

Although more geared towards traditional art, you can make a post on deviantArt. Usually you will get many responses, and then you can give everyone a sample graphic that they have to do, so you can pick the best person that way. If you want, I can set this up.

I can probably help (sent an email)

By the way, are you planning to keep those java applet thingies? I didn't find them very helpful, their illustration doesn't match the one I use "internally" (or when sketching things out on paper), so I suspect they could be improved. Maybe with Venn Diagrams, as Kevin says, maybe with something else.

Edit: it looks like what I was thinking of is called an eikosogram. An interactive eikosogram shouldn't be too hard to make in javascript.

Edit2: though considering the "speed is much more important than beauty" criteria, this kind of bikeshedding on details like that is probably not the most useful.

In any case, that sort of thing could be done more elegantly with the HTML5 Canvas than with Java now (whether matching the current style or using something like Venn diagrams). Applets feel clunky.

I agree that something in javascript would be better, but it may be better to stick to "simple" stuff (with divs) rather than relying on HTML5 that all browsers don't support yet.

I don't think those technical choices are extremely important though.

This is probably the wrong place for this comment. However, this seems to be the most recent thread associated with "An Intuitive Explanation of Bayes's Theorem", so I think this is the least bad location. Unfortunately I may wind up doing this sort of thing a lot, though, as I work my way through The Sequences.

It's a fantastic piece of work, but I have a couple comments and corrections for general discussion. Maybe they are technicalities and aren't worth the trouble of changing, or maybe some are worthwhile.

1) In the egg/pearl problems, it isn’t explicitly stated that all the eggs are either painted red or blue. Similarly, it is possible, at least in the later problems, that there are some other objects in the eggs besides pearls. This means that p(pearl) + p(empty) < 1. This is not an issue in the breast cancer problems, because the reader can safely assume that a patient either has breast cancer or does not; there is no third state. A reader trained in medicine might, however, be inclined to speculate that a mammography test could also come out “inconclusive” or some such third state besides just “positive” and “negative”.

2) The section dealing with the hypothetical “Tams-Braylor” breast cancer test and likelihood ratios doesn’t explicitly show how to how to compute posterior probabilities using only the likelihood ratio and the initial probability. This new equation can be derived in a single step, but the new form of the equation is not as intuitive for me as the original, so I personally had to derive it:

p(cancer|positive) = 0.720.01/(0.720.01+[1-0.01]*0.0048)

This says that the chances of cancer among women who test positive is the % with cancer divided by the total % who test positive (that is to say, the true positives plus the false positives).

p(cancer|positive) = [0.72/0.0048]0.01/([0.72/0.0048]0.01+1-0.01)

This new equation says that the chances of cancer among women who test positive is the % cancer detections per false positive rate divided by the total % who test positive per false positive (that is to say, % cancer detections per false positive rate plus the % false positives).

Only when looking at it afterward did it start to become intuitive, even though I was able to solve all of the previous problems just by thinking about what made sense rather than plugging anything into any equation or algorithm. (Including solving the problem, using your Javascript calculator, that you said “You probably shouldn't try to solve this with just a Javascript calculator, though.”) Although forcing the reader to do a little extra thinking may be good for those who have a technical background and will be able to fill in the missing gaps, the majority of your target audience may not be confident enough in their newfound knowledge to do so. Perhaps you could get the best of both worlds by adding a small paragraph after giving the solution?

3) Perhaps it would also be useful to explicitly point out how understanding various aspects of Bayes’ theorem should prove useful in everyday life, rather than giving the reader the impression that it is merely analogous to everyday problems. This would just be a few sentences scattered throughout.

4) There isn’t a Javascript calculator for the red chip/blue chip in a backpack problem.

Eliezer, I have given your old "An Intuitive Explanation of Bayes' Theorem" a read-through some time ago, but because I'm mathematically illiterate and hardly needed to calculate anything since I left school, it was a little hard for me to understand without putting considerable effort into it. The the concept behind it stuck easily, because intuitively I have been thinking "in terms of probabilities" for a long time already, but the math didn't stick and so I still can't use it.

I have been putting off reading it again for a while now, so I'd love to give the new beta version a try.

Email sent along with examples of work. THIS came to mind as really neat and relevant: Wolfram's Computation Document Format. Downsides are that you need Mathematica to create them and that the user has to download a browser plugin; upside is that... it's just really neat and extremely fun to interact with as a user.