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MrHen comments on What is Bayesianism? - Less Wrong

81 Post author: Kaj_Sotala 26 February 2010 07:43AM

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Comment author: MrHen 26 February 2010 06:49:56PM *  4 points [-]

Possible typo:

A theory about the laws of physics governing the motion of planets, devised by Sir Isaac Newton, or a theory simply stating that the Flying Spaghetti Monster pushes the planets forward>s< with His Noodly Appendage.

In the spirit of aiming low, I don't think you aimed nearly low enough. If I hadn't already read a small amount from the sequences I wouldn't have been able to pick up too much from this article. This reads as a great summary; I am not convinced it is a good explanation.

The rest of this comment is me saying the above in more detail. Do note that this is my perspective. Even a newb such as myself has been tainted with enough keywords to being inferring details that are not explicitly mentioned. This critique is massively excessive compared to the quality of the work. This means that you did a good job but I went all pesky-picky on you anyway.


You've probably seen the word 'Bayesian' used a lot on this site, but may be a bit uncertain of what exactly we mean by that. You may have read the intuitive explanation, but that only seems to explain a certain math formula.

I don't know which is a more successful way to talk to people: Using "you" or not using "you." Rephrasing those two sentences without the word, "You:"

The word "Bayesian" is used a lot on this site but it is a difficult concept to fully grasp. There is an intuitive explanation, but it focuses on the math behind the concept.

And so on. What I like about your opening:

  • Links to previous descriptions
  • Lets the reader know that the Bayesian concept is deeper than math. Math is at the core but for people who are scared of Math another way to think about the subject is possible.
  • Notes that the concept is difficult to understand because it is difficult to understand, not because the reader is an idiot

Things I don't like:

  • As much as I like the intuitive explanation, starting with Math is bad for people scared of math. Even bringing it up can shut them into a, "Oh no, I won't be able to understand this," mode. I don't know if there is a better way to say what needs to be said, however.
  • "You," in this case, is a little patronizing. Not a big deal; just a minor point.
  • Too defensive. The first couple paragraphs are trying to convince the LessWrong crowd that this explanation is needed. That is good, but the final edit should probably leave it out. The intended audience is much, much lower than that.
  • There is no mention of the Simple Truth or an equivalent starting ground. This may not be needed, but it sure helped me get into the right mindset when starting the sequences.

We'll start with a brief example, illustrating Bayes' theorem. Suppose you are a doctor, and a patient comes to you, complaining about a headache. Further suppose that there are two reasons for why people get headaches: they might have a brain tumor, or they might have a cold. A brain tumor always causes a headache, but exceedingly few people have a brain tumor. In contrast, a headache is rarely a symptom for cold, but most people manage to catch a cold every single year. Given no other information, do you think it more likely that the headache is caused by a tumor, or by a cold?

I would drop the term "Bayes' theorem" here. "We'll" is another example of, "You." This paragraph could be touched up a bit but I feel this is more me noticing that my writing style is different from yours.

I am not sold on this being a good first example. I like that it is something that most people will identify with, but the edge cases here are nuts:

  • There are more than two reasons for headaches
  • Do brain tumors always cause a headache?
  • I don't normally get headaches from colds and don't normally associate headaches with colds. When pondering why I have a headache, "colds" is pretty far down the list.
  • More than "exceedingly few" have brain tumors. A heck of a lot more people have colds but "exceedingly few" doesn't immediately translate into "more people have colds."
  • Is the type of headache from a brain tumor the same type of headache from a common cold? This doesn't matter to you, since you don't actually care about the details of the headache, but a reader may very well offer this suggestion as a solution to figuring out if the headache is from a brain tumor or a cold. People like to stick unnecessary details into examples because that is how they solve real-world examples. At this point in the article, they don't care about the example. They are imagining someone with a cold.

Given the chance, I would reword the paragraph as such:

A simple example can be found when someone asks a doctor why they have a headache. The doctor knows that a typical cold will only sometimes cause headaches. The doctor also knows that a brain tumor will almost always causes headaches. If the doctor compared these two causes and decided that it is more likely a brain tumor is at fault, then something went wrong. If you walked into a doctor's office complaining of a headache and were immediately diagnosed with a brain tumor, you would probably be a little suspicious. Bayes' theorem helps us explain what, exactly, went wrong and how to fix it. It uses math to do it, but the basic concept is easy to understand.


Do you want more of this? If not, I can stop now. If so, I can continue later. If you'd like something similar but much shorter and concise, I can do that too.

Comment author: Kaj_Sotala 26 February 2010 07:23:30PM 3 points [-]

This is excellent feedback; please, do go on.

I did wonder if this was still too short and not aiming low enough. I chose to go on the side of briefness, partially because I was worried about ending up with a giant mammoth post and partially because I felt I'd just be repeating what Eliezer's said before. But yeah, looking at it now, I'm not at all convinced of how well I'd have gotten the message if my pre-OB self had read this.

Interesting that you find the usage of "you" and "we" patronizing. I hadn't thought of it like that - I intended it as a way to make the post less formal and build a more comfortable atmosphere to the reader.

Your rewording sounds good: not exactly the way I'd put it, but certainly something to build on.

Hmm, what do people think - if we end up rewriting this, should I just edit this post? Or make an entirely new one? Perhaps keep this one as it is, but work the changes into a future one that's longer?

Comment author: MrHen 01 March 2010 06:51:36PM 5 points [-]

Continuing.

If you thought a cold was more likely, well, that was the answer I was after.

Part of the great danger in explaining a High topic is that people who haven't been able to understand High topics are super wary about looking like an idiot. Math is the most obvious High topic that people hate trying to understand. They would much rather admit to fearing math than trying and failing at understanding it.

This is sad, to me, because math isn't really that hard to understand. It is a daunting subject that never ends but the fundamentals are already understood by anyone who functions in society. They just never put all the pieces together with the right terms.

I am firmly convinced that the Way of Bayes is like this. The sequences are, for the most part, about subjects that could be easy to understand. They make intuitive sense. The details and the numbers are a pain, but the concept itself is something I could explain to nearly everyone I know. (So I think. I haven't actually tried yet.)

A sentence like the one I quoted above is one that will put a layperson on defensive. This pushes Bayesianism into the realm of High topics: Topics that are grasped by the Smart people; the intellectual elite. Asking them questions at all makes them realize they don't know the answer. This is scary. Immediately answering the question and telling them the answer should be obvious could easily make them feel awkward, even if they got the answer correct.

Articles explaining "obvious" things are often explaining not-obvious things and assume that you are following them each step of the way. These articles are full of trick questions and try to make you second guess yourself in an effort to show you what you do not know. This is scary and elitist to someone who has sold their own intelligence short.

Your example is so minor that most people wouldn't have a problem with it. I bring it up because I am picky. This is an example of aiming far, far too high. The audience at LessWrong reads a question/answer like this and enjoys it. They like learning they are wrong and revel in the introspection that follows as they chase down the error in the machine so they can fix it. A layperson dreads this. They think it means they are stupid and unable to understand. They fail at the competition of intelligence whether the competition actually exists or not.

Even if a brain tumor caused a headache every time, and a cold caused a headache only one per cent of the time (say), having a cold is so much more common that it's going to cause a lot more headaches than brain tumors do.

I think this belongs in the description of the example. You could even leave out the actual numbers because they only matter for the people that have the exact numbers. It takes too long to explain that you just made the numbers up because:

  • Every word is more processing that needs to be done
  • The intended audience are probably inexperienced at skimming these sorts of topics
  • The numbers really are irrelevant
  • Someone will disagree with the numbers and make a big stink about something that was irrelevant

Bayes' theorem, basically, says that if cause A might be the reason for symptom X, then we have to take into account both the probability that A caused X (found, roughly, by multiplying the frequency of A with the chance that A causes X) and the probability that anything else caused X. (For a thorough mathematical treatment of Bayes' theorem, see Eliezer's Intuitive Explanation.)

And... the layperson just zoned out. This is the big obstacle in trying to describe Bayesianism. Math scares people away. Even people who are good at math will glaze over when they see As and Xs and words like "probability." I have no idea how to get around this obstacle, honestly. Your attempt was solid. But I still think this is the paragraph where you will lose the lowest rung of your audience.

There should be nothing surprising about that, of course.

What if they were surprised? What if their whole world reeled at the question of what causes headaches? What if, horrifically, they completely misunderstood the previous example and are currently pondering if their headache means they have a brain tumor?

If they are completely bewildered right now, telling them they shouldn't be surprised will make them feel dumb. Even if they are dumb, your article shouldn't make them feel dumb. It should make them feel smart.

Suppose you're outside, and you see a person running. They might be running for the sake of exercise, or they might be running because they're in a hurry somewhere, or they might even be running because it's cold and they want to stay warm. To figure out which one is the case, you'll try to consider which of the explanations is true most often, and fits the circumstances best.

I don't think this example clarifies much. A bullet list:

  • "they're in a hurry somewhere" sounds funny to me. Perhaps, "they're in a hurry to get somewhere" or "they're in a hurry" works better? This could be a style thing.
  • Running because it's cold will mean random things to random people. If I am outside and its cold I don't think of running. I think of doing hard work like shoveling snow or simply going inside. The reason I bring this up is because every second someone thinks, "That's weird, why would you run outside if it's cold?" is a second that the points you made above get shoved further away from the points below.
  • To figure out which one is the case, people could think of (a) asking the runner (b) looking for more evidence. Judging which reason happens most often may not translate well. I didn't even attach this language to the headache on first read. If you know the answer you can see the relation but I am not confident that it is available for every reader.

More coming if you still want it. My lunch break is over. :)

Comment author: Kaj_Sotala 01 March 2010 08:41:57PM 0 points [-]

Very interesting. Actually, I didn't seek to aim that low - I was targeting the average LW reader (or at least an average person who was comfortable with maths). However, I still find this to be very valuable, since I have played around with the idea of trying to write a book that'd attempt to sell (implicitly or explicitly) the idea of "maths / science, especially as applied to rationality / cognitive science is actually fun" to a lay audience.

So I probably won't alter the original article as a reaction to this, but if you want to nevertheless help me in figuring out how to reach to that audience, do continue. :)

Comment author: MrHen 01 March 2010 09:20:00PM 0 points [-]

So I probably won't alter the original article as a reaction to this, but if you want to nevertheless help me in figuring out how to reach to that audience, do continue. :)

Haha, will do. I do realize that some of what I am bringing up is extremely petty, but I have watched some of my articles get completely derailed by what I would consider to be a completely irrelevant point. Even amongst the high quality discussions in the comments I find myself needing to back up and ask a Really Obvious Question.

This is likely a fault in the way I communicate (which is accentuated online) and also a glitch where people are not willing/able to drop subjects that are bugging them. If I was fundamentally opposed to the claim that all brain tumors caused headaches I would feel compelled to point it out in the comments. (This compulsion is something I am trying to curb.)

In any case, I am glad the comments are helpful and I will continue as I find the time. If you ever start drafting something like what you mentioned I am willing to proofread and comment.

Comment author: pjeby 26 February 2010 07:52:00PM 5 points [-]

Interesting that you find the usage of "you" and "we" patronizing. I hadn't thought of it like that - I intended it as a way to make the post less formal and build a more comfortable atmosphere to the reader.

Using "you" is a two-edged sword; it can create greater intimacy with your audience, but only if you know your audience well enough, and don't mind polarizing your response, or are willing to limit yourself to hypotheticals (e.g. "if you walked into a doctor's office")

If you're less certain of your audience, but still want the strong intimacy or identification response, you may want to use "I" instead. By telling a story that your reader can relate to... that is, a story of how you made this discovery, found out why it's important, or applied it in some way to achieve a goal the reader shares or recognizes as valuable, then you allow the reader to simply identify with you on a less conscious/contentious level.

(Notice, for example, how many of Eliezer's best posts begin with such a story, either about Eliezer or some fictional characters.)

Comment author: wnoise 26 February 2010 08:26:58PM 2 points [-]

Hmm, what do people think - if we end up rewriting this, should I just edit this post? Or make an entirely new one? Perhaps keep this one as it is, but work the changes into a future one that's longer?

Personally, I think if it's just minor stylistic changes in expressing the same material, editing the post is the way to go; if it's adding more material, or expressing it radically differently, then a new post is appropriate.

Comment author: h-H 27 February 2010 12:52:11AM *  0 points [-]

it's fine the way it is I think, it covers enough without being too specific. great post.