Controversial opinion: Bayes Theorem is overrated. In real life usually we have no idea about priors, and we have close to zero chance to get any good estimate of the true probability of something. But we can still get by fine for the most part, by focusing on limiting possible loss and staying on the safe side with large margins.
Many of the claimed cognitive biases go away under this view. One textbook example of Bayes theorem is how doctors overestimate the probability of being positive for a disease. But what are the priors? Maybe those who visit the doctor did something risky the day before or are feeling funny. Maybe the cost of false positive is negligible compared to the cost of a false negative, etc. People are less stupid than what the TED talk crowd claims.
It's a cheap trick to start an argument with "controversial opinion" or any other similar phrase.
The funny truth in this case is that it's not only cheap, but a factual counterpoint to your argument:
By stating that what is to follow is controversial, you give a prior to reading your argument. So that when the reader evaluates it, he already does so from the perspective that it's controversial and thus one shouldn't be too harsh in criticizing it further. This is the real life application of the Bayes theorem from the author of the linked article.
You see? You say it's overrated. But you use it anyway.
So the next time you try to shield yourself from critique, try to build a better argument.
> when the reader evaluates it, he already does so from the perspective that it's controversial
He does so from the perspective that the author believes it's controversial. If you are required to actually assume the opinion is controversial because the author said so, I'd start every paragraph with "you owe me money".
How is explicating the prior an advantage? If the prior is arbitrary anyways you could also stick to your unknown prejudice. This shouldn't change any results and if it does you are in trouble anyways, no matter if you explicitly state your prejudice. I'm still suspecting that Bayesian statistics is just kind of a hack to make results look more convincing.
But, this might be negative, because you can’t consciously tweak an unknown prejudice. But, you can tweak a prior until your results support your hypothesis. In that sense, Baysian statistics might be more transparent, but less honest.
True, but the question is if transparency is desirable. I would say it is dangerous for three reasons. First, you might be tempted to tweak your prior until your posterior confirms your hypothesis. Second, using Bayesian reasoning, you make it seem that the first procedure is justified. And third, if everyone does the tweaking for example within in a scientific community, nobody would complain, since everyone automatically would confirm their hypothesis with higher posterior probability.
If by prior you just mean "I know something about it" or "everything happens in context"; then that fine. But if thats what you mean then a diminishingly small number of events have "priors" which can be expressed in a neat analytical form, or be approximated, or even be quantified. This is part of the problem of frame and context that ML v1.0 tried hard to solve.
Recall as well that in the Bayesian approach the model itself is not subject to Bayesian updating: its part of your prior. Except that you never update it. So youre not merely choosing how to update parameters given data; you're also choosing what you're not going to update.
There is always a prior only if you really care about computing probabilities. The implicit assumption in Bayesian data analysis is that you go first to "best possible estimate of probability", then to "decision based on that". My point was that you usually need not do the first step.
Example: I wear a bicycle helmet because it costs me next nothing and it possibly saves my life. I don't do any Bayesian analysis implicitly or explicitly, because on one side there is an outcome with value minus infinity, so it hardly matters what probability I multiply it with.
You don't need to think hard about massively asymmetric payoffs.
Now what if you needed a something like a $5k licence to wear the helmet. Would you feel like thinking harder and analysing further than you did? Most interesting decisions are more like this.
"Possibly saves my life" is your prior there, btw.
Bayes Theorem is one of the most fundamental theorems in the history of mathematics. I have yet to work in a field where it doesn't have deeply fundamental applications. In many cases expert knowledge or heuristic rules serve as prior.
Saying it is overrated is like saying sun or air is overrated.
But hyperbole aside, OP also has a point. If we forget that the estimation of probability in itself has a cost, we could be tempted to put more and more resources into more and more sophiticated methods of data collection and analysis to be more and more certain of your estimate. But if we remember that this process has a cost, some times it's more efficient to just add a margin of safety and move on with your life. Bayes theorem is often used for resource allocation, but the process of optimizing resource allocation in itself has a cost.
I agree with the first part. We get by fine for the most part by our own intuitions driven by fear and risk aversion. We are constantly triggered into action, not persuaded -- not by ourselves or anyone. But I think the blog here is a call to be more rational. I would consider Bayes another tool out of many. Unfortunately that doesn't change how we are though. We're still hungry and trigger driven at the end of the day.
Which is why I disagree with the other thing you said. People are pretty stupid. To think you know anything without prior research is stupid. Priors need to be deliberately created (act of learning and understanding and internalizing) for a guess to be educated. Anything without we default to stupid, so most of us are stupid with most things.
But just getting by is an incredibly low bar. We have been tested however with the covid situation. But take covid. Mask wearing isn't a "priors" issue. It's the understanding of what a mask does and how it influences risk that is important. You don't need authority to understand the benefits of a mask, though once understood, it would definitely fall under "staying on the safe side with large margins".
That's an interesting response, thanks! I think where I disagree is that I think people are pretty smart, at least in one thing, which is survival -- the proof of that is that those who were not, quickly exited the gene pool. That is a powerful filtering that tunes our estimators.
I agree with your last paragraph, but I think it supports my point. I wear a mask because it has zero cost, and it may save my life. When I took this decision, I didn't estimate any probabilities and I haven't used Bayes theorem. Understanding what a mask does exactly and how aerosol transmission of viruses work precisely is almost irrelevant to my decision -- I could be improving my knowledge ("my priors") by studying virology, but there would still be so many uncertainties, that it would hardly influence my decision.
> In real life usually we have no idea about priors
Priors are your previous knowledge on the topic.
> One textbook example of Bayes theorem is how doctors overestimate the probability of being positive for a disease. But what are the priors?
In this example, doctors overestimate precisely because they don't take the priors into account.
Doing something risky the day before / feeling funny is extra evidence that is assimilated (or should be) into the likelihood ratio P(D|H) / P(D). This is information the patient should share with the doctor.
Of course, if they don't, then the Bayes estimate is the best guess given all the information the doctor has.
Edit: Your criticism about how we choose priors is fair. The better you are at this, the more accurate your answers become. I mention more about this in the "putting it to practice" section.
I agree with you, but my point is more broadly that in reality we often don't go through the steps "1. estimate probability" -> "2. make a decision based on the probability distribution", because step 1. is so error-prone and intractable, that we typically jump directly to step 2. and try to limit our downside.
Of course you could look back and say, given the fact that I took some decision, what would have been my prior if I had used Bayes theorem, but my point is that we don't actually use it for taking the decision.
While I think it's fair to say that it's hard to come up with informative priors for many real problems, the Bayesian framework is pretty robust if you use weakly informative priors
Imagine a world where a gun sold is by the US to a poor wartorn nation. When the trigger is pulled, it does facial recognition to figure out who it is aimed at, and if it detects someone friendly to US interests, it will refuse to hit them.
That integrity of the West during and before the cold war included some nasty moves as well (Vietnam to name one). In fact, I find your thesis jingoism at its best.
Yet sidewalks in cities around most of the developed world drown in dog/cat poop and pee, something that would have seemed strange a generation ago, and still seems if you travel from a less pet-crazy place.
I highly doubt this is true. I've never lived in a place outside of the developed world, but I also have never lived or visited a place where the sidewalks drowned in dog/cat poop and pee. In fact, I've never actually watched a cat pee on the sidewalk in places where it cannot be covered up, simply because that's not how cats tend to act.
Where are you getting your information from?
How much have you traveled?
What is your definition of city?
Do you have some proof?
I lived in France for 10 years, virtually nobody picked up waste from their pets. Just wasn't a cultural norm. Not necessarily that different in Italy or Spain as well.
I remember noticing the same in Marseille about 10 years ago, but Paris for example was already quite different back then.
Now I live in Madrid and not picking up after your dog is very much frowned upon, and you see very little pet waste in the streets.
To be fair, the French men also routinely pee on buildings and alleys in public. Your observations of Spain puzzle me though. I always found the Spanish to be exceptionally festidious people with remarkably clean streets.
In Portland, OR, it rarely snows much, but the weeks when we do get a good storm, oh god, there's dog piss everywhere. & then you realize that people are probably walking their dog less now that it's all slippery & cold + that there's probably usually even more dog piss everywhere then what you can now see thanks to the snow.
spent a few months in Athens. Dog shit was everywhere. Greeks don't seem to be the type to pick up after their pets and it was incredibly gross.
I'm in kyiv now and despite seeing more dogs, I have yet to see any such droppings. I guess people are more fastidious about cleaning up after their animals in public places.
In my building we have to put trash bins out in the alley, and people always throw dog shit in those on trash day, too.
I'm not exactly sure where else folks are supposed to put the dog shit except in the trash, honestly. I know people complain about putting shit in their personal trash cans, mind you, but folks are going to put it in a trash can somewhere, even if it is in their own home. And some of those are going to put their trash in the alley.
Do you have a suggestion that doesn't include putting the poop in the trash?
The city has public trash cans on the corner, with bags in them. So you throw your little baggie of dog shit in it, the city collects the bag, and the dog shit is gone.
My trash bin (large, wheeled, plastic variety that lives in an enclosure on the bottom floor of my building) is full of my domestic trash, in several bags, and is not itself lined with a bag. City comes, empties out my bin, it's now an in-theory empty plastic bin. Someone throws a baggie of dog shit in, it just goes to the bottom. It rains, and now there's a slurry of dog shit water in the bottom of my trash bin and it's there forever because my building doesn't have a hose for me to hose it out, nor is there a designated drain for collecting shit water, nor do the city trash collectors upend the bin into the garbage truck - they just grab the bags out and leave the shit-slurry where it lies.
So my suggestion is ... walk to the fucking city trash can literally a half-block away and throw your dog shit in there instead into a domestic trash bin with no bags in it.
Luckily I'm moving the fuck out of this building / neighborhood in December. Wonder what the other tenants will do when they realize no one is putting the building's bins out now...
Really? I have very rarely seen dog dirt here in Germany.
We've got bag dispensers in parks here where dog owners can get bags if they haven't brought any for example.
I live in Berlin. I think it's too dirty and we should do more about it. I don't perceive dogs as a major problem. (My gut feeling would be the top problems are cigarette buds, trash from grilling parties and bottles from alcoholic beverages.)
I agree that in Berlin it is not as _major_ problem as in some other large cities, but still, it is telling that it is widely accepted as normal that all building corners that face the sidewalk are constantly pissed by dogs with the coloring of the walls clearly visible everywhere. As for poop, 90% of the times people pick it up, the rest can still ruin your day if you step into it.
I can tell that this comment has been downvoted, and I don't think it's fair to downvote people with first hand, daily lived experiences.
Perhaps it sheds additional light on the matter - a denizen of Berlin doesn't think the dogs are a problem. This idea both supports and undermines the parent thread's idea under discussion depending on how you take it, but it certainly adds color to it.
Yes. Inhabitants usually get used to it and deny the problem. But Having been to Berlin in a snowy winter, the number of brown and yellow spots dotting the freshly snowed-in sidewalk within hours is very impressive in a negative way. Other german cities are far less bad in this regard (but I didn't visit all of them).
Are they well stocked, too? We've got plenty of those around Paris, especially close to parks and green squares. They often look empty. And in any case, people don't seem to have their own bags either.
I don't have hard numbers, but it's generally a good idea to look where you step on the sidewalks. Although it's true that subjectively it seems somewhat better than a 5-10 years ago.
maybe the humans are parasites on the dogs, although seeing the humans throw out the poop later would certainly complicate the graph of life the aliens were developing for our planet.
You can encode as moderately large (low hundreds of clauses/variables) SAT instances questions of Ramsey-theory and other unsolved combinatorics and those instances will not be solved by any heuristic.
Many of the claimed cognitive biases go away under this view. One textbook example of Bayes theorem is how doctors overestimate the probability of being positive for a disease. But what are the priors? Maybe those who visit the doctor did something risky the day before or are feeling funny. Maybe the cost of false positive is negligible compared to the cost of a false negative, etc. People are less stupid than what the TED talk crowd claims.