4 ms·

No, the hardest part is realizing that there are all kinds of tacit assumptions that we bring to bear merely by formulating a problem for Bayesian analysis. Ta

by lisper 4y ago

No, the hardest part is realizing that there are all kinds of tacit assumptions that we bring to bear merely by formulating a problem for Bayesian analysis. Take the example used in chapter 2 of the book. It assumes that news articles can be classified as "real" or "fake", and there is no middle ground. It assumes that the initial prior produced by experts is reliable. And most of all it assumes that certain features, like exclamation points in the title, are causally related to realness or fakeness. To illustrate this last point, consider analyzing the titles for a different features, the presence of the letter "z" rather than the presence of exclamation points. If it turned out that fake news in the corpus used to generate the priors just turned out to have more zees in their titles, would you then be justified in concluding that a news article about Zanzibar was more likely to be fake because it contained two zees? That example might seem contrived, but if you use a Bayesian spam filter it is actually plausible that the presence of the letter "v" is dignostic of spam because of the prevalence of spam concerning viagra. But again, there is a causal model of this: viagra is a product that is often the subject of spam marketing, and the word "viagra" happens to have a v in it, which is a priori an uncommon letter in English. But all this can fall apart depending on the circumstances. If you one day joined an email discussion of Stradavarius violins, the v signal could suddenly fail. An even more dramatic example: suppose you are an academic who starts to do research on spam filters and you have a collaborator who starts to send you examples of hard-to-filter spam. Now you have a very strong signal, but no straightforward textual analysis will allow you to extract it. The hard part of Bayesian analysis is deciding what features to even look at. All the rest is borderline trivial by comparison.

bumby 4y ago
>the hardest part is realizing that there are all kinds of tacit assumptions that we bring to bear merely by formulating a problem for Bayesian analysis. I think the common argument is this is a strength of Bayesian analysis. Namely, that your priors make you explicitly state your assumptions. All models integrate assumptions, but not all of them make you explicitly quantify them like Bayesian analysis does.
- nerdponx 4y ago
  This was my experience as well, and it's why I recommend learning Bayesian stats to any student of data analysis and statistics. I find that learning how to set up Bayesian models has a strong elucidating effect on model-building in general.
nequo 4y ago
> would you then be justified in concluding that a news article about Zanzibar was more likely to be fake because it contained two zees? I completely agree with you about hidden assumptions. But I don’t think that causal thinking is one of the problems here. Bayes’ rule applies whether or not the relationship between X and Y is causal. Bayes’ rule is a predictive model and prediction does not need causation. The problem in the Zanzibar example is that the model is misspecified. Or at least the model specification does not represent how you as a human being with cultural knowledge think about the problem. You look at Zanzibar and see an island in Tanzania. Your model looks at Zanzibar and sees two a’s and two z’s and a few other letters. So it is the wrong implicit assumption about the underlying model that’s giving you “non-sensical” results.
- lisper 4y ago
  > the model is misspecified... it does not represent how you as a human being with cultural knowledge think about the problem Yes, that is exactly my point. The way "you as a human with cultural knowledge think about the problem" is a major component of Bayesian analysis. The math is almost incidental. By the time you have chosen what features to do the math on, most of the heavy lifting has already been done. This matters because if you just crunch the Bayesian numbers on an arbitrary data set you will almost certainly find features that appear predictive but are not. The more numbers you crunch, the more likely this is to happen. A lot of people lose money in the stock market this way.
  - nequo 4y ago
    Much agreed. Data analysis needs a good theory.
  - harry8 4y ago
    > A lot of people lose money in the stock market this way. This sounds extremely plausible to me. I'd like to use it as an example in something, any data to back it up?
    - kadoban 4y ago
mturmon 4y ago
You’re making an interesting point here. I’m resistant to it because some analysis I do (say, inferring atmospheric composition from the spectra of light you shine through the atmosphere) does fit rather well in the Bayesian setup. In a very real sense, if you are doing a bunch of these inversions and not using Bayesian methods, you are leaving RMSE on the table. Here, the “features” are the spectra you sense and you add some basic prior information based on historical expectations. You don’t have that much wiggle room to invent new variables to confuse the analysis. But the situation changes if you have woolier problems with human judgement in finding “features” — the variables in the prior or likelihood in the spam example you give. And you can fool yourself badly! E.g., to go with your market example, I have two models for the stock market, and 1 month of historical data strongly favors model 1 over model 2, so I bet heavily on model 1 as if that’s the only possibility. But it wasn’t, and I lose. The area of causal inference uses a slightly different set of tools that gets outside the Bayesian setup, including the Do() operator, which allows for manual intervention to probe the linkages in systems like these. There’s a lot of activity there as we’re looking for systems that learn reliably. I don’t know if you listen to podcasts, but Judea Pearl was recently on Sean Carroll’s (excellent) Mindscape podcast. They discuss this at some length, it was very nice. https://www.preposterousuniverse.com/podcast/2022/05/09/196-judea-pearl-on-cause-and-effect/ https://www.preposterousuniverse.com/podcast/2022/05/09/196-... PS: it’s enjoyable to see your comments here.
- lisper 4y ago
  Hi Mike! :-) Thanks for the kind words. I don't know much about atmospheric science, but the canonical "real" example of Bayesian reasoning is a diagnostic test for some disease, where you are told that X% of the population has the disease, where X is typically a small number, so the "surprising" result is that your odds of having the disease are low even if you test positive and the test is generally accurate. The problem is: how can you possibly know what percentage of the population has the disease? To determine that you'd need a reliable test, but there is no such test. That's the whole point! If there were a 100% reliable test you wouldn't need to do any math.
  - mturmon 4y ago

by lisper 4y ago

bumby 4y ago

>the hardest part is realizing that there are all kinds of tacit assumptions that we bring to bear merely by formulating a problem for Bayesian analysis. I think the common argument is this is a strength of Bayesian analysis. Namely, that your priors make you explicitly state your assumptions. All models integrate assumptions, but not all of them make you explicitly quantify them like Bayesian analysis does.

nerdponx 4y ago
This was my experience as well, and it's why I recommend learning Bayesian stats to any student of data analysis and statistics. I find that learning how to set up Bayesian models has a strong elucidating effect on model-building in general.

nequo 4y ago

> would you then be justified in concluding that a news article about Zanzibar was more likely to be fake because it contained two zees? I completely agree with you about hidden assumptions. But I don’t think that causal thinking is one of the problems here. Bayes’ rule applies whether or not the relationship between X and Y is causal. Bayes’ rule is a predictive model and prediction does not need causation. The problem in the Zanzibar example is that the model is misspecified. Or at least the model specification does not represent how you as a human being with cultural knowledge think about the problem. You look at Zanzibar and see an island in Tanzania. Your model looks at Zanzibar and sees two a’s and two z’s and a few other letters. So it is the wrong implicit assumption about the underlying model that’s giving you “non-sensical” results.

lisper 4y ago
> the model is misspecified... it does not represent how you as a human being with cultural knowledge think about the problem Yes, that is exactly my point. The way "you as a human with cultural knowledge think about the problem" is a major component of Bayesian analysis. The math is almost incidental. By the time you have chosen what features to do the math on, most of the heavy lifting has already been done. This matters because if you just crunch the Bayesian numbers on an arbitrary data set you will almost certainly find features that appear predictive but are not. The more numbers you crunch, the more likely this is to happen. A lot of people lose money in the stock market this way.
- nequo 4y ago
  Much agreed. Data analysis needs a good theory.
- harry8 4y ago
  > A lot of people lose money in the stock market this way. This sounds extremely plausible to me. I'd like to use it as an example in something, any data to back it up?
  - kadoban 4y ago

mturmon 4y ago

You’re making an interesting point here. I’m resistant to it because some analysis I do (say, inferring atmospheric composition from the spectra of light you shine through the atmosphere) does fit rather well in the Bayesian setup. In a very real sense, if you are doing a bunch of these inversions and not using Bayesian methods, you are leaving RMSE on the table. Here, the “features” are the spectra you sense and you add some basic prior information based on historical expectations. You don’t have that much wiggle room to invent new variables to confuse the analysis. But the situation changes if you have woolier problems with human judgement in finding “features” — the variables in the prior or likelihood in the spam example you give. And you can fool yourself badly! E.g., to go with your market example, I have two models for the stock market, and 1 month of historical data strongly favors model 1 over model 2, so I bet heavily on model 1 as if that’s the only possibility. But it wasn’t, and I lose. The area of causal inference uses a slightly different set of tools that gets outside the Bayesian setup, including the Do() operator, which allows for manual intervention to probe the linkages in systems like these. There’s a lot of activity there as we’re looking for systems that learn reliably. I don’t know if you listen to podcasts, but Judea Pearl was recently on Sean Carroll’s (excellent) Mindscape podcast. They discuss this at some length, it was very nice. https://www.preposterousuniverse.com/podcast/2022/05/09/196-judea-pearl-on-cause-and-effect/ https://www.preposterousuniverse.com/podcast/2022/05/09/196-... PS: it’s enjoyable to see your comments here.

lisper 4y ago
Hi Mike! :-) Thanks for the kind words. I don't know much about atmospheric science, but the canonical "real" example of Bayesian reasoning is a diagnostic test for some disease, where you are told that X% of the population has the disease, where X is typically a small number, so the "surprising" result is that your odds of having the disease are low even if you test positive and the test is generally accurate. The problem is: how can you possibly know what percentage of the population has the disease? To determine that you'd need a reliable test, but there is no such test. That's the whole point! If there were a 100% reliable test you wouldn't need to do any math.
- mturmon 4y ago