4 ms·

How about you guys are both right, sort of. There are both Bayesian and Frequentist approaches in statistics! They represent very different methods to statist

by qwrusz 10y ago

How about you guys are both right, sort of. There are both Bayesian and Frequentist approaches in statistics! They represent very different methods to statistics, but they are also quite similar. My apologies, I couldn't find one link that gave a good description of Bayesian vs. Frequentist. Here are a couple links to get started: https://xkcd.com/1132/ https://xkcd.com/1132/ http://jakevdp.github.io/blog/2014/03/11/frequentism-and-bayesianism-a-practical-intro/ http://jakevdp.github.io/blog/2014/03/11/frequentism-and-bay... If anyone comes across a link that describes Bayesian and Frequentist clearly, please share it if you don't mind.

lisper 10y ago
That cartoon is actually a pretty good illustration of why frequentists are wrong.
- qwrusz 10y ago
  Do you mean probably wrong? Either way I disagree. Both approaches have pros and cons depending on the type of analysis. At the very least, just the presence of competing approaches in the field has pushed statisticians to have more rigour and do way more double checking than they might have, out of fear the other side actively looking to poke holes. It's easy to lie with statistics and the only people who can call statisticians out on their BS is other statisticians...Need more of this.
  - lisper 10y ago
    > Do you mean probably wrong? Nope. > Both approaches have pros and cons What are the pros of the frequentist approach?
    - danieltillett 10y ago
      Simple maths that can be done without a computer. Useful in the past - not so useful today.
    - rspeer 10y ago
      You can justify that you did everything "by the book" and you don't have to make up priors. Now. You might read this as me saying that Bayesian statistics is all made up, and that's not what I'm saying. I'm saying that if you go Bayesian all the way, and your result is even remotely controversial, someone could easily challenge you by saying "this result would have been different with different priors, and why won't they just come out and say p < 0.01? What are they hiding?" When you do frequentist statistics, the equivalent of priors were, instead, made up for you by long scientific tradition. They're not very good priors, as the relevant xkcd illustrates. But at least it's not you making them up. In a more complex model, there's also the thing where you can't calculate the result exactly, you have to approximate it with Markov Chain Monte Carlo or something, leading to another way to doubt your results (did the MCMC converge correctly?) So instead you do frequentist statistics. You use your favorite stats package and it spits out a nice comforting p-value that will satisfy the reviewers. You have tons of guidance about how to do things. It's not a great thing, but it is a definite advantage of using frequentist statistics.
      - lisper 10y ago
        In other words: the advantage of frequentism is that it gives you better plausible deniability when you get the wrong answer. Did I get that right?
        rspeer 10y ago
        No, and I don't know where you're getting your certainty that the answer is wrong from. How about this: find me a published scientific paper with only Bayesian results in it, no frequentist statistics at all. Argue for its superiority all you want, but I don't think anyone does it. It would be seen as a stunt.
        lisper 10y ago
        Don't know about a paper, but here's a book: https://www.amazon.com/Proving-History-Bayess-Theorem-Historical/dp/1616145595 https://www.amazon.com/Proving-History-Bayess-Theorem-Histor...
    - throw_away_777 10y ago
      The main advantage of the frequentist approach is that you can do the calculations much more easily. Bayesian statistics is great, but often the calculations are much more difficult because of your distribution of priors. You can make up simplified priors to ease the calculations, but then you run into some of the same problems as frequentist statistics. Here is a simple example: lets say you flip a coin 10 times and get 8 heads, what is the probability that the coin is not fair? In frequentist statistics you only have to calculate the likelihood of the results for a null hypothesis, and then you use a p-value. While this approach is flawed, at least you can quickly do the calculation and get an approximate answer. In Bayesian statistics you have to specify the prior distribution, and calculate the likelihood of your results under every possible hypothesis. Correctly specifying this prior distribution and calculating the results is quite challenging - especially if you want to use a realistic prior (not just uniform). This is a pretty simple example, you can imagine how much more challenging this becomes in real-world problems. On the other hand, it is true that the frequentist approach doesn't really answer the question asked, so it is misleading (especially if you choose a p-value that isn't specific to the problem). If you choose p-values based on prior knowledge, than the differences between frequentist and bayesian are less extreme.
      - ska 10y ago
        > Bayesian statistics is great, but often the calculations are much more difficult because of your distribution of priors. This is often a feature, forcing you to actually look at the complexity head on before you sweep it under a rug.
      - lisper 10y ago
        A man was walking down a city street when he saw another man wandering around a lamp post looking at the sidewalk. "What are you doing?" the first man asked. "Looking for my keys," said the second man. "Oh, did you lose them around here?" asked the first man. "No," the second man replied, "but the light is better here."
        throw_away_777 10y ago
        Often times getting close to an answer that is approximately correct is better than trying to find the perfect solution. Most real world problems, especially in analyzing data, don't have perfect answers. For example approximations are made all the time in physics, because without these approximations the calculations can't be done. Knowing when to make approximations and what approximations to make is an essential skill for analyzing data.
- jcahill 10y ago
  All models are wrong. That much is entailed by 'models'. There is no Zuul.
aristus 10y ago
Frequentists count their chickens after they've hatched. Bayesians bet the chickens that they will.
stdbrouw 10y ago
There are some cases when the difference between bayesian and frequentist statistics is just a matter of interpretation, but not in this case: the mathematics for a bayesian statistical test are different from the mathematics of a frequentist statistical test and they will produce different results, because the former accounts for prior probabilities and the latter does not. The article talks about frequentist tests, as does almost everyone else who mentions statistical tests without further specification.

by qwrusz 10y ago

lisper 10y ago

That cartoon is actually a pretty good illustration of why frequentists are wrong.

qwrusz 10y ago
Do you mean probably wrong? Either way I disagree. Both approaches have pros and cons depending on the type of analysis. At the very least, just the presence of competing approaches in the field has pushed statisticians to have more rigour and do way more double checking than they might have, out of fear the other side actively looking to poke holes. It's easy to lie with statistics and the only people who can call statisticians out on their BS is other statisticians...Need more of this.
- lisper 10y ago
  > Do you mean probably wrong? Nope. > Both approaches have pros and cons What are the pros of the frequentist approach?
  - danieltillett 10y ago
    Simple maths that can be done without a computer. Useful in the past - not so useful today.
  - rspeer 10y ago
    You can justify that you did everything "by the book" and you don't have to make up priors. Now. You might read this as me saying that Bayesian statistics is all made up, and that's not what I'm saying. I'm saying that if you go Bayesian all the way, and your result is even remotely controversial, someone could easily challenge you by saying "this result would have been different with different priors, and why won't they just come out and say p < 0.01? What are they hiding?" When you do frequentist statistics, the equivalent of priors were, instead, made up for you by long scientific tradition. They're not very good priors, as the relevant xkcd illustrates. But at least it's not you making them up. In a more complex model, there's also the thing where you can't calculate the result exactly, you have to approximate it with Markov Chain Monte Carlo or something, leading to another way to doubt your results (did the MCMC converge correctly?) So instead you do frequentist statistics. You use your favorite stats package and it spits out a nice comforting p-value that will satisfy the reviewers. You have tons of guidance about how to do things. It's not a great thing, but it is a definite advantage of using frequentist statistics.
    - lisper 10y ago
      In other words: the advantage of frequentism is that it gives you better plausible deniability when you get the wrong answer. Did I get that right?
      - rspeer 10y ago
        No, and I don't know where you're getting your certainty that the answer is wrong from. How about this: find me a published scientific paper with only Bayesian results in it, no frequentist statistics at all. Argue for its superiority all you want, but I don't think anyone does it. It would be seen as a stunt.
        lisper 10y ago
        Don't know about a paper, but here's a book: https://www.amazon.com/Proving-History-Bayess-Theorem-Historical/dp/1616145595 https://www.amazon.com/Proving-History-Bayess-Theorem-Histor...
  - throw_away_777 10y ago
    The main advantage of the frequentist approach is that you can do the calculations much more easily. Bayesian statistics is great, but often the calculations are much more difficult because of your distribution of priors. You can make up simplified priors to ease the calculations, but then you run into some of the same problems as frequentist statistics. Here is a simple example: lets say you flip a coin 10 times and get 8 heads, what is the probability that the coin is not fair? In frequentist statistics you only have to calculate the likelihood of the results for a null hypothesis, and then you use a p-value. While this approach is flawed, at least you can quickly do the calculation and get an approximate answer. In Bayesian statistics you have to specify the prior distribution, and calculate the likelihood of your results under every possible hypothesis. Correctly specifying this prior distribution and calculating the results is quite challenging - especially if you want to use a realistic prior (not just uniform). This is a pretty simple example, you can imagine how much more challenging this becomes in real-world problems. On the other hand, it is true that the frequentist approach doesn't really answer the question asked, so it is misleading (especially if you choose a p-value that isn't specific to the problem). If you choose p-values based on prior knowledge, than the differences between frequentist and bayesian are less extreme.
    - ska 10y ago
      > Bayesian statistics is great, but often the calculations are much more difficult because of your distribution of priors. This is often a feature, forcing you to actually look at the complexity head on before you sweep it under a rug.
    - lisper 10y ago
      A man was walking down a city street when he saw another man wandering around a lamp post looking at the sidewalk. "What are you doing?" the first man asked. "Looking for my keys," said the second man. "Oh, did you lose them around here?" asked the first man. "No," the second man replied, "but the light is better here."
      - throw_away_777 10y ago
        Often times getting close to an answer that is approximately correct is better than trying to find the perfect solution. Most real world problems, especially in analyzing data, don't have perfect answers. For example approximations are made all the time in physics, because without these approximations the calculations can't be done. Knowing when to make approximations and what approximations to make is an essential skill for analyzing data.
jcahill 10y ago
All models are wrong. That much is entailed by 'models'. There is no Zuul.

aristus 10y ago

Frequentists count their chickens after they've hatched. Bayesians bet the chickens that they will.

stdbrouw 10y ago

There are some cases when the difference between bayesian and frequentist statistics is just a matter of interpretation, but not in this case: the mathematics for a bayesian statistical test are different from the mathematics of a frequentist statistical test and they will produce different results, because the former accounts for prior probabilities and the latter does not. The article talks about frequentist tests, as does almost everyone else who mentions statistical tests without further specification.