4 ms·

I'm a little confused - ergodic theory very much cares about the time average. Or do you mean the toy example of betting shouldn't care about it? It seems like

I'm a little confused - ergodic theory very much cares about the time average. Or do you mean the toy example of betting shouldn't care about it? It seems like you think the problem here is too unsophisticated for ergodic theory or something. Which, fine sure. But this isn't an article intended to teach you about betting. It's an article intended to teach you about ergodicity, using betting as a toy example. The author isn't trying to introduce the best way to analyze betting strategies, they're trying to show what non-ergodicity is. And I think they basically succeed. Just meet the article where it is, for its intended usage.

loup-vaillant 6y ago
This is not about the example. What I'm saying that no betting at all should care about the time average. Betting is about having good estimation of outcomes, and time averages only helps you when the process is ergotic. That's a very special case. For everything else (that is, non-ergotic processes), your time average is crap, and you must look at the distribution of outcomes directly. Even the ensemble average is not enough. Averages are crap at visualising skewed distributions. For those you want the median, the quartiles, sometimes even the percentiles. --- To be honest, this "ergotic theory" shows signs of snake oil. The definition of ergodicity itself is dead simple, so it's pretty easy to evaluate. What seems pretty clear is that ergodic processes are the exception. And a pretty uninteresting one at that, since it's a class of processes that people will have good intuitions about. It would then seem that ergodic theory is more interested in the non ergodic processes (the very point of this blog post is to warn us about them). That is, processes that lack some property —the general case. And surprise, since the time average and ensemble averages are different, and you only care about the ensemble average (well, the ensemble distribution really), the time average won't help you. Be afraid, or lose your assets. That's why I see snake oil: what works on non-ergodic processes will also work on the ergodic ones. Unless you need to make a split second decision using your intuition (which while inadvisable is safer with ergodic processes), there's no need to make the distinction at all. Just analyse your process without without assuming it will be ergodic, the results will be applicable even if it is.
- fractionalhare 6y ago
  You say it’s not about the example, then go on to talk about the example...as I said, this article is only about betting insofar as it’s a toy example to illustrate ergodics. In the real world you wouldn’t analyze a bet this particular way, but that’s nitpicking and missing the point. > To be honest, this "ergotic theory" shows signs of snake oil. lol. Alright, I’m checking out of the discussion when a major subfield of mathematics is described as snake oil.
  - loup-vaillant 6y ago
    > You say it’s not about the example, then go on to talk about the example I did not mention those stupid coin tosses, where did you get the impression I was talking about those specifically? > a major subfield of mathematics is described as snake oil. I did not say it was snake oil, just that it shows signs of being such. Then I described those signs. If you have counter arguments or pointers to such, I'd be happy to read them. I'd rather lose an argument and learn something than stay ignorant.

loup-vaillant 6y ago

This is not about the example. What I'm saying that no betting at all should care about the time average. Betting is about having good estimation of outcomes, and time averages only helps you when the process is ergotic. That's a very special case. For everything else (that is, non-ergotic processes), your time average is crap, and you must look at the distribution of outcomes directly. Even the ensemble average is not enough. Averages are crap at visualising skewed distributions. For those you want the median, the quartiles, sometimes even the percentiles. --- To be honest, this "ergotic theory" shows signs of snake oil. The definition of ergodicity itself is dead simple, so it's pretty easy to evaluate. What seems pretty clear is that ergodic processes are the exception. And a pretty uninteresting one at that, since it's a class of processes that people will have good intuitions about. It would then seem that ergodic theory is more interested in the non ergodic processes (the very point of this blog post is to warn us about them). That is, processes that lack some property —the general case. And surprise, since the time average and ensemble averages are different, and you only care about the ensemble average (well, the ensemble distribution really), the time average won't help you. Be afraid, or lose your assets. That's why I see snake oil: what works on non-ergodic processes will also work on the ergodic ones. Unless you need to make a split second decision using your intuition (which while inadvisable is safer with ergodic processes), there's no need to make the distinction at all. Just analyse your process without without assuming it will be ergodic, the results will be applicable even if it is.

fractionalhare 6y ago
You say it’s not about the example, then go on to talk about the example...as I said, this article is only about betting insofar as it’s a toy example to illustrate ergodics. In the real world you wouldn’t analyze a bet this particular way, but that’s nitpicking and missing the point. > To be honest, this "ergotic theory" shows signs of snake oil. lol. Alright, I’m checking out of the discussion when a major subfield of mathematics is described as snake oil.
- loup-vaillant 6y ago
  > You say it’s not about the example, then go on to talk about the example I did not mention those stupid coin tosses, where did you get the impression I was talking about those specifically? > a major subfield of mathematics is described as snake oil. I did not say it was snake oil, just that it shows signs of being such. Then I described those signs. If you have counter arguments or pointers to such, I'd be happy to read them. I'd rather lose an argument and learn something than stay ignorant.