Previous discussion: https://news.ycombinator.com/item?id=15619541
Again, simple summaries of complex things removes nuance.
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#12That gif is wildly intriguing to me. Probability theory is the bread and butter of mainstream science. Have people been doing it wrong this whole time? I want to dig deeper into this but two things come to mind: 1. George Sugihara's and Floris Takens' works on quantifying causation in non-linear systems. Correlation doesn't imply causation, so why not look at causation? Here's a writeup on it: https://www.quantamagaz…
I'm a bit slow today but I'm not sure I got what the GIF was about. It is well known that the mean (1st moment) and stdev/variance (2nd moment) are insufficient to uniquely describe an arbitrary probability distribution except in the case of the normal distribution.
Therefore it shouldn't be surprising that that you can find probability distributions that share the first two moments, but differ wildly in the higher moments (skewness, kurtosis) or even the number of modes (bimodal, trimodal, etc.).
Not everything in the world is Gaussian, but we knew that.
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#13True, probability theory is merely a tool among many and shouldn't be used to attempt to solve every problem there is.
However, the article is misleading about the initial gif being any sort of argument against Bayesian probabilistic approaches, as it's precisely an argument for them. It's an argument against using point estimates and summary stats, as they obviously loose a lot of information and can be misleading (you can get the intuition from a CS perspective as well: compressing a 2D image into 4 numbers is necessarily an extremely lossy compression). Fully Bayesian approaches would maintain the distributions all the way through the calculations, rather than collapse them at some point to one or a few numbers summarizing the distribution.
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#14That gif is wildly intriguing to me. Probability theory is the bread and butter of mainstream science. Have people been doing it wrong this whole time? I want to dig deeper into this but two things come to mind: 1. George Sugihara's and Floris Takens' works on quantifying causation in non-linear systems. Correlation doesn't imply causation, so why not look at causation? Here's a writeup on it: https://www.quantamagaz…
I'm not sure why that gif is so interesting to you; that wasn't the reason I submitted this piece. Average and standard deviation are hardly useful data points in evaluating a dataset, and also don't have anything to do with probability theory. The second half of the post contains the bulk of its interesting content (as I read it).
Maybe I'm missing something? To me, that gif illustrates sets of samples that are on the surface compatible with the the same Gaussian distribution, even if a Gaussian distribution is "obviously" lacking.
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#15Earlier quoted context omitted.
I'm not sure why that gif is so interesting to you; that wasn't the reason I submitted this piece. Average and standard deviation are hardly useful data points in evaluating a dataset, and also don't have anything to do with probability theory. The second half of the post contains the bulk of its interesting content (as I read it).
Maybe I'm missing something? To me, that gif illustrates sets of samples that are on the surface compatible with the the same Gaussian distribution, even if a Gaussian distribution is "obviously" lacking.
I think 0xBABAD00C's comment is on the money. The gif is almost a non-sequitur and does not seem to support the conclusion the article is trying to reach.
The second part of the article makes a claim that is worth discussing -- that probabilistic inference does not work well in nonlinear domains.
I think this is true in one sense, but in many practical situations we can usually to get something to work well enough for it to be useful. Assuming we can (approximately) split up the domain into multiple regions and get probability distributions for each region (with transition functions between them), we can continue to make inferences under nonlinearity. That said, this is a concession. Perhaps there are techniques in deep learning that more general in nature.