9 ms·

A world without statistics

36 points by johndcook 12y ago

mturmon 12y ago
I usually enjoy his posts a lot, but this one let me down. He didn't really put much thought into applications of statistics. Maybe the academic perspective is too limiting. There are lots of non-trivial problems that depend heavily on statistics for solutions. Some examples that come to mind -- signal processing (optimal detectors, say for radar or modems) medical image reconstruction (Poisson counting statistics, regularization) wireless channel allocation source/channel coding (for all radio comms) gzip (and all universal source coding) robotics (localization, object detection) Kalman filters (navigation for planes, etc.) hidden Markov models (for audio/speech processing) weather prediction, data assimilation I'm just getting warmed up. Weird post.
- nn3 12y ago
  gzip (and all universal source coding) I don't think LZW uses anything statistical. Neither Huffman encoding.
  - mturmon 12y ago
    The aim of universal source coding is to get the code rate as close to the source entropy as possible. The proof that this entropy is indeed an absolute limit is statistical (this will be in any introductory text, like Cover and Thomas, that discusses entropy of a stochastic process, i.e. a stream of symbols). And the method of analysis that shows the LZ algorithm itself approaches this limit is also statistical (http://www.cs.duke.edu/courses/spring03/cps296.5/papers/ziv_lempel_1978_variable-rate.pdf http://www.cs.duke.edu/courses/spring03/cps296.5/papers/ziv_...). One of the neat things about LZ is that the algorithm itself really doesn't have a statistical flavor, it's about building dictionaries/codebooks (as you say). But the analysis that shows it actually works is all statistical, or probabilistic, depending on how you define terms.
    - dragontamer 12y ago
      Precisely. Statistics were used in showing that LZ and Huffman Encoding were good from an entropy point of view. There were dozens of compression schemes proposed. How are you to tell which ones are better than other ones? Well... you experiment, and then measure with statistics.
- ggambetta 12y ago
  And we wouldn't have discovered the Hibbs boson, whatever it is.
  - mturmon 12y ago
    Well, you could see the code for the Kalman filter embedded in the Apollo 11 code dump the other day. "Bucy recalls that "no one was very interested in the papers originally." But then researchers at NASA latched onto the Kalman filter as a way of dealing with problems in satellite orbit determination. [...] It was used, for example, in the Ranger, Mariner, and Apollo missions of the 1960s. "In particular, the on-board computer that guided the descent of the Apollo 11 lunar module to the moon had a Kalman filter. ..." From http://www.cs.unc.edu/~welch/kalman/siam_cipra.html http://www.cs.unc.edu/~welch/kalman/siam_cipra.html
- notahacker 12y ago
  He also missed the entire industries that work on statistics (insurance, finance), which seems a bit like writing an article about "the world without computers" and not referencing the internet. The Incas ran a sophisticated and extensive civilization based on statistics (they had a tax system and central planning functions like grain redistribution policies) and maintained meticulous records of quantitative data without bothering to devise a way of writing words or managing to invent the wheel
  - rquantz 12y ago
    You could still have finance without interest. It would consist of lending money at interest based on a subjective estimation of the debtor's ability to repay. Like it used to be. Insurance is harder to imagine...
- cjslep 12y ago
  Radiation applications (medical, isotopic dating, radio, etc) Nuclear reactors The entire life of Boltzmann and the entire application of his statistical mechanics, such as molecular dynamics and chemistry Solving an engineering problem with uncertainties in data or models (ex: Monte Carlo) Some big ones I immediately thought of. Boltzmann especially would roll in his grave, since this kind of dismissal of his work at the time contributed to his suicide.
cwyers 12y ago
God, I love this post so so much. "What good are statistics? At first, I didn't think statistics were all that important. All we'd lose is most modern improvements in automobile safety, comfort and fuel efficience, the FREAKING TRANSISTOR, and possibly even Allied victory in World War 2. But then I thought about it some more, and realized that statistics really are important, not just because otherwise we'd all be driving crappy cars without modern electronics and being governed by the Nazis, but because of how it teaches us to look at the world!" Thanks, guy.
carlob 12y ago
No, seriously there is no physics to be done without statistics. Even in classical mechanics you need to repeat measures and then average, propagate the error and so on. I understand this is all some rhetorical device, but basically all of the facts he quotes about the domains I know are wrong.
- dragontamer 12y ago
  Indeed. NIST was right down the road from my university, and we were constantly reminded that "universal constants" are really just statistically measured values. There was nothing quite "Here's the value of gravity for today:" set to 15 digits, officially from NIST. Remember people, Gravity is a measured value, a _statistic_. The modern transistor in electronic circuits are also measured values. Depending on the fabrication process and other junk, every transistor on a CPU is in fact different. A huge amount of work goes towards making every transistor on a CPU work similarly to each other (as well as statistics to measure the variance). A world without statistics is a world without modern silicon computers. And I bet you that Vacuum Tubes were similarly measured and specified thanks to statistics.
  - tjgq 12y ago
    > "universal constants" are really just statistically measured values. Except for the speed of light, interestingly.
    - deleted 12y ago
      [deleted]
    - resdirector 12y ago
      http://en.m.wikipedia.org/wiki/Speed_of_light http://en.m.wikipedia.org/wiki/Speed_of_light Its value is exactly 299,792,458 metres per second because the length of the metre is defined from this constant and the international standard for time.
herge 12y ago
I disagree with the trowaway line "And without statistics we wouldn’t have modern quality control, so maybe we’d still be driving around in AMC Gremlins and the like. Scary thought, but not a huge deal, I’d think." In a world without statistics and tools for quality control, it would be immensely expensive to produce the most basic of industrial goods. How could I order a nut that would fix a specific bolt without them testing each and every nut and bolt they produce? How expensive would those nuts be if each and every one were measured individually? Or how faulty would a package be if not enough were tested and the factory had no way to guess if their manufacturing process was faulty? How can I even conceive of building a car if I cannot trust (or know how much to trust) each manufactured piece that composes it? Let alone food or medicine? The great value of the industrial revolution was repeatable processes that produced the same quality of material.
- mzs 12y ago
  I get what you are saying, but I got to tour a fastener fabrication and coating facility last year and they in fact do check every one! It was amazing, the simplest machines would sort by size using graduated rails, old tech, but most of the stations used high speed photography and computer vision to validate each one.
cyorir 12y ago
"Science would pretty much be ok." Here the author takes a very limited view of science. Specifically, genetics, neuroscience, and parts of molecular biology are completely ignored in the discussion of statistics and medicine. Sure there is a fine line between methods which are purely statistics-based and methods which have elements of analysis in common with statistics-based methods, but I think the bottom line is that much of 20th century science has depended on statistics. Since the early days of genetics, methods used in statistics have been important to genetics basically going back as far as Mendel. Earlier neuroscience, especially in the 19th century, was not so much quantitative as it was qualitative, but in the past few decades we have seen an incredible surge in the usage of statistics in neuroscience. Statistics is also important in molecular biology, although not all the time and not always in an obvious way. Statistics techniques were important in learning about basic types of molecules in the early 20th century when it wasn't clear that DNA and RNA were the key components of genetic information storage and transmission; the events leading to the development of biostatistics basically paved the way to Watson and Crick's results on the structure of DNA. Likewise, such techniques have become commonplace in chemistry in an era of computational molecular modeling. So a world without statistics would have a very different type of science (a world in which Karl Popper would probably not be so upbeat about the state of scientific knowledge...).
- darkxanthos 12y ago
  It's important to note that the author in question is one of the largest forces pushing Bayesian Statistics forward. I'm not arguing your points but just pointing out that it's arguably against his self interests to put something like this out. Again, just adding the appropriate shading for those not in the know.
  - deleted 12y ago
    [deleted]
minimax 12y ago
In a world without statistics you have none of the risk models that underpin the insurance industry and the financial system. No health insurance. No car insurance. No life insurance. No mortgages. No credit at all, really. It would not be a very friendly place.
- scottlocklin 12y ago
  Insurance companies and the financial system existed a long time before statistics.
SonOfLilit 12y ago
Science wouldn't be OK at all. Not only because he's forgetting all those other scientific discoveries that aren't Newton's or Einstein's, and not only because he's forgetting that there's a world of difference between a scientific result and the work done to get there, but also because we'd have no way to distinguish between a good scientific discovery and http://www.timecube.com/ http://www.timecube.com/ re-stated in numbers. In a world similar to our own but without statistics, probably the first thing we'd do would be to invent statistics.
analog31 12y ago
In my view, a world without statistics would be like a world without 32. Somebody would eventually fill the hole. Would that be a world without probability? Without randomness? Sets?
pdkl95 12y ago
Statistics is not only necessary, it may be one of the most applicable post-algebra subjects in math to most people. You can probably get by without knowing trigonometry, and can certainly get by without taking calculus, but basically everybody faces situations involving odds or risk everyday. Unfortunately, we barely teach the subject in public education. Bad/incorrect use of stats is incredibly widespread - even in groups usually considered "highly educated"[1]. It's even worse once you get to the stuff that can be very non-intuitive such as Bayes. Because of this widespread need, we should really inset a full class on statistics right after algebra in the high-school math schedule. [1] http://www.statisticsdonewrong.com/ http://www.statisticsdonewrong.com/

36 points by johndcook 12y ago

I usually enjoy his posts a lot, but this one let me down. He didn't really put much thought into applications of statistics. Maybe the academic perspective is too limiting. There are lots of non-trivial problems that depend heavily on statistics for solutions. Some examples that come to mind -- signal processing (optimal detectors, say for radar or modems) medical image reconstruction (Poisson counting statistics, regularization) wireless channel allocation source/channel coding (for all radio comms) gzip (and all universal source coding) robotics (localization, object detection) Kalman filters (navigation for planes, etc.) hidden Markov models (for audio/speech processing) weather prediction, data assimilation I'm just getting warmed up. Weird post.

nn3 12y ago
gzip (and all universal source coding) I don't think LZW uses anything statistical. Neither Huffman encoding.
- mturmon 12y ago
  The aim of universal source coding is to get the code rate as close to the source entropy as possible. The proof that this entropy is indeed an absolute limit is statistical (this will be in any introductory text, like Cover and Thomas, that discusses entropy of a stochastic process, i.e. a stream of symbols). And the method of analysis that shows the LZ algorithm itself approaches this limit is also statistical (http://www.cs.duke.edu/courses/spring03/cps296.5/papers/ziv_lempel_1978_variable-rate.pdf http://www.cs.duke.edu/courses/spring03/cps296.5/papers/ziv_...). One of the neat things about LZ is that the algorithm itself really doesn't have a statistical flavor, it's about building dictionaries/codebooks (as you say). But the analysis that shows it actually works is all statistical, or probabilistic, depending on how you define terms.
  - dragontamer 12y ago
    Precisely. Statistics were used in showing that LZ and Huffman Encoding were good from an entropy point of view. There were dozens of compression schemes proposed. How are you to tell which ones are better than other ones? Well... you experiment, and then measure with statistics.
ggambetta 12y ago
And we wouldn't have discovered the Hibbs boson, whatever it is.
- mturmon 12y ago
  Well, you could see the code for the Kalman filter embedded in the Apollo 11 code dump the other day. "Bucy recalls that "no one was very interested in the papers originally." But then researchers at NASA latched onto the Kalman filter as a way of dealing with problems in satellite orbit determination. [...] It was used, for example, in the Ranger, Mariner, and Apollo missions of the 1960s. "In particular, the on-board computer that guided the descent of the Apollo 11 lunar module to the moon had a Kalman filter. ..." From http://www.cs.unc.edu/~welch/kalman/siam_cipra.html http://www.cs.unc.edu/~welch/kalman/siam_cipra.html
notahacker 12y ago
He also missed the entire industries that work on statistics (insurance, finance), which seems a bit like writing an article about "the world without computers" and not referencing the internet. The Incas ran a sophisticated and extensive civilization based on statistics (they had a tax system and central planning functions like grain redistribution policies) and maintained meticulous records of quantitative data without bothering to devise a way of writing words or managing to invent the wheel
- rquantz 12y ago
  You could still have finance without interest. It would consist of lending money at interest based on a subjective estimation of the debtor's ability to repay. Like it used to be. Insurance is harder to imagine...
cjslep 12y ago
Radiation applications (medical, isotopic dating, radio, etc) Nuclear reactors The entire life of Boltzmann and the entire application of his statistical mechanics, such as molecular dynamics and chemistry Solving an engineering problem with uncertainties in data or models (ex: Monte Carlo) Some big ones I immediately thought of. Boltzmann especially would roll in his grave, since this kind of dismissal of his work at the time contributed to his suicide.

cwyers 12y ago

God, I love this post so so much. "What good are statistics? At first, I didn't think statistics were all that important. All we'd lose is most modern improvements in automobile safety, comfort and fuel efficience, the FREAKING TRANSISTOR, and possibly even Allied victory in World War 2. But then I thought about it some more, and realized that statistics really are important, not just because otherwise we'd all be driving crappy cars without modern electronics and being governed by the Nazis, but because of how it teaches us to look at the world!" Thanks, guy.

carlob 12y ago

No, seriously there is no physics to be done without statistics. Even in classical mechanics you need to repeat measures and then average, propagate the error and so on. I understand this is all some rhetorical device, but basically all of the facts he quotes about the domains I know are wrong.

dragontamer 12y ago
Indeed. NIST was right down the road from my university, and we were constantly reminded that "universal constants" are really just statistically measured values. There was nothing quite "Here's the value of gravity for today:" set to 15 digits, officially from NIST. Remember people, Gravity is a measured value, a _statistic_. The modern transistor in electronic circuits are also measured values. Depending on the fabrication process and other junk, every transistor on a CPU is in fact different. A huge amount of work goes towards making every transistor on a CPU work similarly to each other (as well as statistics to measure the variance). A world without statistics is a world without modern silicon computers. And I bet you that Vacuum Tubes were similarly measured and specified thanks to statistics.
- tjgq 12y ago
  > "universal constants" are really just statistically measured values. Except for the speed of light, interestingly.
  - deleted 12y ago
    [deleted]
  - resdirector 12y ago
    http://en.m.wikipedia.org/wiki/Speed_of_light http://en.m.wikipedia.org/wiki/Speed_of_light Its value is exactly 299,792,458 metres per second because the length of the metre is defined from this constant and the international standard for time.

herge 12y ago

I disagree with the trowaway line "And without statistics we wouldn’t have modern quality control, so maybe we’d still be driving around in AMC Gremlins and the like. Scary thought, but not a huge deal, I’d think." In a world without statistics and tools for quality control, it would be immensely expensive to produce the most basic of industrial goods. How could I order a nut that would fix a specific bolt without them testing each and every nut and bolt they produce? How expensive would those nuts be if each and every one were measured individually? Or how faulty would a package be if not enough were tested and the factory had no way to guess if their manufacturing process was faulty? How can I even conceive of building a car if I cannot trust (or know how much to trust) each manufactured piece that composes it? Let alone food or medicine? The great value of the industrial revolution was repeatable processes that produced the same quality of material.

mzs 12y ago
I get what you are saying, but I got to tour a fastener fabrication and coating facility last year and they in fact do check every one! It was amazing, the simplest machines would sort by size using graduated rails, old tech, but most of the stations used high speed photography and computer vision to validate each one.

cyorir 12y ago

"Science would pretty much be ok." Here the author takes a very limited view of science. Specifically, genetics, neuroscience, and parts of molecular biology are completely ignored in the discussion of statistics and medicine. Sure there is a fine line between methods which are purely statistics-based and methods which have elements of analysis in common with statistics-based methods, but I think the bottom line is that much of 20th century science has depended on statistics. Since the early days of genetics, methods used in statistics have been important to genetics basically going back as far as Mendel. Earlier neuroscience, especially in the 19th century, was not so much quantitative as it was qualitative, but in the past few decades we have seen an incredible surge in the usage of statistics in neuroscience. Statistics is also important in molecular biology, although not all the time and not always in an obvious way. Statistics techniques were important in learning about basic types of molecules in the early 20th century when it wasn't clear that DNA and RNA were the key components of genetic information storage and transmission; the events leading to the development of biostatistics basically paved the way to Watson and Crick's results on the structure of DNA. Likewise, such techniques have become commonplace in chemistry in an era of computational molecular modeling. So a world without statistics would have a very different type of science (a world in which Karl Popper would probably not be so upbeat about the state of scientific knowledge...).

darkxanthos 12y ago
It's important to note that the author in question is one of the largest forces pushing Bayesian Statistics forward. I'm not arguing your points but just pointing out that it's arguably against his self interests to put something like this out. Again, just adding the appropriate shading for those not in the know.
- deleted 12y ago
  [deleted]

minimax 12y ago

In a world without statistics you have none of the risk models that underpin the insurance industry and the financial system. No health insurance. No car insurance. No life insurance. No mortgages. No credit at all, really. It would not be a very friendly place.

scottlocklin 12y ago
Insurance companies and the financial system existed a long time before statistics.

SonOfLilit 12y ago

Science wouldn't be OK at all. Not only because he's forgetting all those other scientific discoveries that aren't Newton's or Einstein's, and not only because he's forgetting that there's a world of difference between a scientific result and the work done to get there, but also because we'd have no way to distinguish between a good scientific discovery and http://www.timecube.com/ http://www.timecube.com/ re-stated in numbers. In a world similar to our own but without statistics, probably the first thing we'd do would be to invent statistics.

analog31 12y ago

In my view, a world without statistics would be like a world without 32. Somebody would eventually fill the hole. Would that be a world without probability? Without randomness? Sets?

pdkl95 12y ago

Statistics is not only necessary, it may be one of the most applicable post-algebra subjects in math to most people. You can probably get by without knowing trigonometry, and can certainly get by without taking calculus, but basically everybody faces situations involving odds or risk everyday. Unfortunately, we barely teach the subject in public education. Bad/incorrect use of stats is incredibly widespread - even in groups usually considered "highly educated"[1]. It's even worse once you get to the stuff that can be very non-intuitive such as Bayes. Because of this widespread need, we should really inset a full class on statistics right after algebra in the high-school math schedule. [1] http://www.statisticsdonewrong.com/ http://www.statisticsdonewrong.com/