10 ms·

I still can't believe that they are using statistically safer in an official response. It now have been widely discussed everywhere that 1 occurrence is not eno

by Twisell 10y ago

I still can't believe that they are using statistically safer in an official response. It now have been widely discussed everywhere that 1 occurrence is not enough to draw any reliable statistical conclusion! PS: Beside should one more fatalities occur soon, by they're own standard, Model S would become statistically more deadful. To much risk of backfire, this PR is madness...

agildehaus 10y ago
That they are using it in official statements should tell you exactly how intelligent Tesla is being with self-driving technology. This is also the company that thinks level 4 self-driving can be done without LIDAR. They're idiots, frankly, completely ignoring the difficulties of computer vision (both in computation and optics) that will not be overcome anytime soon. Even their fatality seems to have been rooted in their camera's inability to distinguish the color of the truck from the color of the sky. Tesla hasn't even taught a car to navigate an intersection on its own, much less all the things Google's car is capable of these days. I think what all this shows is the importance of regulators getting off their asses and establishing standards for self-driving vehicles. Perhaps the fatality was the event that will get them in gear. Poor guy.
- _up 10y ago
  Probably because "Our cars are super safe, if in perfect weather conditions, otherwise you are on your own", wouldn't sell very well outside of California.
yummyfajitas 10y ago
That's not really true. Using a beta distribution model (i.e. treating each mile driven as a single event), we can say that with 99% probability the true accident rate is at least 1/1B miles and no more than 7/100M miles. Before the accident occurs, these numbers were 1/100B miles and 5.3/100M miles. If a second fatality occurred, those numbers would increase to 3.4/1B miles and 9.3/100M miles. However, I'm pretty sure that their claims of safety are based on more than just this calculation: "...a wealth of internal data demonstrating safer, more predictable vehicle control performance..." 100M miles of driving is easily enough time to observe things like fewer near misses, greater distance between the Tesla and other cars, etc. In math terms, what Tesla is most likely doing is working off some model relating driving behavior with accident rates and observing that 1 single accident does not invalidate this model.
- emn13 10y ago
  What are you basing that on? Looks like you've misplaced the decimals there someplace, because you're concluding that the likely rate is around 1/10 of the observed rate. Depending on your priors, you can get some difference of course, but that sounds absurd - can you more precisely explain the method you used to arrive at that conclusion?
  - yummyfajitas 10y ago
    Take a uniform prior for gamma = fatality probability | drive one mile. Use Bayes rule. Here is a tutorial: https://www.chrisstucchio.com/blog/2013/bayesian_analysis_conversion_rates.html https://www.chrisstucchio.com/blog/2013/bayesian_analysis_co... Finding that the lower end of a credible interval close to zero is an order of magnitude below the top end is pretty common. It just means you need more data, that the beta hasn't approached a gaussian yet.
    - GFK_of_xmaspast 10y ago
      Some people, when their posterior doesn't match the facts, update their prior.
      - yummyfajitas 10y ago
        Are you asserting that the posterior I described doesn't match the facts? If so, can you explain?
    - emn13 10y ago
      More detail; you're assuming a binomial likelihood function? What exactly is "uniform prior for gamma" supposed to mean?
      - yummyfajitas 10y ago
        Please go read the tutorial I linked to. It explains exactly how this analysis works. Here's the code: In [1]: from scipy.stats import beta In [2]: from numpy import percentile In [3]: data = beta(1, 100e6+1).rvs(1e7) In [4]: percentile(data, 0.5), percentile(data, 50), percentile(data, 99.5) Out[4]: (5.0460240722165642e-11, 6.9295652915902601e-09, 5.3005747758871231e-08)
TeMPOraL 10y ago
> I still can't believe that they are using statistically safer in an official response. It now have been widely discussed everywhere that 1 occurrence is not enough to draw any reliable statistical conclusion! They probably mean that 1 occurrence is not enough to invalidate a statistical model built on wealth of other data.
- emn13 10y ago
  Except that the other data is certainly suspect. I mean - what other source of realistic data can they possibly have that is realistic enough and large enough to be more significant that 100000000 miles of actual usage? At this level, it's the odd, unpredictable events that are going to get you, and whatever models they have cannot include all of those.

by Twisell 10y ago

agildehaus 10y ago

That they are using it in official statements should tell you exactly how intelligent Tesla is being with self-driving technology. This is also the company that thinks level 4 self-driving can be done without LIDAR. They're idiots, frankly, completely ignoring the difficulties of computer vision (both in computation and optics) that will not be overcome anytime soon. Even their fatality seems to have been rooted in their camera's inability to distinguish the color of the truck from the color of the sky. Tesla hasn't even taught a car to navigate an intersection on its own, much less all the things Google's car is capable of these days. I think what all this shows is the importance of regulators getting off their asses and establishing standards for self-driving vehicles. Perhaps the fatality was the event that will get them in gear. Poor guy.

_up 10y ago
Probably because "Our cars are super safe, if in perfect weather conditions, otherwise you are on your own", wouldn't sell very well outside of California.

yummyfajitas 10y ago

That's not really true. Using a beta distribution model (i.e. treating each mile driven as a single event), we can say that with 99% probability the true accident rate is at least 1/1B miles and no more than 7/100M miles. Before the accident occurs, these numbers were 1/100B miles and 5.3/100M miles. If a second fatality occurred, those numbers would increase to 3.4/1B miles and 9.3/100M miles. However, I'm pretty sure that their claims of safety are based on more than just this calculation: "...a wealth of internal data demonstrating safer, more predictable vehicle control performance..." 100M miles of driving is easily enough time to observe things like fewer near misses, greater distance between the Tesla and other cars, etc. In math terms, what Tesla is most likely doing is working off some model relating driving behavior with accident rates and observing that 1 single accident does not invalidate this model.

emn13 10y ago
What are you basing that on? Looks like you've misplaced the decimals there someplace, because you're concluding that the likely rate is around 1/10 of the observed rate. Depending on your priors, you can get some difference of course, but that sounds absurd - can you more precisely explain the method you used to arrive at that conclusion?
- yummyfajitas 10y ago
  Take a uniform prior for gamma = fatality probability | drive one mile. Use Bayes rule. Here is a tutorial: https://www.chrisstucchio.com/blog/2013/bayesian_analysis_conversion_rates.html https://www.chrisstucchio.com/blog/2013/bayesian_analysis_co... Finding that the lower end of a credible interval close to zero is an order of magnitude below the top end is pretty common. It just means you need more data, that the beta hasn't approached a gaussian yet.
  - GFK_of_xmaspast 10y ago
    Some people, when their posterior doesn't match the facts, update their prior.
    - yummyfajitas 10y ago
      Are you asserting that the posterior I described doesn't match the facts? If so, can you explain?
  - emn13 10y ago
    More detail; you're assuming a binomial likelihood function? What exactly is "uniform prior for gamma" supposed to mean?
    - yummyfajitas 10y ago
      Please go read the tutorial I linked to. It explains exactly how this analysis works. Here's the code: In [1]: from scipy.stats import beta In [2]: from numpy import percentile In [3]: data = beta(1, 100e6+1).rvs(1e7) In [4]: percentile(data, 0.5), percentile(data, 50), percentile(data, 99.5) Out[4]: (5.0460240722165642e-11, 6.9295652915902601e-09, 5.3005747758871231e-08)

TeMPOraL 10y ago

> I still can't believe that they are using statistically safer in an official response. It now have been widely discussed everywhere that 1 occurrence is not enough to draw any reliable statistical conclusion! They probably mean that 1 occurrence is not enough to invalidate a statistical model built on wealth of other data.

emn13 10y ago
Except that the other data is certainly suspect. I mean - what other source of realistic data can they possibly have that is realistic enough and large enough to be more significant that 100000000 miles of actual usage? At this level, it's the odd, unpredictable events that are going to get you, and whatever models they have cannot include all of those.