{"items": [{"author": "Alexandre", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120400857552", "anchor": "fb-10100120400857552", "service": "fb", "text": "Do we know how their safety record compared to human driving? I am curious how far such a system can get you.", "timestamp": "1573182700"}, {"author": "Brayden", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882", "anchor": "fb-10100120409674882", "service": "fb", "text": "6226 pedestrians were killed last year by human drivers, from 3.21 trillion miles (1 death per 551M miles). Uber has killed one pedestrian and racked about somewhere around 2 million autonomous miles (1 death per 2M). Rough ballpark is probably up to 275x as deadly as the average human. (Disclaimer: I build autonomous cars for a competitor, but I only used fully public stats for this calculation)", "timestamp": "1573185399"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100120441695712", "anchor": "fb-10100120409674882_10100120441695712", "service": "fb", "text": "→ Brayden observing one death in 2M miles should put your point estimate at 1:4M if you have no prior", "timestamp": "1573212670"}, {"author": "Alexandre", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100120448482112", "anchor": "fb-10100120409674882_10100120448482112", "service": "fb", "text": "→ Brayden Do you know if the 2 million number is 2 million consecutive miles without human intervention? If not, that number would probably overestimate the safety of their system.

(Disclaimer, I also work for a company which builds autonomous cars, though I am totally unrelated to that project.)", "timestamp": "1573219753"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100120454914222", "anchor": "fb-10100120409674882_10100120454914222", "service": "fb", "text": "→ Alexandre absolutely not consecutive miles. In 2018 in CA (which mandates reporting) Uber was at >1 disengagement per mile. Compared to Waymo at 1:11k miles and Cruise at 1:5k.", "timestamp": "1573223282"}, {"author": "Alexandre", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100120464125762", "anchor": "fb-10100120409674882_10100120464125762", "service": "fb", "text": "→ Jeff Kaufman OK. So the 1 death per 4 million miles seems to be a widely optimistic view of their system right?", "timestamp": "1573228610"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100120469300392", "anchor": "fb-10100120409674882_10100120469300392", "service": "fb", "text": "→ Alexandre depends on whether you consider the system to be \"car\" or \"car + safety driver\"", "timestamp": "1573230854"}, {"author": "Alexandre", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100120472434112", "anchor": "fb-10100120409674882_10100120472434112", "service": "fb", "text": "→ Jeff Kaufman The goal being fully autonomous vehicles, I'm just counting the car.", "timestamp": "1573232479"}, {"author": "Brayden", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100120556575492", "anchor": "fb-10100120409674882_10100120556575492", "service": "fb", "text": "→ Yeah lots of uncertainty in these estimates. But just based on public numbers I'd put my 80% confidence interval for their whole system as being more than 30x as deadly as a random US driver, and less than 500x as deadly.", "timestamp": "1573259878"}, {"author": "opted out", "source_link": "#", "anchor": "unknown", "service": "unknown", "text": "→ this user has requested that their comments not be shown here", "timestamp": "1573270577"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100120640382542", "anchor": "fb-10100120409674882_10100120640382542", "service": "fb", "text": "→ Wang yes. Though Uber may have been doing a different sort of testing in CA that required a lot of disengagements?", "timestamp": "1573298771"}, {"author": "Alexandre", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100120670402382", "anchor": "fb-10100120409674882_10100120670402382", "service": "fb", "text": "→ Wang Not all disengagements will be safety issues though. IIRC, some other companies reported disengagements when their vehicle wrongly thought its way was barred and had to be manually operated to stop blocking traffic.", "timestamp": "1573315126"}, {"author": "Patrick", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121142286722", "anchor": "fb-10100120409674882_10100121142286722", "service": "fb", "text": "→ Is that a typo, or was there really a > 5000x difference in frequency of disengagement between Uber and the others?", "timestamp": "1573530831"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121142601092", "anchor": "fb-10100120409674882_10100121142601092", "service": "fb", "text": "→ Patrick not a typo: https://thelastdriverlicenseholder.com/.../update.../

Uber reported 70,165 disengagements and 26,899 miles, while Waymo reported 114 and 1,271,587 miles and GM Cruise reported 86 in 447,621 miles. Other companies were in between.", "timestamp": "1573531081"}, {"author": "Patrick", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121142970352", "anchor": "fb-10100120409674882_10100121142970352", "service": "fb", "text": "→ Holy shit.", "timestamp": "1573531220"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121143005282", "anchor": "fb-10100120409674882_10100121143005282", "service": "fb", "text": "→ Apple, weirdly, was nearly as bad: 69,510 disengagements in 79,745 miles", "timestamp": "1573531305"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121143085122", "anchor": "fb-10100120409674882_10100121143085122", "service": "fb", "text": "→ No other company had even 1/50 as many (other companies had bad ratios, but were very clearly in early testing stages)", "timestamp": "1573531357"}, {"author": "Paul", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121189332442", "anchor": "fb-10100120409674882_10100121189332442", "service": "fb", "text": "→ Jeff Kaufman re your \"if you have no prior\" comment - how are you getting that?", "timestamp": "1573573488"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121192451192", "anchor": "fb-10100120409674882_10100121192451192", "service": "fb", "text": "→ Paul If you run driverless cars for N miles and observe one death, then your best guess is 1/N. If you run driverless cars until they hit someone, and that happens at mile N, then your best guess is 1/(2N).", "timestamp": "1573575450"}, {"author": "Matthew", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121205040962", "anchor": "fb-10100120409674882_10100121205040962", "service": "fb", "text": "→ Jeff, because the first is updating from a poisson observation and the second is updating from a negative binomial, or some different reason?", "timestamp": "1573582643"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121243154582", "anchor": "fb-10100120409674882_10100121243154582", "service": "fb", "text": "→ $ cat ~/tmp.py
import random
true_probability = 1/10000

def miles_until_crash():
miles = 0
while random.random() > true_probability:
miles += 1
return miles

def count_crashes(miles):
crashes = 0
for i in range(miles):
if random.random() <= true_probability:
crashes += 1
return crashes

def avg(x):
if len(x) == 0:
return -1
return sum(x)/len(x)

def avg_miles_if_one_crash():
return avg([miles
for miles in range(100000)
if miles % 10 == 0 and count_crashes(miles) == 1])

def avg_miles_until_crash():
return avg([miles_until_crash()
for i in range(1000)])

print (avg_miles_until_crash())
print (avg_miles_if_one_crash())

$ python ~/tmp.py
9773.831
20636.436893203885", "timestamp": "1573596691"}, {"author": "Matthew", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121253189472", "anchor": "fb-10100120409674882_10100121253189472", "service": "fb", "text": "→ Jeff I'm confused about where the 'miles in range(100000)' is coming from; don't you just want lots of samples from count_crashes(10000), not count_crashes(10) up to count_crashes(100000)?

I think what you're calculating is \"run until you hit someone\" with avg_miles_until_crash and \"run for some amount of time then filter on only hitting one person\" with avg_miles_if_one_crash, which should give us the time after you hit one person and before you hit two, rather than stopping immediately after you hit someone.

Beyond that, there's an inversion here where rather than trying to calculate the estimated number of miles given the true probability, we what to know what estimated probability maximizes the likelihood of our observation (the MLE), which is pretty straightforward to calculate:

https://en.wikipedia.org/.../Negative_binomial...

This suggests that 1/N is the right estimate, and when I use the negative binomial (do trials until you hit 1 success) calculator for 10000 trials, I get a likelihood of 2.7e-5 if I claim the estimated probability is 0.0002, 3.7e-5 if I claim it's 0.0001, and 3.0e-5 if I claim it's 0.00005, which suggests that 1/N is maximizing the likelihood. ( https://stattrek.com/online.../negative-binomial.aspx )", "timestamp": "1573601025"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121260030762", "anchor": "fb-10100120409674882_10100121260030762", "service": "fb", "text": "→ Matthew yeah \"miles in range 100000\" is rough. It's trying to approximate \"if you picked some number of miles and drove that far, and observed one crash, what's the average number of miles you picked\"", "timestamp": "1573604130"}, {"author": "Jeff Kaufman", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121260100622", "anchor": "fb-10100120409674882_10100121260100622", "service": "fb", "text": "→ And the % 10 is just to make it run faster", "timestamp": "1573604175"}, {"author": "Matthew", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121261842132", "anchor": "fb-10100120409674882_10100121261842132", "service": "fb", "text": "→ But if you observe one crash, when it happened is uniformly distributed throughout the whole run, and so on average that crash probably happened in the middle of your run, not the end, which explains the 2X difference between the two.", "timestamp": "1573604856"}, {"author": "Matthew", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120409674882&reply_comment_id=10100121263279252", "anchor": "fb-10100120409674882_10100121263279252", "service": "fb", "text": "→ [Also note this is the Strong Likelihood Principle, from https://en.wikipedia.org/wiki/Likelihood_principle , which showed up in the Sequences here: https://www.lesswrong.com/.../bkSkR.../beautiful-probability . That is, that the stopping rule is irrelevant; where the 2X comes from I believe is explained by my previous comment, where in one case the location of the crash in the run is fixed and in the other case it's allowed to vary. But I'm much less confident in that explanation than I am in the likelihood principle.]", "timestamp": "1573605518"}, {"author": "opted out", "source_link": "#", "anchor": "unknown", "service": "unknown", "text": "this user has requested that their comments not be shown here", "timestamp": "1573186522"}, {"author": "Paul", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100120411765692&reply_comment_id=10100120659494242", "anchor": "fb-10100120411765692_10100120659494242", "service": "fb", "text": "→ I think of Uber as not very different from drug dealers. Drug dealers perform the valuable service of selling people the illegal drugs that they want. But I wouldn't want a cartel of drug dealers to start buiding self-driving cars.", "timestamp": "1573310087"}, {"author": "Rick", "source_link": "https://www.facebook.com/jefftk/posts/10100120291885932?comment_id=10100121319751082", "anchor": "fb-10100121319751082", "service": "fb", "text": "I think many people don't realize that there is a big difference between the Uber self-driving cars and the google self-driving cars. A lot of people will just think all self-driving cars are unsafe.", "timestamp": "1573643674"}, {"author": "drethelin", "source_link": "https://www.lesswrong.com/posts/tTg4bn5rxHYqQJXhD#NzmJ5MFcHPiAgZGzq", "anchor": "lw-NzmJ5MFcHPiAgZGzq", "service": "lw", "text": "It is especially the case that it should prioritize braking in uncertainty when it's a lonely road with no one behind", "timestamp": 1575334329}]}