Tuesday, February 9, 2016

With Driverless Cars, How Safe Is Safe Enough? - Thoughts with Bayesian flavor [Draft]

 Well, that's the news from Lake Wobegon, where all the women are strong, all the men are good looking, and all the drivers are above average, including the robots driving the driverless. 

The Myth of i.i.d

And yet, it could be impossible to accurately gauge safety until many, many autonomous vehicles hit the roads. In the U.S., approximately one fatality occurs for every 100 million miles driven. To prove with 95% confidence that a driverless car achieves, at least, this rate of reliability by driving them around to see, it would require they be driven 275 million miles without a fatality. With a fleet of 100 autonomous vehicles (larger than any known existing fleet) driving 24/7, it would take more than 12 years to drive these miles. But with 10,000 such vehicles, it would take just six weeks. Regulators will have to find other ways of estimating safety, but widespread deployment will be the true test. If safety standards are too strict, this might never happen
The assumption behind the above calculation is that every mile the every test vehicle travels has the identical independent probability of accidents. In chapter 4 of the report Kalra co-authored, many different cases were discussed, where the AVs outperform human in some, and human drivers outperform in some others, and some are challenging to both human and robotic drivers. 

Conditional Probability

There is one thing I learned from the excellent E. T. Jayens, every probability is a conditional probability. So, P(A|AV, H0) = Sigma(P(A|AV, Ci, H0)*P(Ci|AV, H0)
Human drivers' accident rate P(A|Human, H0) are available, and there are models to predict improvement without AVs.  

For regulation to setup the accepting criteria, 

  • Baseline of human reliability
  • a comprehensive list of test cases (Ci), and passing rate for each Ci
  • the modelling of likelihood of each Ci. Also the government can influence the likelihood, and make the AV and human drivers much safer.
  • ???


  • If we can train a pilot using simulator, can we train a robot with simulator? 
  • Can we test/validate a robot with simulator?
  • Open database for all autonomous vehicles developers?

Can the Robot Get a Driver's License

When I first went to the driving school, the instructor told me that everyone could get a driver's license, except the legally blind. The robotic driver can easily beat me in the road test, and get the driver's license. 


  • Ci's are not independent. (Need to pull out my math book...)
  • Scalibility: the outcome of Ci, and also the P(Ci|H0) can vary depending on how many AVs are on the road.
  •  X-ware: hardware (vehicle, sensor, etc.), software, driver/rider, environment, 
  • Interactions: AV2AV, AV2HD, AV2I, AV2Pedestrian
  • Software upgrade
  • AI learning, general learning, and adaptive learning toward the specific environment,  
  • ...

Nidhi Kalra, "With Driverless Cars, How Safe Is Safe Enough?"; Retrieved from http://www.rand.org/blog/2016/02/with-driverless-cars-how-safe-is-safe-enough.html
James M. Anderson, Nidhi Kalra, Karlyn D. Stanley, Paul Sorensen, Constantine Samaras, Oluwatobi A. Oluwatola, "Autonomous Vehicle Technology: A Guide for Policymakers"; Retrieved from http://www.rand.org/content/rand/pubs/research_reports/RR443-1.html

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