On Statistical Methods for Safety Validation of Automated Vehicles

Automated vehicles (AVs) are expected to bring safer and more convenient transport in the future. Consequently, before introducing AVs at scale to the general public, the required levels of safety should be shown with evidence. However, statistical evidence generated by brute force testing using safety drivers in real traffic does not scale well. Therefore, more efficient methods are needed to evaluate if an AV exhibits acceptable levels of risk.This thesis studies the use of two methods to evaluate the AV\u27s safety performance efficiently. Both methods are based on assessing near-collision using threat metrics to estimate the frequency of actual collisions. The first method, called subset simulation, is here used to search the scenario parameter space in a simulation environment to estimate the probability of collision for an AV under development. More specifically, this thesis explores how the choice of threat metric, used to guide the search, affects the precision of the failure rate estimation. The result shows significant differences between the metrics and that some provide precise and accurate estimates.The second method is based on Extreme Value Theory (EVT), which is used to model the behavior of rare events. In this thesis, near-collision scenarios are identified using threat metrics and then extrapolated to estimate the frequency of actual collisions. The collision frequency estimates from different types of threat metrics are assessed when used with EVT for AV safety validation. Results show that a metric relating to the point where a collision is unavoidable works best and provides credible estimates. In addition, this thesis proposes how EVT and threat metrics can be used as a proactive safety monitor for AVs deployed in real traffic. The concept is evaluated in a fictive development case and compared to a reactive approach of counting the actual events. It is found that the risk exposure of releasing a non-safe function can be significantly reduced by applying the proposed EVT monitor

First Observational Tests of Eternal Inflation: Analysis Methods and WMAP 7-Year Results

In the picture of eternal inflation, our observable universe resides inside a single bubble nucleated from an inflating false vacuum. Many of the theories giving rise to eternal inflation predict that we have causal access to collisions with other bubble universes, providing an opportunity to confront these theories with observation. We present the results from the first observational search for the effects of bubble collisions, using cosmic microwave background data from the WMAP satellite. Our search targets a generic set of properties associated with a bubble collision spacetime, which we describe in detail. We use a modular algorithm that is designed to avoid a posteriori selection effects, automatically picking out the most promising signals, performing a search for causal boundaries, and conducting a full Bayesian parameter estimation and model selection analysis. We outline each component of this algorithm, describing its response to simulated CMB skies with and without bubble collisions. Comparing the results for simulated bubble collisions to the results from an analysis of the WMAP 7-year data, we rule out bubble collisions over a range of parameter space. Our model selection results based on WMAP 7-year data do not warrant augmenting LCDM with bubble collisions. Data from the Planck satellite can be used to more definitively test the bubble collision hypothesis.Comment: Companion to arXiv:1012.1995. 41 pages, 23 figures. v2: replaced with version accepted by PRD. Significant extensions to the Bayesian pipeline to do the full-sky non-Gaussian source detection problem (previously restricted to patches). Note that this has changed the normalization of evidence values reported previously, as full-sky priors are now employed, but the conclusions remain unchange