Frame the problem as a two-sample comparison of turning trajectory distributions, where each trajectory is represented by engineered features capturing geometry, dynamics, and variability. Choose statistical tests that respect the nested structure (multiple turns per intersection) and non-normal, multimodal nature of trajectory data, then report both significance and practical effect sizes with confidence intervals.
Pro tip: Emphasize that statistical significance alone is insufficient; Waymo cares about safety-relevant, actionable differences. Use effect sizes like Cohen's d or overlap coefficient and relate them to real-world implications (e.g., collision risk, comfort).
Extract interpretable features from each 2D turning trajectory: turn radius, curvature profile, entry/exit speed, acceleration, jerk, steering angle rate, path length, and lateral deviation from a reference path. Also compute distributional summaries per intersection (mean, variance, skewness) to capture variability.
Plot distributions (histograms, KDEs) and test normality (Shapiro-Wilk, Anderson-Darling). Expect non-normal, possibly multimodal distributions due to different turn types (left vs right, intersection geometry). Consider transformations or non-parametric methods.
For independent samples, use Mann-Whitney U or Kolmogorov-Smirnov for univariate features; for multivariate, use energy distance or maximum mean discrepancy (MMD). Account for clustering by intersection using mixed-effects models or cluster-robust standard errors. If comparing multiple features, control FDR (Benjamini-Hochberg).
Compute Cohen's d, Cliff's delta, or overlap coefficient for each feature. For multivariate, use distance between distributions (e.g., energy distance) and permutation tests for p-values. Report confidence intervals via bootstrap.
Present results with clear visualizations (e.g., violin plots, trajectory overlays) and a table of effect sizes with CIs. Discuss whether differences are safety-relevant, consistent across intersections, and robust to confounders (e.g., turn type, speed limit).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I blanked for a second here because I'd been so focused on the trajectory representation piece.
Acknowledge intersection-level confounding as a key threat to validity, then propose a mixed-effects modeling framework that accounts for both fixed effects (e.g., vehicle type) and random effects (e.g., intersection-level intercepts and slopes). Emphasize the importance of controlling for time-varying and static intersection characteristics, and discuss how to validate the model and interpret results in the presence of confounding.
Pro tip: Frame the problem as a hierarchical data structure where observations are nested within intersections, and highlight that random slopes for vehicle type allow the treatment effect to vary by intersection—this shows you understand both the statistical nuance and the practical need for generalizable insights.
List intersection-level factors (e.g., traffic volume, road geometry, signal timing, weather, time of day) that could correlate with both vehicle type presence and outcome metrics. Ensure these are captured in the data or can be proxied.
Propose a mixed-effects model (or hierarchical model) with random intercepts for intersections to account for unobserved heterogeneity, and consider random slopes for vehicle type if the effect is expected to vary across intersections.
Include fixed effects for key intersection-level covariates (e.g., traffic volume, number of lanes) and temporal factors (e.g., hour of day, day of week) to adjust for measured confounding.
Check for overfitting, convergence issues, and residual confounding using cross-validation, posterior predictive checks, or sensitivity analyses. Compare with simpler models to justify complexity.
Explain how the model isolates the Waymo vs. other vehicles effect while accounting for intersection variability. Discuss limitations and potential for unmeasured confounding, and suggest robustness checks.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.