WOSAC Why feeding GT can't have likelihood=1.0 for kinematic_metrics?

[pengzhenghao]

I try to feed GT (repeated 32 times) into the WOSAC eval pipe and find:

scenario_metrics/metametric: 0.77725
scenario_metrics/average_displacement_error: 0.00000
scenario_metrics/min_average_displacement_error: 0.00000
scenario_metrics/linear_speed_likelihood: 0.39830
scenario_metrics/linear_acceleration_likelihood: 0.47793
scenario_metrics/angular_speed_likelihood: 0.45490
scenario_metrics/angular_acceleration_likelihood: 0.64707
scenario_metrics/distance_to_nearest_object_likelihood: 0.21332
scenario_metrics/collision_indication_likelihood: 0.99997
scenario_metrics/time_to_collision_likelihood: 0.99965
scenario_metrics/distance_to_road_edge_likelihood: 0.57061
scenario_metrics/offroad_indication_likelihood: 0.99997
aggregate_metrics/realism_meta_metric: 0.77725
aggregate_metrics/kinematic_metrics: 0.49455
aggregate_metrics/interactive_metrics: 0.82509
aggregate_metrics/map_based_metrics: 0.87730
aggregate_metrics/min_ade: 0.00000

Is this a normal behavior?

[pengzhenghao]

I wonder if there any issue inside the histogram_estimate of
waymo_open_dataset/wdl_limited/sim_agents_metrics/estimators.py:

If I asking for the log likelihood of all zeros vs all zeros:

If I asking for the log likelihood of the same array:

(in case you need it, I just randomly grab an agent's heading data:

You can find the output of histogram_estimate is quite wierd.