1. A method performed by a computing system implementing a telematics service, the method comprising: obtaining a set of vehicle telematics data for each vehicle of a population of vehicles, wherein for each vehicle of the population, the set of vehicle telematics data is obtained by receiving communications transmitted from that vehicle by a vehicle-based telematics device via a wireless communications network; identifying, within each set of vehicle telematics data, a vehicle identifier of the vehicle from which that set of vehicle telematics data originated and a set of time-based measurements for a measurement type indicated by a measurement type identifier contained within the set of vehicle telematics data, the set of time-based measurements captured by one or more sensors of the vehicle and received from the one or more sensors along with the vehicle identifier of the vehicle by the vehicle-based telematics device via a physical connector of an on-board diagnostics (OBD) interface; combining the set of time-based measurements identified for each vehicle to obtain a combined set of time-based observations for the measurement type indicated by the measurement type identifier contained in each set of vehicle telematics data across the population of vehicles; applying a statistical model to the combined set of time-based observations to obtain a set of one or more probability distributions; identifying an outlier observation from among the combined set of time-based observations that is located outside of the set of one or more probability distributions; for the outlier observation, identifying the vehicle identifier attributed to the outlier observation; determining whether the outlier observation is part of a temporary deviation or a persistent deviation; if the outlier observation is part of a temporary deviation, then reducing an impact of the outlier observation on the set of time-based measurements of which the outlier observation is a member to obtain an augmented set of time-based measurements; if the outlier is part of a persistent deviation, then programmatically characterizing the outlier observation based, at least in part, on the set of time-based measurements of which the outlier observation is a member to obtain a characterization of the persistent deviation; and outputting the augmented set of time-based measurements and/or the characterization of the persistent deviation by forwarding the augmented set of time-based measurements and/or the characterization of the persistent deviation to a mobile device of a subscriber associated with the vehicle identifier attributed to the outlier observation.