Abstract: The current document is directed to improved methods and systems that collect, generate, and store multidimensional metric data used for monitoring, management, and administration of computer systems and that continuously optimize sampling rates for metric data. Multiple different metric-data streams are sampled for each of multiple different distributed-computer-system objects, and are hierarchically organized into a number of different individual and multidimensional metric-data streams. The sampling rates for the different individual and multidimensional metric-data streams are correspondingly hierarchically optimized in order to avoid oversampling the metric data while preserving the relevant information content of the sampled metric data for downstream data analysis.