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Hardware performance counters (HPCs) that measure low-level architectural and microarchitectural events provide dynamic contextual information about the state of the system. However, HPC measurements are error-prone due to non determinism (e.g., undercounting due to event multiplexing, or OS interrupt-handling behaviors). In this paper, we present BayesPerf, a system for quantifying uncertainty in HPC measurements by using a domain-driven Bayesian model that captures microarchitectural relationships between HPCs to jointly infer their values as probability distributions. We provide the design and implementation of an accelerator that allows for low-latency and low-power inference of the BayesPerf model for x86 and ppc64 CPUs. BayesPerf reduces the average error in HPC measurements from 40.1% to 7.6% when events are being multiplexed. The value of BayesPerf in real-time decision-making is illustrated with a simple example of scheduling of PCIe transfers.