Evaluation of systematic frequency shift and uncertainty of an optical clock based on Bayesian hierarchical model

Optical clocks are the most accurate time–frequency measurement devices currently available. In order to evaluate the performance quickly and conveniently, we build a Bayesian hierarchical model to initially evaluate the systematic frequency shift and the corresponding uncertainty of the ¹⁷¹Yb optical lattice clock. Significant time savings is achieved through the Bayesian model compared to the traditional method during the absolute frequency measurement. The model is implemented via the R2jags package in R, samples are drawn from the target posterior distribution of the parameters by the Markov Chain Monte Carlo simulation (MCMC). The simulation result of the total systematic frequency shift is −1.595 Hz, with an uncertainty of 6.71 × 10⁻¹⁶, which is close to the actual measurement value. This method provides us a new way to evaluate optical clocks.