This paper presents a Bayesian approach to infer about two mean-field plasma turbulence models, a first based on the turbulent kinetic energy k⊥, and a second based on k⊥ and the turbulent enstrophy ζ⊥. These models contain several closure terms with unknown constants that have to be determined through fitting to reference data from turbulence simulations or experiments. In this paper, we compare two techniques to solve the Bayesian inference problem: the Laplace approximation and the adaptive Metropolis–Hastings (AMH) algorithm. Our Bayesian inference allows for parameter uncertainty quantification, identification of parameter cross-correlations and model comparison through the Bayesian evidence. Our results indicate that while a diffusive k⊥–ζ⊥ scaling for the anomalous diffusion coefficient provides a better approximation to the turbulent particle flux when based on exact turbulence simulation data, at present large modelling uncertainties and parameter cross-correlations in the full k⊥–ζ⊥ model make it less performant than the more simple k⊥ model. For the cases studied here, the cross-correlations can be removed by a reparameterization of the k⊥–ζ⊥ model with fewer parameters. The results can form the basis for further development of the turbulence models.
Learning how structures form in drift-wave turbulence