The impact of statistical models on scalings derived from multi-machine H-mode threshold experiments

The predicted H-mode power threshold, P_L-H, for ITER is generally estimated from the international global H-mode threshold database (IGDBTH) by ordinary least squares log-linear (OLS) regressions. Such fits assume that errors are uncorrelated and (i) errors in P_L-H are much greater than those in the other parameters, (ii) errors are normally distributed and (iii) relative errors are equal for all experiments. In this paper, the validity of this statistical model for the IGDBTH is examined, by use of the more generalized maximum-likelihood method. Results indicate that all three assumptions bias the resulting scaling and so need to be relaxed. A fit relaxing all three constraints lies outside the error bars of the OLS, indicating that the choice of the statistical model makes a significant contribution to the resulting scaling. A chi-squared analysis shows that none of the studied models are entirely consistent with the data, indicating that further refinement of the physical and statistical model is required. For ITER-like parameters, a maximum-likelihood analysis shows a predicted threshold of 38.4 MW, compared with 31.1 MW for the OLS, indicating that OLS tends to under predict and that quoted confidence intervals tend to be too small. However, further studies of the sources of errors in the IGDBTH would be required before estimates based on more detailed statistical models can be given with confidence.