Table 4. Comparing likelihood gradients for simulated data by computing correlations of gradients computed using a 1500-point quadrature with the correct σA value (0.70) and those obtained using four different approximation methods, as outlined in the main text, and the maximum-likelihood estimate of σA given the approximation of the likelihood function.
The reported entries are estimated values of σA and the gradient correlation.
| Method | 〈Z/σZ〉 = 0.25 | 〈Z/σZ〉 = 0.5 | 〈Z/σZ〉 = 1.5 |
|---|---|---|---|
| Sivia | 0.35/68.8% | 0.52/82.1% | 0.64/93.5% |
| French–Wilson | 0.44/80.5% | 0.53/87.7% | 0.64/94.3% |
| Normal | 0.68/96.9% | 0.66/97.4% | 0.67/97.9% |
| Student’s t | 0.73/100% | 0.70/100% | 0.71/100% |