Table 5. Comparing likelihood gradients for simulated data by computing correlations of gradients computed using a 1500-point quadrature with the correct σA value (0.90) 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 | 0.50/63.1% | 0.64/73.6% | 0.85/93.2% |
| French–Wilson | 0.64/60.3% | 0.65/74.9% | 0.79/88.4% |
| Normal | 0.91/97.0% | 0.88/96.9% | 0.87/97.6% |
| Student’s t | 0.94/98.7% | 0.91/99.9% | 0.89/99.9% |