Table 3. Bias in the estimation of λ(n,n) of the island, direct and censored direct methods, and their relative speeds.
n | Bias (%) | Speed ratio | |||
|
Island |
Direct |
Censored |
Island:direct |
Island:censored |
2400 | +0.9 | –0.2 | –0.2 | 60 | 60 |
1200 | +0.7 | 0.0 | 0.0 | 14 | 14 |
800 | +0.8 | +0.4 | +0.4 | 6 | 6 |
600 | +0.6 | +0.5 | +0.5 | 3 | 3 |
480 | +0.5 | +0.8 | +0.6 | 2 | 2 |
400 | +0.4 | +0.8 | +0.3 | 1.4 | 1.5 |
343 | +0.4 | +1.2 | +0.4 | 1.0 | 1.2 |
300 | +0.3 | +1.4 | +0.5 | 0.8 | 1.1 |
267 | +0.1 | +1.4 | +0.3 | 0.6 | 1.0 |
240 | 0.0 | +1.6 | +0.1 | 0.5 | 0.9 |
218 | –0.1 | +1.4 | –0.1 | 0.4 | 0.8 |
200 | 0.0 | +1.6 | –0.1 | 0.3 | 0.8 |
Maximum-likelihood estimates λ were derived using the island, direct and censored methods from n × n sequence comparisons. For the island method with cutoff score c = 28, approximately 106 scores were generated, yielding a standard error of 0.1%. For the direct method, approximately 6.1 × 105 scores were generated, yielding a standard error of 0.1%. For the censored method, sufficient scores above the threshold c = 28 were generated to yield a standard error of 0.1% (23); this number ranged from 6.1 × 105 for n = 2400 to 8.4 × 105 for n = 200. Biases are calculated assuming the correct values for λ(n,n) are those of the points plotted in Figure 4. Speed ratios are the computation times required, respectively, by the direct and censored methods divided by the time required by the island method; high speed ratios favor the island method.