

![0_image_0.png](0_image_0.png)

| f      |
|--------|
| a      |
| min    |
| median |
| max    |

BN algorithm captured in Figure 6.  The displayed fragment of the conditional probability table belongs to node gas Acute which is a parent of one of the evidence nodes.
stably after three updating steps. The learned probabilities in Step 10 are close to the exact results. In this example, the difference between Pr( x i | pa( X i ), e ) and Pr( x i | pa( X i )) is very large. Sampling from Pr( x i | pa( X i )) instead of Pr( x i | pa( X i ), e ) would introduce large variance into our results.

Figure 8 shows the MSE for all 75 test cases in our experiments with the summary statistics in Table 2.  A paired one-tailed t-test resulted in statistically highly significant differences between the AIS-BN and SIS algorithms ( p < 3.1 × 10-20 ), and also between

| LW       |        |        |
|----------|--------|--------|
| AIS-BN   | SIS    |        |
| 0.000 82 | 0.110  | 0.148  |
| 0.000 22 | 0.076  | 0.093  |
| 0.00049  | 0.0016 | 0.0031 |
| 0.000 78 | 0.105  | 0.154  |
| 0.001 84 | 0.316  | 0.343  |

the SIS and LW algorithms ( p < 1.7 × 10- 8 ). As far as the magnitude of difference is