

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

![0_image_1.png](0_image_1.png)

To compare the variational algorithm to a time-limited version of the likelihood-weighted sampler we ran the latter algorithm for a period of time (8.83 seconds per case) roughly comparable to the running time of the variational algonthm (0.29 seconds per case). Figure 11 s hows the corres ponding plot of false positives against true positives, where we have averaged over ten independent runs. We see that the curve increases significantly more steeply than the variational curve. To find the 20 most likely diseases with the variational method we would only need to entertain the top 30 diseases in the list of approximately ranked diseases. For the sampling method we would need to entertain the top 70 approximately ranked diseases.

## 5.3  Interval Bounds On The Marginal Probabilities

Thus far we have utilized the variational approach to produce approximations to the posterior marginals. The approximations that we have discussed originate from upper and lower