In one of his lectures Geoff Hinton explains that a big problem of sigmoid belief nets is the explaining away phenomenon. I didn't fully understand this. I see that the induced width of the graph representing Variable Elimination might increase due to the fill-in edges being introduced at the V structures. But is there a more intuition-based way to see this, rather than an appeal to the rigor of the induced graph?
Consider a simple example where the RVs are: did an earthquake occur, did a burglary occur, and did an alarm trigger. The graph is a V structure with the Earthquake and the Burglary as the parents and the Alarm as the child. If a human being were to try and reason about the true $P(Alarm|Earthquake)$ or $P(Alarm|Burglary)$ what sort of difficulty would this V-structured relationship cause?