Looks like I tightened up the confidence interval just a bit too much. Here's the convergence plot for the same query posted earlier in the week. This time the uncertainty bounds are "real" confidence intervals (except that they're wrong). Ideally, the true value would be between the blue lines 95% of the time.
The convergence path is just a bit slower due to the fact that the algorithm thinks it's doing better than it is so it's not picking strata as well. More importantly, the stopping rule is the width of the confidence interval, so the algorithm terminates before the desired confidence has been reached. I had it set to $1000 to ensure it ran out nearly to the end (note, the scale on the left is in billions). For an all-expense query like this, the actuaries would probably want things to the nearest $50-million or so, which would end it at block 282, but it was still off by $225 million at that point.
Not sure which of my assumptions is being violated in a bad way, but I'm going to leave it at this for the week. Definitely good enough progress to turn my attention to far greater matters for a few days. Happy Easter; I won't be posting again until Monday.
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