I'm trying to build a monte-carlo simulation that can revise it's distribution of outcomes of a project based on observed measurements after the project has started.
I have a few questions about the best way to do this. I'm not a statistician, so please correct me if I am doing something wildly wrong.
For example, let's say I've observed that task
x has been selected by person
y (whose original 90% CI estimate for the task was [
h]) , and that
y has logged
w hours of work to the task.
I can use that data to re-simulate the project under new constraints and compute a new, more accurate, distribution of outcomes.
For example, if
l, then I know that the lower bound for the time to complete x is now
l, and can adjust the distribution used accordingly. However,
w is not a 5% lower bound. It's a 0% lower bound (i.e. the limit), so using [
h] as a 90% CI didn't quite seem correct. As a result I was thinking I could just pick some arbitrarily small number for
p(w), say 0.0001, and continue using .05 for
p(h) and then generate a new distribution for [
h] (of course, I would just use the number of deviations for
w rather than the probabilities).
Is that sound?
What's not immediately clear is what I would do in the case where
h. I have calibrated estimates with a 90% CI, so I should expect to see this 5% of the time. If I ask: "what do I know in that case", I come up with the following:
- I know
wand I know my arbitrarily low
- From the original confidence interval (which assumes a normal distribution), I can determine
p(w + sigma).
- So, I could produce:
[w, w + sigma]as an interval, using
p(w + sigma), and then derive a normal distribution from that (again, just using the z-values).
Is that sound as well?