Comments on: Tues Mar 6

By: Thomas Kraynak

Thomas Kraynak — Tue, 06 Mar 2012 14:25:44 +0000

I’m having trouble understanding why the function of an approximately normal vector would be approximately normally distributed, could you go over this?

By: Rob Rasmussen

Rob Rasmussen — Tue, 06 Mar 2012 14:09:42 +0000

For section 9.1.1, how would you go about finding the resulting pdf of a distribution, given the initial pdf and an arbitrary transform?

By: Kelly

Kelly — Tue, 06 Mar 2012 13:57:36 +0000

The methods of assessing and controlling for propagation of uncertainty seem at least broadly analogous to methods used for assessing and correcting for heteroskedasticity in regressions, such as Weighted Last Squares / Feasible General Least Squares (which we recently covered in my econometrics class). The parallel is probably not exact, but it made me wonder something. In econometrics we were told that when constructing an FGLS model one should only do transformations on the data that yield positive values (e.g., exponential). However, this does not seem to be a concern in the examples listed in 9.1. Why not? Or maybe a better way to ask this would be, what’s different about FGLS that makes having only positive values a concern there when it isn’t here? Again, the 2 situations might not be analogous at all, so my question might not actually mean much, but I was wondering.

By: Matt Bauman

Matt Bauman — Tue, 06 Mar 2012 13:40:30 +0000

I understand that these methods for propogation of uncertainty contain much more information than simple confidence intervals, but will they result in the same intervals as my old high school chemistry method of simply performing the transformation on the original bounds? To my mind, I think it should be the same if the transformation is linear.

By: Amanda Markey

Amanda Markey — Tue, 06 Mar 2012 13:05:43 +0000

1. If f(x) does not meet the specifications given in the scalar case (p254) or the multivariate normal (p258) – what exactly does this mean for our ability to estimate mu(y) and sigma(y)? Does it mean our only option is the bootstrap or is there a closed form solution for functions that aren’t as tidy, but still possible to find?

By: Rex Tien

Rex Tien — Tue, 06 Mar 2012 12:28:34 +0000

Are there specific guidelines for how many generated iterations (G) is enough? You mention that you should observe approximately equal results after several runs. However, in the case of a very computationally expensive procedure, we may want to use as few iterations as possible. How much variability in the results is allowable?

By: Matt Panico

Matt Panico — Tue, 06 Mar 2012 07:07:43 +0000

When you say “near” is defined probabilistically (where f’(x) =/= 0), what exactly does this mean? f’(x) cannot cross 0 within a standard deviation of the mean?

By: David Zhou

David Zhou — Tue, 06 Mar 2012 06:22:53 +0000

Can you talk more about the brute force computer simulation methods that you refer to in propagation of uncertainty? Why is this sometimes easier than mathematically deriving the source of uncertainty? Are there advantages to this other than to get the confidence intervals?

By: Ben Dichter

Ben Dichter — Tue, 06 Mar 2012 04:04:22 +0000

I can see that there are complicated situations where the simulation based approach to error propagation is preferable to the analytical approach, but are there situations where the analytical approach is better?

By: Jay Scott

Jay Scott — Tue, 06 Mar 2012 03:53:03 +0000

p254: ” ‘near’ being defined probabilistically, in terms of σX” — Does this mean there is an actual analytical method to determine whether f′(x) is near enough to μX for us assume Y = f(X) is ≈ normal?