Propagation of errors using simulation If I construct confidence intervals for a calculation based on simulating inputs rather than using error propagation formulas, would this be considered as belonging to 'Monte Carlo' methods?
I would have several inputs into the calculation and they would each have standard errors that I would use to generate random numbers from a distribution using R. I would use many inputs and then get the standard error of the outputs.
Using the error propagation formulas would be possible, but it would be tedious and prone to mistakes in my opinion. Is this method usually acceptable and what name would I use to best describe the method?
 A: Yes, this is a monte carlo method and it is perfectly acceptable.
My understanding of your situation is you have various input variables for which you are prepared to make assumptions about their distributions - both shape and parameters (which should include their covariance - too often forgotten in this situation and it can make a huge difference, if some of the variables are related as they often are).  You have a complex calculation that draws on those variables and produces an output of interest.  You intend to run a large number - 10,000 or so - of simulations and to report a final empirical distribution of the end output (along with your carefully described assumptions).
A: The Guide to Uncertainty in Measurement (the GUM) is an international standard that addresses the propagation and reporting of uncertainty in measurements:
Joint Committee for Guides in Metrology, "Evaluation of measurement data – Guide to the expression of uncertainty in measurement", (GUM 1995 with minor corrections) JCGM 100:2008
The GUM uses the Taylor Series Method (TSM) of propagating uncertainty, i.e., the "law of propagation of uncertainty". To address the limitations of the TSM, the JCGM issued a supplement that discusses the use of Monte Carol simulations to verify that the TSM is valid for a particular application and to use for calculations that are too complex for the TSM:
Joint Committee for Guides in Metrology Evaluation of measurement data –Supplement 1 to the “Guide to the expression of uncertainty in measurement” – Propagation of distributions using Monte Carlo method  JCGM 101:2008 
I suggest that you take a look at this supplement, which appears to address what you are trying to do.
