Which method for the estimation of uncertainty in a simulation result is basically more appreciated? Direct estimation of uncertainty from the final simulation result or by going through the usual analytical method of propagation of uncertainty?
Block analysis is a solid method to estimate uncertainty in molecular simulations, if done properly!. Here is an excellent paper by Alan Grossfield on Block analysis and other aspects of uncertainty, http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2865156/.
By direct estamiation from the final simulation result I assume you mean analysis of the model residuals. The problem there is that you are assuming that the model residuals are a good measure of the uncertainty. This depends on how you define the uncertainty, and what you are using it for. The problem with using the model residuals as a basis for estiamting the uncertainty is that a more highly parameterised model will generally give smaller residuals (in calibration), and hence you would concllude that the uncertainty is smaller. This might not be true when simulating the result for a different set of data, but that depends on the difference in the conditions between the two data sets.
While analysis of the model residuals is easiest, it can give misleading results. Propagation of uncertainty is the better method, but requires more detailed understanding of the uncertainty in the model inputs (data and parameters). This approach gives an estimate of the uncertainty that doesn't include the uncertainty in whether the model structure correctly represents the system. Analysis of the model structure uincertainty should be done using the model residuals, comparing the residuals with the uncertainty obtained by the propagation method.
In short - you should do both to properly understand the uncertainty in the model predictions.
You might be interested in a paper from 2009 which looks at using model uncertainty through the propagation method to modeify objective functions to relax the "independent and identically distributed" condition on the uncertainties.
https://www.researchgate.net/publication/228371805_Representing_uncertainty_in_objective_functions_extension_to_include_the_influence_of_serial_correlation
Conference Paper Representing uncertainty in objective functions: extension t...
Call for Papers: "12th International Probabilistic Workshop" held in Weimar Germany, on November 4th and 5th 2014"
https://www.researchgate.net/post/Call_for_Papers_12th_International_Probabilistic_Workshop_held_in_Weimar_Germany_on_November_4th_and_5th_2014
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