@ Traden4AlphaQuoteQuoteOriginally posted by: katastrofaTraden4Alpha:@"Yet it is still a blunt tool in the sense of having a very limited ability to resolve the features of the system"@"MC only gives statistical results and only for those specific parameters that were tried."When you model a stochastic system, like those I described, a distributional result is usually all you need and can get. When the model parameters are correlated, multistage and time-dependent, you won't see any straightforward trends or scaling laws in the results. Besides, from my experience MC has generally better convergence than deterministic methods (for high dimensional systems), and there are techniques (which you should probably know better than I, e.g. path-wise differentiation) to obtain dependencies on input parameters without rerunning the simulation. In specific cases you can sometimes come up with a better deterministic model, but it doesn't make MC blunt...The popular approximations usually don't work in complex systems in chemistry and biology. Not to mention the models of a population or a market microstructures.Part of MC's bluntness is that it does not actually give a distribution as an output, only a discrete set of simulated empirical events. The probability density for any outcomes that were not observed during the runs (e.g., those outside the min-to-max range or those between any adjacent pairs of samples) is unknown. If the true PDF has spikes or holes, these might not be apparent. If the true PDF does "bad things" in the tails -- a major concern for QF -- the sparsity of events in the tail can pose a problem. Of course, tricks like importance sampling can help in the tails and examining the analytic structure within the sample generator might let one surmise that those unobserved values can occur with a probability that can be estimated from the frequency of observed events in that neighborhood.I think we start walking in circles. I don't find any of these a valid argument against the MC technique, mostly because the same criticism applies to deterministic numerical methods (even when you're solving a differential equation, you do this on a lattice). As I said, one should ideally solve the problem analytically as far as possible, but when this cannot be done, MC is generally the most effective, efficient and flexible approach. When you poke your nose out of the tiny plot of quantitative finance, MC is not only used as a "tool" but often it is the most natural representation of the actual simulated phenomenon, like in the examples I gave you. But thanks anyway for elaborating on the author's behalf what the esoteric statement meant.QuoteMC is like a chainsaw: powerful and gets jobs done that other tools can't (e.g., complex systems in chemistry and biology) but it is blunt (and noisy).Not a good metaphor either: if chainsaws were blunt The Texas Chainsaw Massacre wouldn't be such a good movie.@CuchulainnQuote1. The results are not reproducible (unless the same seed is used).You need to fix your pseudrandom numbers
Like this: https://picasaweb.google.com/lh/photo/Z ... linkQuote2
. Sharp error results in an appropriate norm are incomplete.2_A. It is missing the concept of a function as in real analysis.This is generally a problem (?) with numerical methods.