It's also super useful for exploring the spectrum of potential outcomes in financial projections / retirement scenarios. People are sometimes tempted to think in the simpler terms of average rates of return and not fully consider issues like sequence risk. MC can help build better intuitions around the real chances of success given a broader range of
varying market conditions.
The beginning of the Monte Carlo method (1987) [pdf]
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Re: The beginning of the Monte Carlo method (1987) [pdf]
#22Earlier quoted context omitted.
You should be able to model "infinite" complexity, the way people design analog circuits is basically this.
Sorry for stupid question, what is infinite complexity in analog circuit ? Any examples/model ?
I think it's an ad-hoc term. But basically, MC simulations are needed because circuit elements such as transistors, resistors may be mismatched, for example Vth in MOS transistors. This can create input offsets in op-amps, or timing differences in logic. You can run exactly the same simulations as normally (DC operating point, AC transfer function, time-domain with many thousands of points) just over and over with new random parameters according to the distribution estimated in device characterization (I think mostly Gaussian).
Transistors models like BSIM are crazy complicated these days and there's no way to find an analytical solution for all that.
Re: The beginning of the Monte Carlo method (1987) [pdf]
#23I didn't realize how integral Monte Carlo sims were to our early advances in nuclear technology. It makes sense to me though- it seems like the Monte Carlo method lets you punch above your weight class in terms of measuring and predicting phenomena that are too complex, or too expensive to deterministically model. My intuition tells me that it's effectiveness would fall off as the complexity of the in/out relationshi…
It is hard to generalise about the suitability of Monte Carlo methods. In practical applications it is almost always used in hybrid systems, combined with analytical methods and problem specific short cuts. How one should apply Monte Carlo methods to a problem tends to be an open ended question.
Re: The beginning of the Monte Carlo method (1987) [pdf]
#24It's not a very good history.
It says "In the late 1940s, Stanislaw Ulam invented the modern version of the Markov Chain Monte Carlo method", but as far as I know, this is incorrect. He invented a Monte Carlo method, but not a Markov chain Monte Carlo method. Markov chain Monte Carlo is generally attributed to Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller. See https://en.wikipedia.org/wiki/Metropolis-Hastings_algorithm
The article fails even to distinguish simple Monte Carlo based on independently sampled points from Markov chain Monte Carlo. It seems rather confused in other respects too, such as in its discussion of "mean field" methods.
Re: The beginning of the Monte Carlo method (1987) [pdf]
#25Nuclear engineer here (specialty in core design/simulation). It's fun to see the Monte Carlo method be used in so many other fields now. Even in nuclear, deterministic methods are still orders of magnitude faster for most 'normal' reactor analyses on reactor configurations that are common enough to have all the important deterministic effects known. But with computers so fast, it's quite common for people, especially…
That sounds super interesting, how does one get into simulating reactor cores? I'm very familiar with MC methods from computer graphics.
Re: The beginning of the Monte Carlo method (1987) [pdf]
#26It's not a very good history. It says "In the late 1940s, Stanislaw Ulam invented the modern version of the Markov Chain Monte Carlo method", but as far as I know, this is incorrect. He invented a Monte Carlo method, but not a Markov chain Monte Carlo method. Markov chain Monte Carlo is generally attributed to Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller. See https://en.wikipedia.org/wiki/Metropolis-Hasting…
Here is an article "The beginning of the Monte Carlo method" by N. Metropolis: https://lib-www.lanl.gov/cgi-bin/getfile?00326866.pdf
Re: The beginning of the Monte Carlo method (1987) [pdf]
#27It's not a very good history. It says "In the late 1940s, Stanislaw Ulam invented the modern version of the Markov Chain Monte Carlo method", but as far as I know, this is incorrect. He invented a Monte Carlo method, but not a Markov chain Monte Carlo method. Markov chain Monte Carlo is generally attributed to Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller. See https://en.wikipedia.org/wiki/Metropolis-Hasting…
What do you think comes next after HMC/NUTS for general purpose turn-key sampling?
Re: The beginning of the Monte Carlo method (1987) [pdf]
#28Nuclear engineer here (specialty in core design/simulation). It's fun to see the Monte Carlo method be used in so many other fields now. Even in nuclear, deterministic methods are still orders of magnitude faster for most 'normal' reactor analyses on reactor configurations that are common enough to have all the important deterministic effects known. But with computers so fast, it's quite common for people, especially…
That sounds super interesting, how does one get into simulating reactor cores? I'm very familiar with MC methods from computer graphics.
An Exact MCNP Modeling of Pebble Bed Reactors:
https://www.researchgate.net/publication/264537140_An_Exact_...
OP's link was a rabbit hole (in a v. good way), sent me down some paper on the LCG random number generator used for MCNP modelling, which somehow led to that.
Re: The beginning of the Monte Carlo method (1987) [pdf]
#29Nuclear engineer here (specialty in core design/simulation). It's fun to see the Monte Carlo method be used in so many other fields now. Even in nuclear, deterministic methods are still orders of magnitude faster for most 'normal' reactor analyses on reactor configurations that are common enough to have all the important deterministic effects known. But with computers so fast, it's quite common for people, especially…
>But with computers so fast, it's quite common for people, especially in conceptual design space, to use Monte Carlo methods since it's a lot easier to believe the answer once you get it.
Is it really easier to "believe" an answer on a purely stochastical level? I'm kinda surprised, I would be way more confident (if I were to choose) with answers from deterministic descriptions/equations despite being more abstract and potentially harder to "visualize".
I find more often than not supposed 'comprehensibility' on the surface level to be quite misleading. Of course if one doesn't have clue where to start and enough processing power the Monte Carlo method and alike certainly can help to jumpstart/brute force the process.
Re: The beginning of the Monte Carlo method (1987) [pdf]
#30For those interested, the first Monte Carlo program, which ran on the ENIAC, has been found and documented (840 instructions long). It was also the first stored program ever run.
https://eniacinaction.com/the-articles/3-los-alamos-bets-on-...
https://eniacinaction.com/wp-content/uploads/2014/02/LosAlam...