Talk:Monte Carlo method

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Contents 1 main: 2 Simple Description 3 Factorisation 4 explanation 5 Commercial software packages 6 intro 7 move to Monte Carlo algorithm 8 Lack of Technical Details 9 Eddit

[edit] main:

Hello. The current revision says "It's well known that Monte Carlo methods were central to the simulations required for the Manhattan Project." Since there weren't electronic computers, how were the simulations carried out? Who was responsible for setting them up? Since the publications generally used to establish credit for the method date from the 50's, it seems this sentence needs to be clarified. Happy editing, Wile E. Heresiarch 15:11, 4 Mar 2004 (UTC)

I'm not sure of the details, most of the article is paraphrased from the referenced textbook and I don't remember it saying anything more about it. However I know Fermi's work with neutrons was pre-electronic computing. Apparently he used a mechanical calculator (like a Comptometer or similar). I'm not sure what he used for a random number source. -- Tim Starling 23:06, Mar 4, 2004 (UTC)

I believe there were computers in that time. Consider the Atanasoff-Berry Computer, for example. -Stimpy 21:24, 30 November 2006 (UTC)

Just querying whether 'To be written' should be in the article, or here? Something I've been thinking about actually: Do we keep a strict dichotomy between wiki and metawiki (ie, the content, and writing about it) with their respective namespaces, OR do we do whichever is considered most efficient for improving the article? As always, just throwing ideas about. nsh 22:18, Mar 19, 2004 (UTC) (talk)

In 2002 and before, to-do notes in articles were exceedingly popular. They're not so fashionable anymore but they're not against policy. -- Tim Starling 05:34, Mar 20, 2004 (UTC)

There's some advice to the effect that omissions should be noted. I find this unrealistic (in particular in mathematical topics, where completeness is unlikely, to say the least).

Charles Matthews 12:59, 12 Jun 2004 (UTC)

This article links to the disambiguation page for degree of freedom. I think it should link directly to the degree of freedom (statistics) page, but I don't know enough to be sure. Hopefully someone else does.

I think degrees of freedom (physics and chemistry) is the best page to link to, and I changed the article accordingly. Others may differ. -- Jitse Niesen (talk) 10:55, 7 September 2005 (UTC)

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What's wrong with including GAs? They are a reasonably good method for optimisation in many-dimensional spaces. -- Tim Starling 07:59, Mar 31, 2004 (UTC)

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Hi, I changed the reference from "central limit theorem" to "law of large numbers" in the description of the rate of convergence in numeric integration. The law of large numbers is the theorem about convergence of a sample mean to the population mean, and the central limit theorem is about convergence in distribution of a sample mean to a normal r.v. Since normality doesn't matter here, the LLN is the correct theorem. It's not quite obvious because it's applied to the square of the sum and not the sum itself. Gray 23:06, 17 June 2006 (UTC)

[edit] Simple Description

This article is quite technical. It would be nice to have a simpler layman's description too. --129.67.35.21 11:51, 20 September 2005 (UTC)

I'm not sure every scientific topic should have a layman's description. That could course some very long articles. However, I remember a teacher introduced Monte Carlo simulations with this example: Imagine you are walking on a beach and suddenly find that you can't remember the numerical value of pi. What can you do? Draw a square and a circle within the square, with the circle as large as possible. Then throw a number of sandgrains (say 1000) randomly in the square (I guess you would have to find a different color of sand to tell the difference). Since we know the ratio between the area of the circle and the area of the square is pi/4 we can find an approximation to pi by counting the grains outside (or inside) the circle and the deviation can be found from the number of grains.

This could be illustrated with a square, a circle and a number of "randomly" distributed dots, and used as an illustration for this article, with the explanation in the image text. Do you think that would be relevant? Zarniwoot 10:00, 24 January 2006 (UTC)

[edit] Factorisation

How about adding some words about the use of a monte carlo method to find factors. Eiler7 10:55, 4 February 2006 (UTC)

[edit] explanation

Perhaps I'm missing something, but the article seems to lack a description of what the Monte Carlo method is, instead only describing applications. AaronSw 03:35, 30 May 2006 (UTC)

I totally agree with you. I looked this up because I want to be able to answer the question: "What is a Monte Carlo simulation?" with a two or three sentence summary. I still can't do that after reading the article. (Aug 8, 06)

How doesn't "Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems. They are distinguished from other simulation methods (such as molecular dynamics) by being stochastic, that is nondeterministic in some manner - usually by using random numbers (or more often pseudo-random numbers) - as opposed to deterministic algorithms." answer the question? Would moving the mention of nondeterminism to the first sentence help? Fredrik Johansson 22:27, 8 August 2006 (UTC)

It doesn't, in fact, answer the question. The sentence you quoted gives an extremely broad classification, and then explains the differences with other methods. But it lacks an (adequately) informative definition of what the method really is, or at least how it's supposed to work. Some parts of the article later hint at the fact that MC is a form of evaluation based on repeated simulations from a set of randomized inputs (which is what I think it really is, though I'm not an expert at all - so don't quote me on that), but that info should probably be placed in the intro in a clearer form. 87.9.179.29 20:55, 8 February 2007 (UTC).

Reading the rest of the talk page, I see that this is not the only request for a simpler explaination. Maybe adding a simple example (like the classic circle area by hit/miss, as suggested somewhere above) after the definition may help. -- Sergio Ballestrero 08:04, 9 August 2006 (UTC)

Good idea. Numerical integration is probably the best example of a Monte Carlo method, and possibly the simplest to understand for non-technical readers. By the way, after reading the definition in the Dictionary of Algorithms and Data Structures, I'm inclined to agree that the one used here could be improved. The following distinction is made between two main types of randomized algorithm: "A Monte Carlo algorithm gives more precise results the longer you run it. A Las Vegas algorithm gives exactly the right answer, but the run time is indeterminate." Fredrik Johansson 13:55, 9 August 2006 (UTC)

And our lead section's definition is conflicted. It says the difference is the process is not deterministic, but typically PRNGs are used, making the process fully deterministic, just similar to a stochastic one. That and I agree the definition isn't really clear. I don't have any good books in front of me or ideas off the top of my head how to make the lead better, but I'll see what I can do. Any proposals for a clearer and more accurate lead would be great. Adding an example is not a bad idea, but the explanation shouldn't depend on it. - Taxman ^Talk 17:18, 9 August 2006 (UTC)

I absolutely agree that this article could be much clearer by providing just a short, clear answer to the question : What is the key property which makes the Monte Carlo method the Monte Carlo method? I have a good background in CS and maths, and was just looking to this article for a quick refresher on what made something a Monte Carlo simulation. Which I ended up going to google and going somewhere else for. It just needs to be made clear that the Monte Carlo method is and provides a quick way to provide a good, approximate numerical value when actually calculating the exact value is either impossible or too time consuming. 24.61.226.243 16:13, 17 March 2007 (UTC)

[edit] Commercial software packages

This section was accumulating nonnotable specialized software or other links that looked to be linkspam. So I partially cleaned it out and rephrased the lead to include phrasing on general purpose use and notability. My gut feeling is that Crystal Ball and @Risk are the pre-eminent tools and I could see only including them plus other software that is (or becomes) equally well accepted. However, I lack a non-OR source for this so I leave it to the group to comment. Martinp 21:41, 10 July 2006 (UTC)

I'm a little puzzled by external software links on a page like "Monte Carlo methods", a technique, by the way, that is completely software-dependent. Crystal Ball and @Risk are certainly widely-used tools and should be noted here. However, the fact that only spreadsheet add-ins are listed here is very misleading, as it implies that spreadsheets are the state-of-the-art in Monte Carlo simulation. While they are certainly widely used (because spreadsheets are ubiquitous), I find it hard to believe that any academic or practitioner would state that they are state-of-the-art in terms of Monte Carlo simulation tools. We have a tool (GoldSim) that is a general purpose Monte Carlo simulator, but is repeatedly removed from this external software list (while spreadsheet add-ins remain). It is both relevant (the software is completely focused on Monte Carlo simulation) and notable (used worldwide by government, commercial and research organizations, including the very national labs where the Monte Carlo method was first widely used: Los Alamos, Sandia, Argonne, Lawrence Berkeley). I understand the need to limit linkspam, but if you are going to have external software links at all on a topic like this (and I think you should, as without software, the method is not practical), it seems to me that some attempt should be made to be comprehensive regarding the tools that are actually used in the community.

[edit] intro

too many hyphens for my taste. The asides should be mentioned later, preferably in separate sentences. then again, it sets the mode for the randomness theme... Ojcit 17:47, 15 September 2006 (UTC)

[edit] move to Monte Carlo algorithm

I suggest the article be swapped with Monte Carlo algorithm to comply with other articles with similar names, e.g. Las Vegas algorithm. Stimpy 16:17, 5 November 2006 (UTC)

[edit] Lack of Technical Details

Sorry - I would add this to the above comments but still working out how to do this.

In my opinion there is insufficient technical detail in this document for it to be of any use - i.e. how does it work and why does it work.

I completely agree. Explanations given do not qualify for more than broad descriptions. I suggest rewriting or at least giving some examples. Ben ^T/_C 18:18, 22 February 2007 (UTC)

[edit] Eddit

Carlo should be in CAPPS