Sometimes poor approximations are satisfactory because the aim is merely to determine the strategic variables of a problem. There are also numerical problems that can be solved by deterministic methods but can be more simply solved approximately by the Monte Carlo method. A familiar example is the estimation of the probability of winning a game of pure chance: Sometimes the only reasonably simple method of estimation is to play the game several times. The main advantage of Monte Carlo is that other methods can be more costly or impracticable. The importance of the method arises primarily from the need to solve problems for which other methods are more expensive or impracticable, and from the increased importance of all numerical methods because of the development of the electronic digital computer. In many of the useful applications, the mathematical problem itself arises in a problem of probability in physics or other sciences, operational research, image analysis, general statistics, mathematical economics, or econometrics. ![]() ![]() The estimate is usually given as the average value, in a sample, of some statistic whose mathematical expectation is equal to x. ![]() A technique for estimating the solution, x, of a numerical mathematical problem by means of an artificial sampling experiment.
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