Monte Carlo Simulation: Exploring Error, Accuracy and Variance

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Discussion Overview

The discussion revolves around Monte Carlo simulation, focusing on its definition, applications, and the relationship between random number generation and statistical distributions. Participants explore the breadth of the subject, its implementation in various fields, and seek resources for better understanding.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about books that explain Monte Carlo simulation, noting that many tutorials discuss error, accuracy, and variance without detailing how to perform the simulations.
  • Another participant clarifies that Monte Carlo simulation encompasses more than just generating random numbers, highlighting its applications in various fields such as traffic simulation and queueing theory.
  • A different participant explains that Monte Carlo simulations involve drawing pseudo-random numbers, which may not necessarily follow a normal distribution, and describes the typical process of generating numbers from a uniform distribution before transforming them into other distributions.
  • A later reply shares personal experience with simulations using different distributions in Matlab, indicating a realization that these were indeed Monte Carlo simulations, despite the terminology used in literature.

Areas of Agreement / Disagreement

Participants express differing views on the scope of Monte Carlo simulation and its relationship to random number generation. There is no consensus on the best resources for learning about the topic.

Contextual Notes

Some participants mention specific distributions and applications, but there is no resolution on the definitions or methodologies associated with Monte Carlo simulations.

stn
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Hello,
1. Does anybody know which book that gives a good explanation about monte carlo simulation?
I've read many tutorials, it mentions about its error, accuracy, variance.
But, many of them don't actually show, how to perform monte carlo simulation.

Questions
2. Is it actually the same as generating random numbers? Gaussian distribution?
so, it is actually random variables with normal distribution?


thanks
 
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No. Monte Carlo simulation is a very large subject that is studied extensively in Operations Research. It is much broader than just generating random numbers of a known distribution. It includes simulating any situation where randomness has a significant effect (traffic simulation, combat, queueing theory, spares management, etc.) Some (admittedly old) books to give you an idea of the breadth of the subject are "Monte Carlo Methods" by Hammersley and Handscomb and "Computer Simulation Techniques" by Naylor, Balintfy, Burdick, and Chu. The first emphasizes the math and the second emphasized the computer implementation (given the limited simulation languages at that time). Maybe someone can suggest more recent references.
 
Last edited:
stn said:
Hello,
1. Does anybody know which book that gives a good explanation about monte carlo simulation?

Can you write computer programs? "Monte-Carlo simulation" is very general subject. Suppose your wrote a computer program which had steps in it where the computer drew pseudo-random numbers to determine the outcome. The program might simulate physics, economics or just a game. Such a program is a "Monte-Carlo simulation" and if you ran it many times to get the statistics of its output, you could say you were using "Monte-Carlo simulation".

2. Is it actually the same as generating random numbers? Gaussian distribution?
so, it is actually random variables with normal distribution?

Monte-Carlo simulations on computers do use functions that generate pseudo-random numbers. The numbers are not always from normal distributions. The usual procedure is to generate pseudo-random numbers from a uniform distribution and then, if another type of distribution is desired, apply an algorithm to these uniformly distributed numbers to produce other distributions.
 
hi Stephen,
Thanks for the explanation, it helps me a lot.
I did lots of simulation using different distributions such as Normal distribution & Rayleigh distribution in Matlab to obtain Bit error rate in wireless telecommunication without realizing that actually I've monte carlo simulation.
Only few papers mention monte carlo simulation, the rest just mention add this AWGN or Rayleigh distribution, that's why i am not clear myself.
 

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