Monte Carlo Simulation: Exploring Error, Accuracy and Variance

[stn]

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

 

[FactChecker]

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.

 

[Stephen Tashi]

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.

 

[stn]

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.

 

[blue_raver22]

for your question!

Monte Carlo simulation is a powerful tool used in various fields of science and engineering to model and analyze complex systems. It involves using random numbers to simulate a large number of possible outcomes and then analyzing the results to gain insights into the behavior of the system. There are many books that provide a good explanation of Monte Carlo simulation, such as "Monte Carlo Methods in Financial Engineering" by Paul Glasserman and "Monte Carlo Simulation and Finance" by Don L. McLeish. These books not only explain the theory behind Monte Carlo simulation but also provide practical examples and step-by-step instructions on how to perform the simulation.

In terms of error, accuracy, and variance, Monte Carlo simulation allows for the exploration of these concepts by running multiple simulations with varying parameters. This allows for a better understanding of how different factors can affect the results and how to minimize errors and increase accuracy.

To answer your questions, Monte Carlo simulation involves generating random numbers, but it is not the same as simply generating a set of random numbers. The numbers are generated according to a specific distribution, such as a Gaussian distribution, to accurately represent the real-world system being simulated. This means that the random variables used in Monte Carlo simulation do not follow a uniform distribution, but rather a distribution that is relevant to the system being studied. This allows for a more realistic representation of the system and its behavior.

I hope this helps to clarify any confusion you may have about Monte Carlo simulation. It is a complex but valuable tool that can provide valuable insights and aid in decision-making processes in various fields.