Strengths And Weaknesses Of Monte Carlo Simulation

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What is Monte Carlo simulation?
Answer: Monte Carlo simulation is a technique that allows people to run simulation many times to obtain numerical results or distribution of an unknown probabilistic entity. It was invented by Stanislaw Ulam in the late 1940s at the Los Alamos National Laboratory and was named after the Monte Carlo Casino where Ulam’s uncle often gambled [1].

Why is it used in analysis (generally)?
Answer: Monte Carlo simulation is a very flexible technique and could easily be adapted or extended. Usually, when it is difficult or, sometimes, even impossible to obtain a closed-form expression of certain results or attributes, it becomes very useful [1]. Because, through repeated random sampling, we might be able to obtain approximate values of our desired results or attributes.

What are its strengths and weaknesses (contrast with, say, the Design of Experiments)?
Answer: The strengths and weaknesses of Monte Carlo simulation contrasting with the Design of Experiments are listed below:
Strengths: Very flexible with very few limits to the analysis, able to handle empirical distributions, can be easily adapted and extended, very intuitive and easily understood, computationally tractable when the dimensions of uncertainty increase
Weaknesses: Not as well controlled as Designed of Experiments, usually requires more computing resources, and relies on large amount of repeated random sampling in order to obtain an approximate result

What is a random number generator and what properties should it have?
Answer: A random number generator is a computational device which is able to generate a sequence of numbers or symbols that lack any pattern and appear to be random [3]. Ideally, a good random number generator should b...

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... these parameters. We would be able to have a holistic view of the performance of this agent-based model over the feature space. In the meanwhile, we could identify the parameters which contribute most to variances in the output and identify the potential danger in certain feature space.

Typical analysis such as analytical analysis (PDE, ODE etc), numerical analysis (finite element analysis) might not be so attractive in the settings of my research problem above. One of the big disadvantages for typical analysis in my research problem is that typical analysis is computationally intractable due to the high dimensions in the above problems. Secondly, typical analysis is usually not as flexible and adaptable as Monte Carlo simulations. Some analytical analysis such as PDE does not even fit the setting of the above research problems, as it is empirical by its natural.

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