Statistical Simulation: Introduction and Issues

Simulation is used before an existing system is altered or a new system is built, to reduce the chances of failure to meet specifications, eliminate unforeseen bottlenecks, prevent under or over-utilization of resources, and optimize system performance. Simulation is used in many contexts, such as simulation of technology for performance optimization, safety engineering, training testing, education, and video games. Often, computer experiments are used to study simulation models. Models are simulated versions/results.
Statistical Simulation depends on unknown (or external/ impositions/ factors) parameters and statistical tools depend on estimates. In statistics, simulation is used to assess the performance of a method, typically when there is a lack of theoretical background. With simulations, the statistician knows and controls the truth.

In statistical simulation, data is generated artificially to test out a hypothesis or statistical method. Whenever a new statistical method is developed (or used), some assumptions need to be tested and verified (or confirmed). Statisticians use simulated data to test these assumptions.

• The simulation follows finite sample properties (have to specify $n$)
• The reasoning of statistical simulation can’t be proofed mathematically)
• Simulation is used to illustrate things.
• Simulation is used to check the validity of methods.
• Simulation is a technique of representing the real world via a computer program.
• A simulation is an act of initiating the behavior of some situation or some process utilizing something suitably analogous. (especially for study or some personal training)
• A simulation is a representation of something (usually on a smaller scale).
• Simulation is the act of giving a false/artificial appearance.

Issues In Statistical Simulation

• What distribution does the random variable have
• How do we generate these random variables for simulation
• How do we analyze the output of simulations
• How many simulation runs do we need
• How do we improve the efficiency of the simulation?

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