# Statistical Simulation: Introduction and Issues (2012)

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 simulations are widely used in many fields:

• Science: Scientists use statistical simulations to model complex systems, such as the climate or the spread of disease.
• Business: Businesses use statistical simulations to forecast sales, evaluate the risks of new investments, and design logistics networks.
• Government: Governments use simulations to model the effects of economic policies, assess the risks of natural disasters, and plan for future events.
• Gambling: Casinos use simulations to design games that are fair and profitable.

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.

In summary, statistical simulation is a technique used to imitate the behavior of a system or process under various conditions. It involves creating a computer model of the system and running the model repeatedly with different inputs. The outputs of the model are then analyzed to learn about the behavior of the real system.

### 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?