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Monte Carlo Simulation

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Explain the concept of risk analysis and how Monte Carlo simulation can provide useful information for making decisions. Please be detailed.

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The Monte Carlo Method is used to determine the uncertainty in risk assessment and can be attached to effect estimates obtained from observational data. It tries to account for confounding, selection biases, and measurement error (Greenland, 2001). The Monte Carlo method used algorithms and random sampling to compute its results and is used in computer simulations for mathematical systems. They are most useful when there is no deterministic algorithm, which means that the system does not behave predictably and will not always return to the same answer. Instead, it is stochastic and incorporates random events. These random events get incorporated in the Monte Carlo method by implementing random inputs based on a probability distribution over the domain (Sugiyami, 2008). However, note that Monte Carlo method assumes that the probability distribution is Gaussian, or normal, for each parameter (Greeenland, 2001).

Think of this as money going into a piggy bank. A deterministic algorithm would always have the same number of steps and the same amount of money ...

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The expert explains the concepts of risk analysis and how Monte Carlo simulations can provide useful information for making decisions.

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Monte Carlo Simulation and Sensitivity Analysis

A decision maker is working on a problem that requires her to study the uncertainty surrounding the payoff of an investment. There are three possible levels of payoff -$1,000, $5,000, and $10,000. As a rough approximation, the decision maker believes that each possible payoff is equally likely. But she is not fully comfortable with the assessment that each probability is exactly 1/3, and so would like to conduct a sensitivity analysis. In fact, she believes that each probability could range from 0 to ½.
1. Show how a Monte Carlo simulation could facilitate a sensitivity analysis of the probabilities of the payoff
2. Suppose the decision maker is willing to say that each of the three probabilities could be chosen from a uniform distribution between 0 and 1. Could you incorporate this information into your simulation? If so, how? If not, explain why not, or what additional information you would need

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