Chapter 6 Monte Carlo methods for inference

Monte Carlo Methods may refer to any statistical or numerical method where simulation is used. When we talk about Monte Carlo methods for inference we just look at these inference processes. In this way, we can use Monte Carlo to estimate:

• Parameters of sampling
• Distribution of a statistic
• Mean squared error (MSE)
• Percentiles
• Other measures of interest.

In statistical inference there is uncertainty in any estimate. The methods we are going to see use repeated sampling from a given probability model, known as parametric bootstrap. We simulate the stochastic process that generated the data, repeatedly drawing samples under identical conditions. Other MC methods known as nonparametric use repeated sampling from an observed sample.