Monte Carlo Method: Simulation and Inference

This lecture introduces the Monte Carlo method as a simulation tool for making statistical inferences based on random events. The instructor explains how to compute statistical quantities using a stochastic model, realizations of random variables, and sample mean estimators. The lecture covers the properties of the estimator, unbiasedness, accuracy quantification, variance estimation, and confidence intervals. It also discusses the consistency and asymptotic normality of the estimator, error control, adaptive strategies for choosing sample sizes, and the probabilistic nature of Monte Carlo simulations.