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CS(17) Introduction to Statistical Inference and Simulation
Statistical inference is a critical component of data analysis. It focuses on making conclusions about a population based on information obtained from a sample. The main goal is to estimate unknown parameters or test hypotheses about the population’s characteristics. This process relies on probability theory to quantify uncertainty and ensure the reliability of the results.
In many real-world situations, analytical solutions for statistical inference problems are too complex or impossible to derive. For instance, in high-dimensional data analysis or when dealing with intricate probability distributions, calculating exact probabilities or parameter estimates analytically can be overwhelming. This is where simulation techniques, especially Monte Carlo become indispensable.
Key Question in Statistical Inference
When we aim to estimate a parameter 𝜽 of a random variable X based on a sample X1, X2, … Xn two fundamental questions arise:
Which estimator should we use for 𝜽?
How can we evaluate the quality of this estimator? This involves understanding properties like bias, consistency, and efficiency.
For example, suppose we want to estimate the mean 𝞵 of a population. While the sample mean Ẋ is…