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November 01, 2005
First Day of Statistics
On the day after Halloween, we formally started our study of statistics.
Probability theory tells us how the world would look given the true model. Statistics is the process of making inferences about the true model given what we observe.
The Central Limit Theorem is the most important tool in statistics.
The classic problem is asking "What is mu?" Our estimate of mu should have two properties, unbiasedness and efficiency.
Estimators that take a weighted average with unequal weights are unbiased, but not efficient.
Once we have our estimate of mu, we construct a confidence interval that makes a formal probability statement about how accurate our estimate is.
In classical statistics, mu is a fixed, but unknown parameter. The confidence interval is random because the sample mean is random. There is a 95% probability that the random 95% confidence interval includes the fixed, but unknown mu.
Posted by bparke at November 1, 2005 10:50 PM