Statistical Inference
Estimators, likelihood, the bootstrap, hypothesis testing, multiplicity and what a confidence interval really claims.
7concepts
149flashcards
51minutes of reading
- 01 Estimators, Bias, Variance and Consistency What makes one estimator better than another, why the mean squared error splits cleanly into bias squared plus variance, and why an unbiased estimator is frequently the wrong thing to want.
- 02 Hypothesis Tests, Error Types and the Neyman–Pearson Lemma A hypothesis test is a decision rule with two error rates that trade against each other, and the Neyman–Pearson lemma says the likelihood ratio is the rule that buys the most power for a fixed false-positive rate.
- 03 P-Values, Multiplicity and the Garden of Forking Paths What a p-value actually claims, why running twenty tests guarantees a false discovery, and the difference between controlling the family-wise error rate and controlling the false discovery rate.
- 04 Sampling Distributions and the Central Limit Theorem Every standard error and every normal-theory interval is a statement about a distribution you never observe, and the central limit theorem is a promise about that distribution whose speed of delivery depends on skewness, tails and dependence.
- 05 The Bootstrap and Resampling Resampling the data you have to simulate the sampling distribution you never observed, why the percentile interval is not always the right one, and the specific statistics for which the bootstrap silently fails.