Statistical Inference
Estimators, likelihood, the bootstrap, hypothesis testing, multiplicity and what a confidence interval really claims.
7concepts
149flashcards
51minutes of reading
- 01 Confidence Intervals and Coverage What the 95% in a 95% interval refers to, why the Wald interval for a proportion is badly behaved near zero, and how a confidence interval differs from the credible interval people usually think they are reading.
- 02 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.
- 03 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.
- 04 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.
- 05 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.
- 06 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.
- 07 Likelihood Ratio, Wald and Score Tests Three asymptotically equivalent ways to test a parameter from the log-likelihood, which measure the vertical drop, the horizontal distance and the slope at the null, and which can disagree wildly in exactly the samples where the answer matters.