Statistics Topics

  1. Estimators

    1. Bias, Variance, MSE

    2. Cramer-Rao bound

    3. Information Geometry

    4. Sufficiency

    5. Consistency

    6. Asymptotic Properties

    7. Maximum likelihood

    8. Bias-Variance Tradeoff

    9. James-Stein Paradox

  2. Goodness of fit

    1. chi-square test

    2. other tests

    3. anomoly detection

  3. Hypothesis Testing

    1. Simple vs. Compound hypotheses

    2. Nuisance Parameters

    3. TypeI and TypeII error

    4. Test statistics

    5. Neyman-Pearson Lemma

    6. Connection to classification

    7. multiple testing

      1. look elsewhere effect

      2. Family wise error rate

      3. False Discovery Rate

      4. Asymptotics, Daves, Gross and Vitells

  4. Confidence Intervals

    1. Interpretation

    2. Coverage

    3. Power

    4. No UMPU Tests

    5. Neyman-Construction

    6. Likelihood-Ratio tests

    7. Profile likelihood

    8. Profile construction

    9. Asymptotic Properties of Likelihood Ratio

  5. Bayesian Model Selection

    1. Bayes Factors

    2. BIC, etc.

  6. Bayesian Credible Intervals

    1. Interpretation

    2. Metropolis Hastings

    3. Variational Inference

      1. LDA

  7. Causal Inference

    1. Elements of Causal Inference by Jonas Peters, Dominik Janzing and Bernhard Schölkopf free PDF

  8. Statistical Decision Theory

    1. Admissible decision rule

    2. Experimental Design

      1. Expected Information Gain

      2. Bayesian Optimization