Daniel Linares
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Statistics: informal notes

  • Probability and random variables
    • Probability
    • Random variables
    • Expectation
    • Stochastic processes
  • Statistical Decision Theory
    • Frequentist methods
      • Estimation
        • Point estimation
          • Methods
            • Method of moments
            • Maximum likelihood
              • Properties
              • Examples
                • Normal distribution
                • Poisson distribution
                • Binomial distribution
        • Confidence intervals
        • Examples
          • Sample mean
          • Sample variance
          • Pooled variance
          • Effect size
            • Difference family
              • Cohen’s d, Hedges g
      • Hypothesis testing
        • Tests
          • Likelihood ratio
            • Examples
              • Normal known variance
              • Normal unknown variance
              • Psychometric functions
            • Goodness-of-fit
              • Examples
                • Psychometric functions
          • Pearson \(X^2\)
          • Wald test
        • Sequential analysis
        • Examples
          • Signal detection theory (SDT)
            • Categorial judgment
              • Yes-No task
                • Normal model (equal-variance)
                • Normal model (unequal-variance)
                • Exponential model
              • Rating task
            • 2AFC task
          • High threshold theory (HHT)
            • Categorial judgment
              • Yes-No task
                • Bernoulli
      • Model selection
        • Information theory
          • AIC
        • Cross-validation
          • Exhaustive
            • Leave-p-out
          • Non-exhaustive
            • k-fold
      • Examples
        • Distributions \(\{ f(x,\theta): \theta \in \Theta \}\)

        • Regression and classification (supervised learning)

          • Examples
            • Neural encoding
          • Linear models
            • Interval
              • Simple linear regression
              • Multiple linear regression
            • Categorical
              • t-test
              • ANOVA
                • One-way
              • Non-parametric tests
                • Kruskal-Wallis
            • Interval and categorical
              • ANCOVA
            • Linear mixed models
          • Generalized linear models
            • Non mixed
              • Binomial response variable
                • Logistic
                • Psychometric functions
                  • MLE of the psychometric function: theory
                  • MLE of the psychometric function: practice
                  • quickpsy
            • Generalized linear mixed models
          • Non linear models
            • Binomial response variable
              • Fiting psychometric functions using a transducer function
            • Poisson response variable
              • Neural decoding using MLE
        • Methods

          • Tree-based methods
            • Random forests
          • Support vector machines
          • Boosting
          • Neural networks
    • Bayesian methods
      • Parametric models
        • Estimation
          • Point estimation
          • Examples
            • Normal prior and likelihood
          • Confidence intervals
          • Examples
            • Perception as probabilistic inference
        • Hypothesis testing
          • Methods for finding tests
            • Posterior odds
          • Examples
            • Signal detection theory (SDT)
              • Categorial judgment
                • Yes-No task
                  • Optimal performance (ideal observer)
            • High threshold theory (HHT)
        • Model selection
          • BIC
      • Non-parametric models
  • Unsupervised learning
    • PCA