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