Statistics: informal notes

• Methods
  • Method of moments
  • Maximum likelihood
    • Properties
    • Examples
      • Normal distribution
      • Poisson distribution
      • MLE for the binomial distribution

• Likelihood ratio test
  • Examples
    • Normal known variance
    • Normal unknown variance
    • Psychometric functions
  • Goodness-of-fit
    • Examples
      • Psychometric functions
• Wald test

• Signal detection theory (SDT)
  • Categorial judgment
    • Yes-No task
      • Normal model
      • Exponential model
    • Rating task
  • 2AFC task
• High threshold theory (HHT)
  • Categorial judgment
    • Yes-No task
      • Bernoulli

Distributions \(\{ f(x,\theta): \theta \in \Theta \}\)

• Linear models
  • Normal response variable
    • Comparing means
    • Linear regression
      • MLE for linear regression
    • ANOVA
      • One-way
• Generalized linear models
  • Classification
    • Binomial response variable
      • Psychometric functions
        • MLE of the psychometric function: theory
        • MLE of the psychometric function: practice
        • quickpsy
• Non linear models
  • Binomial response variable
    • Fiting psychometric functions using a transducer function
  • Poisson response variable
    • Neural decoding using MLE

• Normal prior and likelihood

• Perception as probabilistic inference

• Posterior odds

• Signal detection theory (SDT)
  • Yes-No task
• High threshold theory (HHT)