Statistics: informal notes

• Examples
  • Sample mean
  • Sample variance
• 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

• AIC

• Exhaustive
  • Leave-p-out
• Non-exhaustive
  • k-fold

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

• Linear models
  • Categorical
    • t-test
    • ANOVA
      • One-way
  • Interval
    • Simple linear regression
    • Multiple linear regression
• Generalized linear models
  • Binomial response variable
    • Logistic
    • 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

• Tree-based methods
  • Random forests
• Support vector machines
• Boosting
• Neural networks

• Point estimation
• Examples
  • Normal prior and likelihood
• Confidence intervals
• Examples
  • Perception as probabilistic inference

• Methods for finding tests
  • Posterior odds
• Examples
  • Signal detection theory (SDT)
    • Yes-No task
  • High threshold theory (HHT)

• BIC