$$

Dimensional statistics

• Dispersions
• moments and related notions
  • p-norms#$p$-mean
  • Moment-generating function
  • Variance
    • Mean–variance spectrum
  • Correlation
  • Effect size
  • Cumulants and Wick products
• High-dimensional statistics

Dimensionless statistics

• Statistical distances
• Couplings
• Ratio divergences
  • Variational representations
• Generalized entropies
• Power entropies and divergences
• Mix, reject, replace

Measures of information

• Information divergence
  • Sanov’s theorem
• Entropy
  • Entropy deficit
  • Cross-entropy
  • Entropy maximizers are never surprised
• Mutual information

Inequalities

• Inequalities between divergences
• Data processing inequalities
• Shearer’s lemma
• Reverse entropic inequalities

Applications

• concentration bounds
  • Hoeffding bound
  • Chernoff bound
  • Variational representations
• boolean analysis
  • Edge-isoperimetric inequality
  • Level-1 inequality
• combinatorics
  • A constant lower bound for the union-closed sets conjecture
  • Repairing distributions

Inference

• Inference
  • Density functions
  • Weak and strong priors
• Variational inference
  • Variational free energy
• Fisher information matrix