Formulas for Bayesian models

Beta conjugate prior distribution

• Bernoulli-beta conjugate model
  • Posterior predictive distribution
  • Proofs
• Binomial-beta conjugate model
  • Posterior predictive distribution
  • Proofs
• Geometric-beta conjugate model
  • Posterior predictive distribution
  • Proofs
• Negative binomial-beta conjugate model
  • Posterior predictive distribution
  • Proofs

Gamma conjugate prior distribution

• Exponential-gamma conjugate model
  • Posterior predictive distribution
  • Proofs
• Poisson-gamma conjugate model
  • Posterior predictive distribution
  • Proofs

Normal-inverse-gamma prior distribution

• Normal-normal-inverse-gamma conjugate model
  • Posterior predictive distribution
  • Proofs
  • References

Pareto conjugate prior distribution

• Uniform-Pareto conjugate model
  • Posterior predictive distribution
  • Proofs