اپلیکیشن اندرویدی فلش‌کارت آموزشی توزیع‌های پیشین غیر اطلاعاتی ضعیف: یک راهنمای عملی برای کاربرد MCMC

🎓 دوره آموزشی جامع

📚 اطلاعات دوره

عنوان دوره: دوره توزیع‌های پیشین غیر اطلاعاتی ضعیف: یک راهنمای عملی برای کاربرد MCMC

موضوع کلی: روش‌های نمونه‌گیری مونت‌کارلو مارکوف (MCMC) در آمار بیزی

موضوع میانی: توزیع پیشین (Prior Distribution)

📋 سرفصل‌های دوره

• 1. Bayesian foundation: why MCMC requires deliberate prior specification
• 2. Weak informative vs uninformative: mapping the prior spectrum
• 3. Mandatory properties every valid prior distribution must possess
• 4. Critical red flags: overconfident priors that break MCMC convergence
• 5. Decision framework for establishing weak informativity in prior design
• 6. Balancing prior strength with model identifiability constraints
• 7. Structuring a formal sensitivity analysis for prior choices
• 8. Empirical Bayes estimation of weakly informative priors from data
• 9. Reference priors: construction, interpretation, and MCMC applicability
• 10. Hierarchical prior structures for multi-level Bayesian models
• 11. Specifying priors for regression coefficients in linear Bayesian models
• 12. Prior selection for scale parameters and dispersion terms
• 13. Prior distribution choices for correlation matrices in multivariate settings
• 14. Implementing weakly informative priors for logistic regression models
• 15. Prior design for Poisson and other count data Bayesian models
• 16. Hierarchical modeling: prior specification for group-level effects
• 17. Managing multimodality when using weak prior specifications
• 18. Interpreting R-hat and effective sample size through prior influence
• 19. Prior-driven optimization of effective sample size in practice
• 20. Posterior predictive checks: evaluating prior impact on inferences
• 21. MCMC algorithm selection: Metropolis-Hastings versus Gibbs with priors
• 22. NUTS sampler geometry and how priors affect traversal efficiency
• 23. Reparameterization techniques to improve MCMC mixing with priors
• 24. Practical strategies to reduce autocorrelation via prior tuning
• 25. Hands-on exercise: building a custom MCMC loop with hand-specified priors
• 26. PyMC4/3: syntax and best practices for weakly informative priors
• 27. R brms and rstanarm: leveraging default weak informativity structures
• 28. Case study: Bayesian linear regression applied with weak priors
• 29. Case study: Bayesian logistic regression for binary outcome analysis
• 30. Case study: Survival analysis using MCMC with prior sensitivity
• 31. Troubleshooting divergent MCMC transitions due to prior misspecification
• 32. Prior reparameterization methods for challenging posterior geometries
• 33. Weakly informative priors for random effects in mixed-effects models
• 34. Combining cross-validation with prior predictive checking workflows
• 35. Interpreting and reporting posterior results with explicit prior roles
• 36. Ethical and practical guidelines for prior selection in scientific work
• 37. Comparative analysis: default versus custom weakly informative priors
• 38. Design exercise: eliciting priors from domain matter expertise
• 39. Design exercise: running grid-based sensitivity analysis on priors
• 40. Advanced topic: scale-location transformations for prior stability
• 41. Advanced topic: shrinkage priors (lasso, horseshoe) within MCMC frameworks
• 42. Advanced topic: robust priors for outlier-heavy or heavy-tailed data
• 43. Quiz design: identifying prior types and predicting MCMC behavior impacts
• 44. Comparative study: default prior behavior across PyMC, Stan, and JAGS
• 45. Common pitfalls: avoiding over-parameterization with weak priors in MCMC
• 46. Research translation: documenting prior choices for peer review transparency
• 47. Advanced technique: adaptive MCMC with prior feedback loops
• 48. Practical roadmap: steps to transition from uninformative to weakly informative priors
• 49. Capstone challenge: design a prior structure for a given Bayesian model
• 50. Capstone execution: run MCMC, diagnose, and interpret prior influence