اپلیکیشن اندرویدی فلش‌کارت آموزشی توزیع پسین: نقشه راه به سوی قدرت

🎓 دوره آموزشی جامع

📚 اطلاعات دوره

عنوان دوره: دوره توزیع پسین: نقشه راه به سوی قدرت

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

موضوع میانی: توزیع پسین (Posterior Distribution)

📋 سرفصل‌های دوره

• 1. Bayesian Inference Core Principles
• 2. Posterior Distribution Fundamentals
• 3. Likelihood and Prior Interaction
• 4. Conjugate Prior Families
• 5. Analytical Posterior Solutions
• 6. When Computation Is Intractable
• 7. Introduction to Monte Carlo Methods
• 8. Random Sampling Basics
• 9. Markov Chain Concepts
• 10. Stationary Distributions
• 11. Metropolis Algorithm Origins
• 12. Metropolis-Hastings General Form
• 13. Proposal Distribution Strategies
• 14. Acceptance Probability Derivation
• 15. Detailed Balance Condition
• 16. Gibbs Sampling Derivation
• 17. Full Conditional Distributions
• 18. Gibbs for Normal Models
• 19. Hamiltonian Monte Carlo Theory
• 20. Hamilton's Equations in Statistics
• 21. Leapfrog Integrator Basics
• 22. No-U-Turn Sampler Mechanics
• 23. NUTS Stopping Criterion
• 24. Stan Implementation Essentials
• 25. PyMC3 Model Specification
• 26. RStan Interface Workflow
• 27. Convergence Diagnostics: R-hat E
• 28. Potential Scale Reduction Rate
• 29. Effective Sample Size Computation
• 30. Trace Plot Analysis Guide
• 31. MCMC Burn-In Period Handling
• 32. Thinning Chains Rationale
• 33. Correlation Time Estimation
• 34. Autocorrelation Function Plot
• 35. Variance Estimation from Samples
• 36. Bayesian Linear Regression MCMC
• 37. Posterior Predictive Checking
• 38. P-Value Bayesian Reinterpretation
• 39. Model Selection with DIC
• 40. WAIC and Cross-Validation
• 41. Hierarchical Model Construction
• 42. Partial Pooling Mechanics
• 43. Random Effects MCMC
• 44. Dirichlet Process Clustering
• 45. Nonparametric Posteriors
• 46. Sequential Monte Carlo Overview
• 47. Particle System Resampling
• 48. Importance Sampling Weights
• 49. Rao-Blackwell Theorem Application
• 50. Control Variates Technique
• 51. Sequential MCMC Updates
• 52. Parallel Tempering MCMC
• 53. Replica Exchange Methods
• 54. Distributed MCMC Computing
• 55. Big Data Bayesian Analysis
• 56. Streaming Posterior Updates
• 57. Approximate Bayesian Computation
• 58. ABC-SMC Algorithm
• 59. Variational Inference Foundations
• 60. Mean-Field Approximation Details