MCMC

Main work:

Overview of MCMC.

Methods of accelerating MCMC.

Others:

Compare acceleration effect.

Catalogue

• Introductions
• 1. Notations
  • 1.1
  • 1.2
  • 1.3
  • 1.4
• 2. Preparatory knowledge
  • 2.1 Bayesian inference
  • 2.2 Monte Carlo integral
  • 2.3
  • 2.4
• 3. Basic MCMC
  • 3.1 Metroplis algorithm
  • 3.2 Metroplis-Hastings algorithm (MH)
  • 3.3 Gibbs sampler
• 4. Adaptive MCMC
  • 4.1 General Adaptive Metropolis (AM) Algorithm
  • 4.2 Adaptive Rejection Metropolis Sampling (ARMS)
  • 4.3 Independent doubly adaptive rejection Metropolis sampling (IA$^2$RMS)
• 5. Gradient-based techniques
  • 5.1 Metropolis adjusted Langevin algorithm (MALA)
  • 5.2 Hamiltonian Monte Carlo (HMC)
  • 5.3 Riemann manifold MALA (MMALA) and HMC (RMHMC)
  • 5.4 The ”No‐U‐Turn Sampler” (NUTS)
• 6. Importance Sampling
  • 6.1 Stantard importance sampling
  • 6.2 Adaptive importance sampling
  • 6.3 Convergence and variance
  • 6.4 Group inportance sampling
  • 6.5 Sequential inportance sampling
• 7. MC-within-MCMC methods
  • 7.1 Multiple-try Metroplis (MTM)
  • 7.2 Independent multiple-try Metroplis (I-MTM) schemes
  • 7.3 Group Metroplis sampling
• Summary
  • 小结
• Notes
• Reference
• 致谢
• 后记