Monte-Carlo
  • Introduction
  • AIS
  • Generate R.V.
    • Special Distribution
    • Copulas
    • Minimum of Two Exponential
  • Gibbs
    • Comparing two groups
    • Linear Regression
    • Simulation of Exp-Abs-xy
  • Markov Chain
  • MC Approximation
  • MC Integration
    • Rao-Blackwellization
  • MC Optimization
  • MCMC
    • MCMC diagnostics
  • Metropolis-Hastings
    • Metropolis
    • Independent MH
    • Random Walk MH
    • ARMS MH
  • PBMCMC
  • RJMCMC
  • Diagnosing Convergence
  • SMCTC
  • Tempering
    • Parallel Tempering
  • Misc
    • R vs. Julia
  • References
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MCMC

PreviousMC OptimizationNextMCMC diagnostics

Last updated 6 years ago

provides the following definition:

For illustration, you can visit the jupyter notebook on

Working principle: For an arbitrary starting value x(0)x^{(0)}x(0), a chain X(t)X^{(t)}X(t) is generated using a transition kernel with stationary distribution fff, which ensures the convergence in distribution of X(t)X^{(t)}X(t) to a random variable from fff.

Some good materials about MCMC.

https://cosx.org/2013/01/lda-math-mcmc-and-gibbs-sampling
Robert and Casella (2013)
MCMC_example