Contents
Is detailed balance a necessary condition for a sampler?
Detailed balance is a sufficient, but not necessary, condition for converging to the target distribution.
Is detailed balance necessary?
Thus, the principle of detailed balance is a sufficient but not necessary condition for entropy increase in Boltzmann kinetics.
Is global balance a necessary condition for reaching equilibrium?
Top left: Global balance, a necessary condition for the convergence towards equilibrium. The total flow ∑ c φ c → a into any configuration a must equal the total flow ∑ c φ a → c out of it.
Is it true that MCMC fulfilling detailed balance always yield the stationary distribution?
It is not true that MCMC fulfilling detailed balance always yield the stationary distribution. You also need the process to be ergodic. Let’s see why: Consider x to be a state of the set all possible states, and identify it by the index i.
Is the chain in MCMC positive recurrent or irreducible?
So the chain that we construct in MCMC is irreducible, aperiodic and positive recurrent, which means it is an ergodic chain. We know that for an irreducible ergodic chain a stationary distribution exists which is unique and independent of initial distribution. Thanks for contributing an answer to Cross Validated!
What does MCMC do during burn-in period?
I am studying mcmc and I am wondering what mcmc does during burn-in period. And also what is the difference during burning period and after the burn-in period? MCMC relies on building a Markov chain whose stationary distribution is a joint distribution you wish to sample from.
What does MCMC do in multivariate space?
MCMC relies on building a Markov chain whose stationary distribution is a joint distribution you wish to sample from. But you don’t start at the stationary distribution, you start at some initial value (in multivariate space). It may take some time for the process to “wash out” the initial conditions.