The detailed balance condition requires that for any two states x and y, the probability flow from x to y exactly equals the flow from y to x. This bidirectional equilibrium guarantees that the target distribution is stationary for the Markov chain.
Conditions: Must hold for all pairs of states x and y in the state space.; P(x) and P(y) are probabilities under the target distribution.; T(y∣x) and T(x∣y) are transition probabilities.
The detailed balance condition requires that for any two states x and y, the probability flow from x to y exactly equals the flow from y to x. This bidirectional equilibrium guarantees that the target distribution is stationary for the Markov chain.
Conditions: Must hold for all pairs of states x and y in the state space.; P(x) and P(y) are probabilities under the target distribution.; T(y∣x) and T(x∣y) are transition probabilities.
The burn-in period consists of the initial samples generated by an MCMC algorithm before it has converged to its stationary distribution. These samples must be discarded because they are influenced by the arbitrary starting point and do not accurately represent the target distribution.
Conditions: Applies to MCMC sampling.; Requires discarding initial samples before using the rest for inference.; The chain starts from an arbitrary point.
The burn-in period consists of the initial samples generated by an MCMC algorithm before it has converged to its stationary distribution. These samples must be discarded because they are influenced by the arbitrary starting point and do not accurately represent the target distribution.
Conditions: Applies to MCMC sampling.; Requires discarding initial samples before using the rest for inference.; The chain starts from an arbitrary point.