TheMCMC defines transition probabilities that ensure convergence to the stationary distribution. So, what is “Stationary Distribution”?
Stationary Distribution
If a distribution satisfy below, it is said as “Stationary Distribution”.
\int p_{*}(x) p(x, y) \, dx = p_{*}(y)A sufficient condition for ( p ) to become a stationary distribution is the detailed balance condition.
Detailed Balance Condition
The condition required for a Markov chain to converge to a stationary distribution is called the detailed balance condition.
Ergodicity
Additionally, the property that allows convergence to the stationary distribution from any initial distribution is known as ergodicity.
