15.2 Convergence

By definition, a Markov chain generates samples from the target distribution only after it has converged to equilibrium (i.e., equilibrium is defined as being achieved when \(p(\theta^{(n)})\) is the target density). The following point cannot be expressed strongly enough:

  • In theory, convergence is only guaranteed asymptotically as the number of draws grows without bound.

  • In practice, diagnostics must be applied to monitor convergence for the finite number of draws actually available.