For a metropolis hastings algorithm, suppose that the stationary distribution is defined as the Gibbs Boltzmann distribution $\pi_T(x)= \frac{1}{Z_T}e^{-\frac{V(x)}{T} }$ where $Z_T = \sum_{y\in V} e^{-\frac{V(y)}{T}}$.

It is known why there is no need to calculate the normalizing constant $Z_T$ for the posterior distribution but I am wondering if there are methods or articles presented how to approximate it especially for metropolis hastings in applications because sometimes it appears again when computing the convergence speed!


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