Metropolis sampling starts by suggesting a new configuration \( \boldsymbol{x}^{k+1} \). In the brute force method this is done by some random change of the visible units. The new configuration is then accepted with the acceptance probability $$ \begin{align} A(\boldsymbol{x}^k \rightarrow \boldsymbol{x}^{k+1}) = \text{min} (1, \frac{P(\boldsymbol{x}^{k+1})}{P(\boldsymbol{x}^k)}), \tag{6} \end{align} $$ where we need the marginalized probability $$ \begin{align} P(\boldsymbol{x}) &= \sum_\mathbf{h} P_{rbm}(\mathbf{x}, \mathbf{h}) \tag{7}\\ &= \frac{1}{Z}\sum_\mathbf{h} e^{-E(\mathbf{x}, \mathbf{h})}. \tag{8} \end{align} $$