I have a distribution like this
$$f(x_{n}|\boldsymbol{x}_{v_{n}},\gamma\ ^2) \sim \exp\left( \frac{1}{\gamma\ ^2} \sum_{n'\epsilon v_{n}}^n \frac{(x_{n}-x_{n'})^2}{d_{n,n'}}\right)$$
and I would like to get this joint prior $$f(\boldsymbol{x}|\gamma\ ^2) \sim (\gamma\ ^2) ^{-\frac{N-1}{2}} e^{\frac{(-x^T\delta\ x )}{2 \gamma\ ^2}}.$$
However I am not sure how to get this joint prior. What steps should I follow. Any help will be amazing.