I am trying to apply the method proposed by Chib in Marginal Likelihood from the Metropolis Hastings Output to calculate the marginal likelihood of a logit model the includes latent variables. Specifically, $Pr(Y=1)=\exp\frac{\beta x+z}{1+\exp(\beta x + z)}$ where an unobserved variable $z \sim N(0,\sigma)$. I will be very thankful for tips on how to calculate the marginal likelihood of the model!