Bayesian Ridge Regression applied to binary classification. How to compare the closed-form solution with the MCMC solution?

Question

I am working with Bayesian Ridge Regression applied to binary classification (I am using 2d-array -- n samples x r features). My questions are:

1. How do I compare the closed-form solution with the MCMC solution? In particular, in the closed-form, I compute theta as (X^T X + λI)^(−1)X^Ty, to which value obtained by MCMC (Hastings) I can compare this theta? 2. How can I verify if this comparison (e.g., the difference between theta and MCMC value) converges?
2. How can I check the convergence of the MCMC algorithm?

The comparison that I have performed at this momement seems to not converge