$$p(\mathbf{\theta} | \mathbf{y}) = \frac{p(\mathbf{y|\theta}) p(\mathbf{\theta})} {\int p(\mathbf{y|\theta}) p(\mathbf{\theta})d\mathbf{\theta}} \propto p(\mathbf{y|\theta}) p(\mathbf{\theta}) $$ where $\beta$ is