In Doing Bayesian Data Analysis 2ed, by Kruschke, in chapter 10, we get two equations (10.1, 10.2) for which no hint as to how they are obtained is given...

How does one get $$p(\theta_1,\theta_2,...,m|D)= \frac{p(D|\theta_1,\theta_2,...,m)p(\theta_1,\theta_2,...,m)}{\sum_m \int p(D|\theta_1,\theta_2,...,m)p(\theta_1,\theta_2,...,m)\ d\theta_m}=\frac{\prod_m p_m(D|\theta_m,m)p_m(\theta_m|m)p(m)}{\sum_m \int \prod_m p_m(D|\theta_m,m)p_m(\theta_m|m)p(m)\ d\theta_m}$$ ?

I would think that $p(D|\theta_1,\theta_2,...,m)= p_m(D|\theta_m,m)$? I would say there's a typo in the first equality, and that the second is wrong... But I'm the one most probably wrong.

In Doing Bayesian Data Analysis 2ed, by Kruschke, in chapter 10, we get two equations (10.1, 10.2) for which no hint as to how they are obtained is given...

How does one get the second equality in the following decomposition$$p(\theta_1,\theta_2,...,m|D)= \frac{p(D|\theta_1,\theta_2,...,m)p(\theta_1,\theta_2,...,m)}{\sum_m \int p(D|\theta_1,\theta_2,...,m)p(\theta_1,\theta_2,...,m)\ d\theta_m}=\frac{\prod_m p_m(D|\theta_m,m)p_m(\theta_m|m)p(m)}{\sum_m \int \prod_m p_m(D|\theta_m,m)p_m(\theta_m|m)p(m)\ d\theta_m}$$ ?

I would think that $p(D|\theta_1,\theta_2,...,m)= p_m(D|\theta_m,m)$? I would say there's a typo in the first equality, and that the second is wrong... But I'm the one most probably wrong.