Let's say that one has run $m$ parallel MCMC chains where each chain has had burn-in. Let the resulting chains be denoted by $$ x_1^{(i)},\dots,x_N^{(i)} \quad \text{ for } i=1,\dots,m,$$ where $N$ is the length of each chain after burn-in.
If one would want to combine these chains into one long chain, is it as simple as concatenating them as $$x_1^{(1)},\dots,x_N^{(1)},\dots, x_1^{(m)},\dots, x_N^{(m)} ?$$
In my case, each $x_i$ is a parametervector $\theta_i$. My goal is to sample from the posterior $$ p(\theta \mid y),$$ where $y$ is the data. The reason for why I am interested in parallel chains is because they are needed for calculating potential scale reduction factor (PSRF).