enter image description here

Above is from my Bayesian notes, I have questions as:

  1. I know for discrete case, the stationary distribution $p(\theta)$ is defined as $$p(\theta) = A p(\theta)$$ where $A$ is the Markov Chain. But what is the definition for stationary distribution $p(\theta)$ in continuous cases?

  2. In the definition of $A(\theta, S)$, what does it actually mean? I thought (might be not correct) since $\theta \in S$, so $p(S|\theta)$ is just the probability that moves from any $\theta$ in $S$ to any elements in $S$. Thus, $p(S|\theta)$ contains the situation that maps $\theta$ to itself. If this is the case, why we need not moving term $r(\theta)I(\theta \in S)$? Or might be I misunderstood it...

  3. In the proof part, for the last step, why the second term just canceled? Might be again as the second question I did not understand the $r(\theta)$.

  4. The last line, "The above auto-regressive process converges to $N(0,1.33)$". Does this $N(0,1.33)$ just pop out from nowhere? Or might be I just do not know why we get it...


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.