Make performance linear

[idontgetoutmuch]

Since I just did this, I thought I would share it with you.

transformed parameters {
  vector[N] log_p;
  {
    vector[N+1] log_p_e;
    vector[N+1] log_p_l;
    log_p_e[1] = 0;
    log_p_l[1] = 0;
    for (i in 1:N) {
      log_p_e[i + 1] = log_p_e[i] + normal_lpdf(D[i] | mu1, sigma1);
      log_p_l[i + 1] = log_p_l[i] + normal_lpdf(D[i] | mu2, sigma2);
    }
    log_p = rep_vector(-log(N) + log_p_l[N + 1], N) + head(log_p_e, N) - head(log_p_l, N);
  }
}

[gmodena]

Hi @idontgetoutmuch,
thanks for the contribution. I incorporated your suggestion in the model, and updated the article.

[josswright]

I've been trying to wrap my head around this. I'm not sure I've quite understood it.

My main interest is whether this could be generalised to an arbitrary number of changepoints.

[idontgetoutmuch]

I am not sure what your model is but you could certainly have two changepoints but I suspect performance will take a hit. I am not sure how to model an arbitrary number of changepoints. I've used a hidden markov model successfully to model a process moving between a finite set of states. Stan can then be used to infer the transition and observation matrices (functions) but I don't know if that is what you want. I suggest asking on https://discourse.mc-stan.org. There are some very knowledgeable and helpful folks there :)

[josswright]

Thank you! I've just put up a post there.

It was the specifics of the dynamic programming approach that I was wondering about. As I haven't quite got my head around what the code snippet in the first post is doing, I wasn't sure whether it would be possible to extend that approach to, say, two or three changepoints.

I've got the default "slow" method from the Stan user guide just about working, but given the slowdown associated with multiple changepoints in the first place, I was really hoping that I might be able to take advantage of a similar dynamic programming trick.