I’ve been struggling with modelling simple periodic functions, discovering that the likelihood topography is massively multimodal in very unintuitive ways. But recently I had the idea to reframe things with a hidden markov model applied to the slope of the function derivative. I’ve had some seeming …

I think adding that noise parameter over fits: [Screen Shot 2021-04-21 at 5.08.20 AM] Instead of using a normal, I think it is better to make a categorical variable using y. I’ve made a noisy measure of the “hidden state” by taking the difference in y and getting the sign. functions { int sign…

Solved it! Just had to make f a parameter and express its derivative in the hmm part: data{ int n ; vector[n] y ; } parameters{ simplex[2] p0 ; // initial state probabilities simplex[2] tp_pn ; // transition probability for positive to negative simplex[2] tp_np ; // transition probability for …

Oh wait, noise probably shouldn’t be involved in this part, but I don’t know what should be there: for(i_n in 2:n) { state_ll[1,i_n-1] = normal_lpdf((f[i_n]-f[i_n-1]) | pos_slope, noise) ; state_ll[2,i_n-1] = normal_lpdf((f[i_n]-f[i_n-1]) | neg_slope, noise) ; }

Maybe sqrt(square(noise) + square(noise))? EDIT: on second thought no, it should be the variance of the mean function. EDIT2: actually I have no idea, forget I said anything.

[image] Koalha: Maybe sqrt(square(noise) + square(noise))? EDIT: on second thought no, it should be the variance of the mean function. EDIT2: actually I have no idea, forget I said anything. Ha, I tried precisely the same thing last night. Or at least with y~normal(f,noise) then dy~hmm(...,…

Thanks! Diving into your solution now…

Hm, I think with your formulation, inference on f is indistinguisable from not having any of the HMM structure in there at all. Indeed, commenting out all that structure and re-running yields pretty much identical posteriors on f. But your trick of getting the sign of the difference and doing the HM…

yea I ran it both ways and noticed the output was the same. I know that you were just making a contrived example. Does having the HMM and what I’ve done sample better on your actual problem where not using the HMM doesn’t sample well?

Unfortunately my real data is much noisier, hence the desire to be working with the latent variable f in the HMM part. I actually came up with an alternative idea that I’ll post as a separate thread in a bit and link back here in case you’re interested. Still only 10% worked out, but “feels” like a…

Hidden markov modelling the derivative of a latent function

Modeling

mike-lawrence April 22, 2021, 4:47pm 11

Topic		Replies	Views
Name for hidden markov model lpdf Developers hmm	10	1280	April 9, 2020
Multivariate Hidden Markov Model Modeling rstan	6	1707	January 15, 2021
Covariates in Hidden Markov Model with hmm_marginal Modeling ecology , hmm	19	3537	September 19, 2023
Examples for hidden Markov models with longitudinal data General hmm	8	3332	May 6, 2020
Ideas for modelling a periodic timeseries Modeling specification	58	4471	May 3, 2022

Hidden markov modelling the derivative of a latent function

Related topics