Hi all. I’m trying to fit multilevel wave models for my research in brms. I’ve beens struggling to get the models to converge on my actual data, so I’ve moved to working with simple simulated examples to try and figure out what might be causing the problem. It seems like the frequency parameter in …

Hi! Fitting sinoidal functions to data can be quite a headache. Although I don’t fully grasp the model you are describing (the forum interface has interpreted some of the code in your post as formatting instructions, garbling the shown code), your trace plots show what’s going on. With the priors th…

I fully agree @mike-lawrence ! I meant to say that without very restrictive priors on parameters that determine phase-translations and frequencies, multi-modality is massive.

Given that the multimodality relates to the location of the true frequency, I think the priors need not merely be restrictive but truly highly informed by theory/prior data. Possibly this is what you meant though.

Thank you both for your timely responses! @mike-lawrence I will check out those suggestions you link to. I’ve also edited the post now so that the code should be properly formated. Sorry about that, I’m new to these forums. I was wondering about the multi-modality issue. As is hopefully now clear …

yes, the data is generated from a single frequency, but when you then compute the likelihood across a range of candidate true frequencies, that likelihood function is multimodal. And it’s not simply peaks at harmonics, it’s a much more complicated multimodality affected by the sample-rate & duratio…

Note that just recently I received the advice from @avehtari to try SMC sampling for periodic models, and so far using the SMC sampler in PyMC, chains seem to indeed mix better.

I add the explanation why SMC. If the period is unknown, there are multiple modes in the posterior for the period length or frequency. Many of the modes are such that they are no close to true frequency, but still some of the periods fit the data. If there are many observations, these modes can be d…

Thanks so much for these suggestions @mike-lawrence and @avehtari ! I will give them a try.

Oh, neat. I’d actually found that for very simple models, running SMC but giving it all the data at once still yielded better rhats than HMC, but then started getting bad rhats as I bumped up the model complexity. I’ll now see if feeding in data sequentially helps as you suggest.

Fitting Multilevel Wave Models

Modeling

mike-lawrence October 26, 2023, 12:06pm 3

In my experience, periodic models have massive multimodality that is inherent to the likelihood (n.b. Not the prior @LucC). Lots of ideas here but nothing I found generally robust.

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Fitting Multilevel Wave Models

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