first hmm example

[AlexanderFengler]

hmm-ssm first notebook example.
Needs a bit of refinement but it's a poc.

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[digicosmos86]

LGTM!

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krishnbera commented on 2026-03-11T18:30:36Z
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minor: consider making the title more informative for not-so-technical audience who might be interested in latent processes?

Eg. Joint Modeling of Latent Cognitive States and Decision Processes: Utilizing HMM with DDM Emissions

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krishnbera commented on 2026-03-11T18:30:37Z
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broken github repo link here.

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krishnbera commented on 2026-03-11T18:30:38Z
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Line #3.    

Can probably introduce a blurb about how the likelihood is computed for such models? Might help ppl who are not already familiar with it?

See eg. blurb below --

The likelihood of an HMM-DDM is calculated by integrating the continuous DDM densities into a discrete Hidden Markov Model framework using the Forward Algorithm.

The Core Process

1. Local DDM Densities: For every trial $t$, we calculate the likelihood of the observed response time and choice under each possible hidden state $k$.
2. State Filtering: We use a "forward pass" to track the probability of being in state $k$ at time $t$, given all previous observations.
3. Recursive Update: This forward probability is updated trial-by-trial by multiplying the previous trial's beliefs by the transition matrix $P$ and the current trial's DDM density.
4. Total Likelihood: By summing these probabilities at the final trial $N$, we obtain the marginal likelihood of the entire dataset across all possible state sequences.

[krishnbera]

@AlexanderFengler this already is in a great shape!
Made few minor comments. Ability to use HMMs with SSMs in such an easily accessible manner is def something a lot of people would find interesting.