prior distributions for subject specific offsets

[jainraj]

I am trying to replicate the HDDM's Bayesian hierarchical model (see below image - from https://hddm.readthedocs.io/en/latest/methods.html)

Is the following the correct configuration for the boundary parameter?

{
    "name": "a",
    "formula": "a ~ 1 + (1|participant_id)",
    "link": "identity",
    "prior": {
        "Intercept": {
            "name": "Gamma",
            "mu": 1.5,
            "sigma": 0.75,
        },
        "1|participant_id": {
            "name": "Gamma",
            "mu": 0,
            "sigma": {
                "name": "HalfNormal",
                "sigma": 0.1,
            },
        },
    },
    "bounds": (0.0, numpy.inf),  
},

In the generated graph I see following nodes:

• a_1|participant_id_offset ~ Normal - what exactly is this?
• a_1|participant_id_sigma ~ HalfNormal
• a_1|participant_id ~ Deterministic connected to _offset and _sigma
• a_Intercept ~ Gamma

And when I look at plot_priors for a_1|participant_id - they all look Gaussian - Shouldn't they be Gamma distributed?. Seems like I am missing something basic.

PS: It is my first time using Hierarchical Bayesian models

[AlexanderFengler]

Hey @jainraj ,

I think the correct way to specify exactly as in HDDM for a would be to use a ~ 0 + (1|participant_id), with,

"1|participant_id": {
            "name": "Gamma",
            "mu": {"name": "Gamma",
                   "mu": 1.5,
                   "sigma": 0.75,
                  }
,
            "sigma": {
                "name": "HalfNormal",
                "sigma": 0.1,
            },
        },

Best,
Alex

[jainraj]

So @AlexanderFengler,

1. Does the 0 indicate that we are not learning the common offset, i.e., not a mixed-effects model (which HDDM couldn't do)?
2. The model graph shows up like this, which is a bit weird. Why isn't the "mu" connected to any node? Is it a plotting problem or does it actually mean that this parameter won't be tuned?

[jainraj]

So, I ran a simple model with this version, and it seems like the mu parameter does get tuned. Makes me think that this is more of a plotting problem. @AlexanderFengler if you can confirm this, maybe this can be taken as a bug and discussion can be closed?