[Python] how to set truncated t-distribution prior in bambi

%pip install bambi==0.15.0
%pip install numpy==1.26.4


import bambi as bmb
import polars as pl
from polars import col, lit
import pandas as pd
import numpy as np
import arviz as az

np.random.seed(42)
num_rows = int(10e3)

# Generate random data
shape, scale = 10, 6 # Gamma parameters to achieve mean of 60
revenue = np.random.gamma(shape, scale, size=num_rows)

# Create Polars DataFrame
pl_a = pl.DataFrame({
"recipe": "A",
"revenue": revenue
})

# Generate random data
shape, scale = 11, 6 # Gamma parameters to achieve mean of 66
revenue = np.random.gamma(shape, scale, size=num_rows)

# Create Polars DataFrame
pl_b = pl.DataFrame({
"recipe": "B",
"revenue": revenue
})

pl_ab = pl.concat([pl_a, pl_b])

m_lm = bmb.Model(
"revenue ~ recipe",
pl_ab.to_pandas(),
family="gaussian",
priors={
"Intercept": bmb.Prior("Normal", mu=60, sigma=2),
"recipe": bmb.Prior("Normal", mu=0, sigma=2),
"sigma": bmb.Prior("StudentT", nu=3, mu=20, sigma=5)
# bmb.Prior("HalfStudentT", nu=3, sigma=5)
}
)

m_lm.fit()


In the above code I can specify a StudentT or HalfStudentT prior for sigma, but I am unsuccessful in setting a truncated StudentT with a specified mu.

I have failed to set a truncated prior in every way I could imagine:

m_trunc = bmb.Model(
"revenue ~ recipe",
pl_ab.to_pandas(),
family="gaussian",
priors={
"Intercept": bmb.Prior("Normal", mu=60, sigma=2),
"recipe": bmb.Prior("Normal", mu=0, sigma=2),
"sigma": bmb.Prior(
"Truncated",
prior=bmb.Prior("StudentT", nu=3, mu=20, sigma=5),
lower=0, upper=np.inf
)
}
)

m_trunc.fit()


TypeError: Truncated.dist() missing 1 required positional argument: 'dist'

m_trunc = bmb.Model(
"revenue ~ recipe",
pl_ab.to_pandas(),
family="gaussian",
priors={
"Intercept": bmb.Prior("Normal", mu=60, sigma=2),
"recipe": bmb.Prior("Normal", mu=0, sigma=2),
"sigma": bmb.Prior(
"Truncated",
dist="StudentT",
nu=3, mu=0, sigma=1,
lower=0, upper=np.inf
)
}
)

m_trunc.fit()


TypeError: 'str' object is not callable

m_trunc = bmb.Model(
"revenue ~ recipe",
pl_ab.to_pandas(),
family="gaussian",
priors={
"Intercept": bmb.Prior("Normal", mu=60, sigma=2),
"recipe": bmb.Prior("Normal", mu=0, sigma=2),
"sigma": bmb.Prior(
"StudentT", nu=3, mu=0, sigma=1, lower=0, upper=5 # Truncation applied here
)
}
)

m_trunc.fit()


TypeError: RandomVariable.make_node() got an unexpected keyword argument 'lower'

import pymc as pm

m_trunc = bmb.Model(
"revenue ~ recipe",
pl_ab.to_pandas(),
family="gaussian",
priors={
"Intercept": bmb.Prior("Normal", mu=60, sigma=2),
"recipe": bmb.Prior("Normal", mu=0, sigma=2),
"sigma": bmb.Prior(
pm.Bound(pm.StudentT, lower=0, upper=5), # Bound the StudentT prior
nu=3, mu=0, sigma=1 # Parameters for StudentT
)
}
)

m_trunc.fit()


AttributeError: module 'pymc' has no attribute 'Bound'

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