import arviz as az
import bambi as bmb
import numpy as np
import pandas as pdHorseshoe Prior
In this example, we will use the Horseshoe Prior (Carvalho et al., 2009) to model a large number of variables, with only a few slopes being significantly different from zero.
Here is what we did:
- We defined an intercept.
- We defined a vector of 50 betas, 5 of which were drawn from a normal(5,1) distribution, and then assigned a random sign.
- We created the design matrix with normal(0,1) entries and set \(\sigma\) to 1.
- We calculated the deterministic means \(\mu\) using the intercept and the design matrix multiplied by the betas.
- We simulated 100 response variables (observations) from a normal distribution with mean \(\mu\) and standard deviation \(\sigma\).
Next, we proceeded with the Bayesian estimation of the model. We proposed the horseshoe prior, for which the following parameters were calculated:
\[\mu_i = \alpha + \beta_1 x_{1i} + \beta_2 x_{2i} + ... + \beta_p x_{pi}\]
\[y_i \sim N(\mu_i, \sigma^2)\]
\[\alpha \sim N(0,1)\]
\[\beta_j \sim N(0,\lambda_j^2 \tau^2)\]
\[\lambda_j \sim C^+(0,1)\]
\[\tau \sim T^+(df=3)\]
\[\sigma^2 \sim N^+(0,1)\]
D = 50
D0 = 5
SEED = 123456789 # for reproducibility
rng = np.random.default_rng(SEED)
INTERCEPT = rng.uniform(-3, 3) # simulate an intercept
COEF = np.zeros(D)
# Simulate the slopes for significant variables
COEF[:D0] = rng.choice([-1, 1], size=D0) * rng.normal(5, 1, size=D0)
N = 100
X = rng.normal(size=(N, D))
SIGMA = 1.0
# Simulate the data
y = INTERCEPT + X.dot(COEF) + rng.normal(0, SIGMA, size=N)Here we create the dataframe and the term name for the set of variables, to define the formula.
df = pd.DataFrame(X)
df.columns = [f"x{i}" for i in range(X.shape[1])]
df["y"] = yterm_name = "c(" + ", ".join([f"x{i}" for i in range(X.shape[1])]) + ")"
formula = f"y ~ {term_name}"
formula'y ~ c(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x40, x41, x42, x43, x44, x45, x46, x47, x48, x49)'Finally, we call the Horseshoe prior and create the model
priors = {
term_name: bmb.Prior("Horseshoe"),
}
model = bmb.Model(formula, df, priors=priors)
model.set_alias({term_name: "predictors"})
model.build()
model.graph()ERROR (pytensor.graph.rewriting.basic): Rewrite failure due to: random_make_inplace
ERROR (pytensor.graph.rewriting.basic): node: t_rv{"(),(),()->()"}(*0-<RandomGeneratorType>, *1-<NoneTypeT>, *2-<Scalar(float64, shape=())>, 0.0, *3-<Scalar(float64, shape=())>)
ERROR (pytensor.graph.rewriting.basic): TRACEBACK:
ERROR (pytensor.graph.rewriting.basic): Traceback (most recent call last):
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1933, in process_node
replacements = node_rewriter.transform(fgraph, node)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1086, in transform
return self.fn(fgraph, node)
~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/rewriting/basic.py", line 50, in random_make_inplace
new_outputs = new_op.make_node(*node.inputs).outputs
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/op.py", line 368, in make_node
size = normalize_size_param(size)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/utils.py", line 190, in normalize_size_param
shape = cast(as_tensor_variable(shape, ndim=1, dtype="int64"), "int64")
~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/__init__.py", line 50, in as_tensor_variable
return _as_tensor_variable(x, name, ndim, **kwargs)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/functools.py", line 934, in wrapper
return dispatch(args[0].__class__)(*args, **kw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/basic.py", line 113, in _as_tensor_Variable
raise TypeError(
f"Tensor type field must be a TensorType; found {type(x.type)}."
)
TypeError: Tensor type field must be a TensorType; found <class 'pytensor.tensor.type_other.NoneTypeT'>.
ERROR (pytensor.graph.rewriting.basic): Rewrite failure due to: random_make_inplace
ERROR (pytensor.graph.rewriting.basic): node: t_rv{"(),(),()->()"}(*0-<RandomGeneratorType>, *1-<NoneTypeT>, *2-<Scalar(int8, shape=())>, 0.0, *3-<Scalar(float32, shape=())>)
ERROR (pytensor.graph.rewriting.basic): TRACEBACK:
ERROR (pytensor.graph.rewriting.basic): Traceback (most recent call last):
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1933, in process_node
replacements = node_rewriter.transform(fgraph, node)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1086, in transform
return self.fn(fgraph, node)
~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/rewriting/basic.py", line 50, in random_make_inplace
new_outputs = new_op.make_node(*node.inputs).outputs
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/op.py", line 368, in make_node
size = normalize_size_param(size)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/utils.py", line 190, in normalize_size_param
shape = cast(as_tensor_variable(shape, ndim=1, dtype="int64"), "int64")
~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/__init__.py", line 50, in as_tensor_variable
return _as_tensor_variable(x, name, ndim, **kwargs)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/functools.py", line 934, in wrapper
return dispatch(args[0].__class__)(*args, **kw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/basic.py", line 113, in _as_tensor_Variable
raise TypeError(
f"Tensor type field must be a TensorType; found {type(x.type)}."
)
TypeError: Tensor type field must be a TensorType; found <class 'pytensor.tensor.type_other.NoneTypeT'>.
ERROR (pytensor.graph.rewriting.basic): Rewrite failure due to: random_make_inplace
ERROR (pytensor.graph.rewriting.basic): node: t_rv{"(),(),()->()"}(*0-<RandomGeneratorType>, *1-<NoneTypeT>, *2-<Scalar(int8, shape=())>, 0.0, *3-<Scalar(float32, shape=())>)
ERROR (pytensor.graph.rewriting.basic): TRACEBACK:
ERROR (pytensor.graph.rewriting.basic): Traceback (most recent call last):
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1933, in process_node
replacements = node_rewriter.transform(fgraph, node)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1086, in transform
return self.fn(fgraph, node)
~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/rewriting/basic.py", line 50, in random_make_inplace
new_outputs = new_op.make_node(*node.inputs).outputs
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/op.py", line 368, in make_node
size = normalize_size_param(size)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/utils.py", line 190, in normalize_size_param
shape = cast(as_tensor_variable(shape, ndim=1, dtype="int64"), "int64")
~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/__init__.py", line 50, in as_tensor_variable
return _as_tensor_variable(x, name, ndim, **kwargs)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/functools.py", line 934, in wrapper
return dispatch(args[0].__class__)(*args, **kw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/basic.py", line 113, in _as_tensor_Variable
raise TypeError(
f"Tensor type field must be a TensorType; found {type(x.type)}."
)
TypeError: Tensor type field must be a TensorType; found <class 'pytensor.tensor.type_other.NoneTypeT'>.
ERROR (pytensor.graph.rewriting.basic): Rewrite failure due to: random_make_inplace
ERROR (pytensor.graph.rewriting.basic): node: t_rv{"(),(),()->()"}(*0-<RandomGeneratorType>, *1-<NoneTypeT>, *2-<Scalar(int8, shape=())>, 0.0, *3-<Scalar(float32, shape=())>)
ERROR (pytensor.graph.rewriting.basic): TRACEBACK:
ERROR (pytensor.graph.rewriting.basic): Traceback (most recent call last):
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1933, in process_node
replacements = node_rewriter.transform(fgraph, node)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1086, in transform
return self.fn(fgraph, node)
~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/rewriting/basic.py", line 50, in random_make_inplace
new_outputs = new_op.make_node(*node.inputs).outputs
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/op.py", line 368, in make_node
size = normalize_size_param(size)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/utils.py", line 190, in normalize_size_param
shape = cast(as_tensor_variable(shape, ndim=1, dtype="int64"), "int64")
~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/__init__.py", line 50, in as_tensor_variable
return _as_tensor_variable(x, name, ndim, **kwargs)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/functools.py", line 934, in wrapper
return dispatch(args[0].__class__)(*args, **kw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/basic.py", line 113, in _as_tensor_Variable
raise TypeError(
f"Tensor type field must be a TensorType; found {type(x.type)}."
)
TypeError: Tensor type field must be a TensorType; found <class 'pytensor.tensor.type_other.NoneTypeT'>.
ERROR (pytensor.graph.rewriting.basic): Rewrite failure due to: random_make_inplace
ERROR (pytensor.graph.rewriting.basic): node: t_rv{"(),(),()->()"}(*0-<RandomGeneratorType>, *1-<NoneTypeT>, *2-<Scalar(float64, shape=())>, 0.0, *3-<Scalar(float64, shape=())>)
ERROR (pytensor.graph.rewriting.basic): TRACEBACK:
ERROR (pytensor.graph.rewriting.basic): Traceback (most recent call last):
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1933, in process_node
replacements = node_rewriter.transform(fgraph, node)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1086, in transform
return self.fn(fgraph, node)
~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/rewriting/basic.py", line 50, in random_make_inplace
new_outputs = new_op.make_node(*node.inputs).outputs
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/op.py", line 368, in make_node
size = normalize_size_param(size)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/utils.py", line 190, in normalize_size_param
shape = cast(as_tensor_variable(shape, ndim=1, dtype="int64"), "int64")
~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/__init__.py", line 50, in as_tensor_variable
return _as_tensor_variable(x, name, ndim, **kwargs)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/functools.py", line 934, in wrapper
return dispatch(args[0].__class__)(*args, **kw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/basic.py", line 113, in _as_tensor_Variable
raise TypeError(
f"Tensor type field must be a TensorType; found {type(x.type)}."
)
TypeError: Tensor type field must be a TensorType; found <class 'pytensor.tensor.type_other.NoneTypeT'>.
ERROR (pytensor.graph.rewriting.basic): Rewrite failure due to: random_make_inplace
ERROR (pytensor.graph.rewriting.basic): node: t_rv{"(),(),()->()"}(*0-<RandomGeneratorType>, *1-<NoneTypeT>, *2-<Scalar(int8, shape=())>, 0.0, *3-<Scalar(float32, shape=())>)
ERROR (pytensor.graph.rewriting.basic): TRACEBACK:
ERROR (pytensor.graph.rewriting.basic): Traceback (most recent call last):
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1933, in process_node
replacements = node_rewriter.transform(fgraph, node)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1086, in transform
return self.fn(fgraph, node)
~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/rewriting/basic.py", line 50, in random_make_inplace
new_outputs = new_op.make_node(*node.inputs).outputs
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/op.py", line 368, in make_node
size = normalize_size_param(size)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/utils.py", line 190, in normalize_size_param
shape = cast(as_tensor_variable(shape, ndim=1, dtype="int64"), "int64")
~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/__init__.py", line 50, in as_tensor_variable
return _as_tensor_variable(x, name, ndim, **kwargs)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/functools.py", line 934, in wrapper
return dispatch(args[0].__class__)(*args, **kw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/basic.py", line 113, in _as_tensor_Variable
raise TypeError(
f"Tensor type field must be a TensorType; found {type(x.type)}."
)
TypeError: Tensor type field must be a TensorType; found <class 'pytensor.tensor.type_other.NoneTypeT'>.
idata = model.fit(target_accept = 0.95, chains=2)Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [sigma, Intercept, predictors_tau, predictors_lam, predictors_raw]Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 97 seconds.
There were 107 divergences after tuning. Increase `target_accept` or reparameterize.
We recommend running at least 4 chains for robust computation of convergence diagnosticspriors = {
term_name: bmb.Prior("Horseshoe", tau_nu = 3, lam_nu = 3),
}
model = bmb.Model(formula, df, priors=priors)
model.set_alias({term_name: "predictors"})
model.build()
model.graph()ERROR (pytensor.graph.rewriting.basic): Rewrite failure due to: random_make_inplace
ERROR (pytensor.graph.rewriting.basic): node: t_rv{"(),(),()->()"}(*0-<RandomGeneratorType>, *1-<NoneTypeT>, *2-<Scalar(float64, shape=())>, 0.0, *3-<Scalar(float64, shape=())>)
ERROR (pytensor.graph.rewriting.basic): TRACEBACK:
ERROR (pytensor.graph.rewriting.basic): Traceback (most recent call last):
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1933, in process_node
replacements = node_rewriter.transform(fgraph, node)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1086, in transform
return self.fn(fgraph, node)
~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/rewriting/basic.py", line 50, in random_make_inplace
new_outputs = new_op.make_node(*node.inputs).outputs
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/op.py", line 368, in make_node
size = normalize_size_param(size)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/utils.py", line 190, in normalize_size_param
shape = cast(as_tensor_variable(shape, ndim=1, dtype="int64"), "int64")
~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/__init__.py", line 50, in as_tensor_variable
return _as_tensor_variable(x, name, ndim, **kwargs)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/functools.py", line 934, in wrapper
return dispatch(args[0].__class__)(*args, **kw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/basic.py", line 113, in _as_tensor_Variable
raise TypeError(
f"Tensor type field must be a TensorType; found {type(x.type)}."
)
TypeError: Tensor type field must be a TensorType; found <class 'pytensor.tensor.type_other.NoneTypeT'>.
ERROR (pytensor.graph.rewriting.basic): Rewrite failure due to: random_make_inplace
ERROR (pytensor.graph.rewriting.basic): node: t_rv{"(),(),()->()"}(*0-<RandomGeneratorType>, *1-<NoneTypeT>, *2-<Scalar(float64, shape=())>, 0.0, *3-<Scalar(float32, shape=())>)
ERROR (pytensor.graph.rewriting.basic): TRACEBACK:
ERROR (pytensor.graph.rewriting.basic): Traceback (most recent call last):
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1933, in process_node
replacements = node_rewriter.transform(fgraph, node)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1086, in transform
return self.fn(fgraph, node)
~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/rewriting/basic.py", line 50, in random_make_inplace
new_outputs = new_op.make_node(*node.inputs).outputs
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/op.py", line 368, in make_node
size = normalize_size_param(size)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/utils.py", line 190, in normalize_size_param
shape = cast(as_tensor_variable(shape, ndim=1, dtype="int64"), "int64")
~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/__init__.py", line 50, in as_tensor_variable
return _as_tensor_variable(x, name, ndim, **kwargs)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/functools.py", line 934, in wrapper
return dispatch(args[0].__class__)(*args, **kw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/basic.py", line 113, in _as_tensor_Variable
raise TypeError(
f"Tensor type field must be a TensorType; found {type(x.type)}."
)
TypeError: Tensor type field must be a TensorType; found <class 'pytensor.tensor.type_other.NoneTypeT'>.
ERROR (pytensor.graph.rewriting.basic): Rewrite failure due to: random_make_inplace
ERROR (pytensor.graph.rewriting.basic): node: t_rv{"(),(),()->()"}(*0-<RandomGeneratorType>, *1-<NoneTypeT>, *2-<Scalar(float64, shape=())>, 0.0, *3-<Scalar(float32, shape=())>)
ERROR (pytensor.graph.rewriting.basic): TRACEBACK:
ERROR (pytensor.graph.rewriting.basic): Traceback (most recent call last):
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1933, in process_node
replacements = node_rewriter.transform(fgraph, node)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1086, in transform
return self.fn(fgraph, node)
~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/rewriting/basic.py", line 50, in random_make_inplace
new_outputs = new_op.make_node(*node.inputs).outputs
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/op.py", line 368, in make_node
size = normalize_size_param(size)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/utils.py", line 190, in normalize_size_param
shape = cast(as_tensor_variable(shape, ndim=1, dtype="int64"), "int64")
~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/__init__.py", line 50, in as_tensor_variable
return _as_tensor_variable(x, name, ndim, **kwargs)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/functools.py", line 934, in wrapper
return dispatch(args[0].__class__)(*args, **kw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/basic.py", line 113, in _as_tensor_Variable
raise TypeError(
f"Tensor type field must be a TensorType; found {type(x.type)}."
)
TypeError: Tensor type field must be a TensorType; found <class 'pytensor.tensor.type_other.NoneTypeT'>.
ERROR (pytensor.graph.rewriting.basic): Rewrite failure due to: random_make_inplace
ERROR (pytensor.graph.rewriting.basic): node: t_rv{"(),(),()->()"}(*0-<RandomGeneratorType>, *1-<NoneTypeT>, *2-<Scalar(float64, shape=())>, 0.0, *3-<Scalar(float32, shape=())>)
ERROR (pytensor.graph.rewriting.basic): TRACEBACK:
ERROR (pytensor.graph.rewriting.basic): Traceback (most recent call last):
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1933, in process_node
replacements = node_rewriter.transform(fgraph, node)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1086, in transform
return self.fn(fgraph, node)
~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/rewriting/basic.py", line 50, in random_make_inplace
new_outputs = new_op.make_node(*node.inputs).outputs
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/op.py", line 368, in make_node
size = normalize_size_param(size)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/utils.py", line 190, in normalize_size_param
shape = cast(as_tensor_variable(shape, ndim=1, dtype="int64"), "int64")
~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/__init__.py", line 50, in as_tensor_variable
return _as_tensor_variable(x, name, ndim, **kwargs)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/functools.py", line 934, in wrapper
return dispatch(args[0].__class__)(*args, **kw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/basic.py", line 113, in _as_tensor_Variable
raise TypeError(
f"Tensor type field must be a TensorType; found {type(x.type)}."
)
TypeError: Tensor type field must be a TensorType; found <class 'pytensor.tensor.type_other.NoneTypeT'>.
ERROR (pytensor.graph.rewriting.basic): Rewrite failure due to: random_make_inplace
ERROR (pytensor.graph.rewriting.basic): node: t_rv{"(),(),()->()"}(*0-<RandomGeneratorType>, *1-<NoneTypeT>, *2-<Scalar(float64, shape=())>, 0.0, *3-<Scalar(float64, shape=())>)
ERROR (pytensor.graph.rewriting.basic): TRACEBACK:
ERROR (pytensor.graph.rewriting.basic): Traceback (most recent call last):
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1933, in process_node
replacements = node_rewriter.transform(fgraph, node)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1086, in transform
return self.fn(fgraph, node)
~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/rewriting/basic.py", line 50, in random_make_inplace
new_outputs = new_op.make_node(*node.inputs).outputs
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/op.py", line 368, in make_node
size = normalize_size_param(size)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/utils.py", line 190, in normalize_size_param
shape = cast(as_tensor_variable(shape, ndim=1, dtype="int64"), "int64")
~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/__init__.py", line 50, in as_tensor_variable
return _as_tensor_variable(x, name, ndim, **kwargs)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/functools.py", line 934, in wrapper
return dispatch(args[0].__class__)(*args, **kw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/basic.py", line 113, in _as_tensor_Variable
raise TypeError(
f"Tensor type field must be a TensorType; found {type(x.type)}."
)
TypeError: Tensor type field must be a TensorType; found <class 'pytensor.tensor.type_other.NoneTypeT'>.
ERROR (pytensor.graph.rewriting.basic): Rewrite failure due to: random_make_inplace
ERROR (pytensor.graph.rewriting.basic): node: t_rv{"(),(),()->()"}(*0-<RandomGeneratorType>, *1-<NoneTypeT>, *2-<Scalar(float64, shape=())>, 0.0, *3-<Scalar(float32, shape=())>)
ERROR (pytensor.graph.rewriting.basic): TRACEBACK:
ERROR (pytensor.graph.rewriting.basic): Traceback (most recent call last):
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1933, in process_node
replacements = node_rewriter.transform(fgraph, node)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/graph/rewriting/basic.py", line 1086, in transform
return self.fn(fgraph, node)
~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/rewriting/basic.py", line 50, in random_make_inplace
new_outputs = new_op.make_node(*node.inputs).outputs
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/op.py", line 368, in make_node
size = normalize_size_param(size)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/random/utils.py", line 190, in normalize_size_param
shape = cast(as_tensor_variable(shape, ndim=1, dtype="int64"), "int64")
~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/__init__.py", line 50, in as_tensor_variable
return _as_tensor_variable(x, name, ndim, **kwargs)
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/functools.py", line 934, in wrapper
return dispatch(args[0].__class__)(*args, **kw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/home/tomas/oss/bambinos/bambi/.pixi/envs/dev/lib/python3.13/site-packages/pytensor/tensor/basic.py", line 113, in _as_tensor_Variable
raise TypeError(
f"Tensor type field must be a TensorType; found {type(x.type)}."
)
TypeError: Tensor type field must be a TensorType; found <class 'pytensor.tensor.type_other.NoneTypeT'>.
idata = model.fit(target_accept=0.97)Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [sigma, Intercept, predictors_tau, predictors_lam, predictors_raw]Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 81 seconds.
There were 57 divergences after tuning. Increase `target_accept` or reparameterize.ax, = az.plot_forest(
idata,
var_names=["predictors"],
coords={"predictors_dim": range(D0)},
kind='ridgeplot',
ridgeplot_truncate=False,
ridgeplot_alpha=0.5,
hdi_prob=0.95,
combined=True,
figsize=(8, 6)
)
ax.scatter(COEF[:D0][::-1], ax.get_yticks(), c='C1', label="Actual value");
ax.set_xlabel(r"$\beta_i$");
ax.set_ylim(bottom=None, top=1.55 * ax.get_yticks().max())
ax.set_yticklabels(range(D0)[::-1]);
ax.set_ylabel(r"$i$");
ax.legend(loc='upper center');
ax.set_title("Posterior distribution of nonzero coefficients");
%load_ext watermark
%watermark -n -u -v -iv -wLast updated: Sun Sep 28 2025
Python implementation: CPython
Python version : 3.13.7
IPython version : 9.4.0
numpy : 2.3.3
arviz : 0.22.0
pandas: 2.3.2
bambi : 0.14.1.dev57+g7b2bb342c.d20250928
Watermark: 2.5.0