observation.priors#

Hyperpriors and prior distributions for observation model parameters.

Classes

`ObsParamsHyperPrior`	Homogeneous hyperpriors for observation model parameters.
`ObsParamsHyperPriorStructured`	Structured hyperpriors with per-group, per-latent control.
`ObsParamsPrior`	Prior distributions over observation model parameters.

class ObsParamsHyperPrior( *, a_alpha: float = 1e-12, b_alpha: float = 1e-12, a_phi: float = 1e-12, b_phi: float = 1e-12, beta_d: float = 1e-12, )[source]#

Homogeneous hyperpriors for observation model parameters.

Scalar values broadcast to all groups/latents. Typical for inference with uninformative priors.

Parameters:

a_alphafloat, default 1e-12: Shape parameter of the ARD prior (Gamma). Must be > 0.
b_alphafloat, default 1e-12: Rate parameter of the ARD prior (Gamma). Must be > 0.
a_phifloat, default 1e-12: Shape parameter of the observation precision prior (Gamma). Must be > 0.
b_phifloat, default 1e-12: Rate parameter of the observation precision prior (Gamma). Must be > 0.
beta_dfloat, default 1e-12: Precision of the observation mean prior (Gaussian). Must be > 0.

Examples

>>> priors = ObsParamsHyperPrior()  # Use defaults (uninformative)
>>> priors = ObsParamsHyperPrior(a_alpha=1e-6, b_alpha=1e-6)

class ObsParamsHyperPriorStructured( *, a_alpha: ndarray, b_alpha: ndarray, a_phi: float = 1.0, b_phi: float = 1.0, beta_d: float = 1.0, )[source]#

Structured hyperpriors with per-group, per-latent control.

Enables sparsity constraints (np.inf in a_alpha forces zero loadings) and incorporation of prior knowledge.

Parameters:

a_alphandarray of float, shape (n_groups, x_dim): Shape parameters for ARD priors. Use np.inf to force zero loadings (sparsity pattern).
b_alphandarray of float, shape (n_groups, x_dim): Rate parameters for ARD priors. Typically ones or matched to a_alpha.
a_phifloat, default 1.0: Shape parameter of observation precision prior. Must be > 0.
b_phifloat, default 1.0: Rate parameter of observation precision prior. Must be > 0.
beta_dfloat, default 1.0: Precision of observation mean prior. Must be > 0.

Examples

>>> # 3 groups, 4 latents, with sparsity pattern
>>> sparsity = np.array([
...     [1, 1, np.inf, 1],      # Group 0: latents 0,1,3
...     [1, np.inf, 1, 1],      # Group 1: latents 0,2,3
...     [np.inf, 1, 1, 1],      # Group 2: latents 1,2,3
... ])
>>> priors = ObsParamsHyperPriorStructured(
...     a_alpha=100 * sparsity,
...     b_alpha=100 * np.ones((3, 4)),
... )

class ObsParamsPrior( hyperprior: ObsParamsHyperPrior | ObsParamsHyperPriorStructured, )[source]#

Prior distributions over observation model parameters.

Encapsulates p(C, d, phi, alpha) and handles correct sampling order (alpha must be sampled before C, since C|alpha ~ N(0, alpha^-1)).

Parameters:

hyperpriorObsParamsHyperPrior or ObsParamsHyperPriorStructured: Hyperprior parameters controlling the prior distributions.

sample( y_dims: ndarray, x_dim: int, rng: Generator, ) → ObsParamsRealization[source]#

Sample from joint prior p(alpha)p(C|alpha)p(d)p(phi).

Parameters:

y_dimsndarray of int, shape (n_groups,): Dimensionalities of each observed group.
x_dimint: Number of latent dimensions.
rngnumpy.random.Generator: Random number generator.

Returns:

ObsParamsRealization: Sampled parameter values.