Prior

from SymbolicDSGE.bayesian import Prior, make_prior

Prior combines a distribution and a transform into a prior defined on unconstrained space.

Core API:

Name	Signature	Description
logpdf	Prior.logpdf(z)	Log-density in transformed space.
grad_logpdf	Prior.grad_logpdf(z)	Gradient of log-density in transformed space.
rvs	Prior.rvs(size, random_state)	Sampling in distribution space.
support	Prior.support	Distribution support.
maps_to	Prior.maps_to	Transform target support.

 

make_prior(
    distribution: str, # (1)!
    parameters: dict[str, Any], # (2)!
    transform: str, # (3)!
    transform_kwargs: dict[str, Any] | None = None, # (4)!
) -> Prior

1. Distribution family string from DistributionFamily.
2. Parameter overrides merged with distribution defaults.
3. Transform method string from TransformMethod dispatch.
4. Extra kwargs for transform constructors that require bounds.

Space Convention

Prior.logpdf(z) expects z in transformed (typically unconstrained) space. Internally it inverse-transforms to parameter space and applies Jacobian correction.

Distribution Families

Accepted distribution values in make_prior(...):

Enum Member	String	Parameter Keys	Defaults
NORMAL	"normal"	mean, std, random_state	0.0, 1.0, None
LOGNORMAL	"log_normal"	mean, std, random_state	0.0, 1.0, None
HALFNORMAL	"half_normal"	std, random_state	1.0, None
TRUNCNORMAL	"trunc_normal"	low, high, mean, std, random_state	-6.0, 6.0, 0.0, 1.0, None
HALFCAUCHY	"half_cauchy"	gamma, random_state	1.0, None
BETA	"beta"	a, b, random_state	1.0, 1.0, None
GAMMA	"gamma"	mean, std, random_state	1.0, 1.0, None
INVGAMMA	"inv_gamma"	mean, std, random_state	1.0, 1.0, None
UNIFORM	"uniform"	low, high, random_state	0.0, 1.0, None
LKJCHOL	"lkj_chol"	eta, K, random_state	1.0, -1, None

Parameterization Convention

Distribution constructors use the current library API directly. Canonical families stay canonical, and no SciPy-style loc / scale wrapper parameters are exposed in make_prior(...). The only bounded normal family is trunc_normal, which takes explicit low and high truncation bounds.

LKJ Parameter

LKJCHOL requires K to be set meaningfully by the user; the default K=-1 is only a placeholder and is not a valid runtime shape.

Transform Methods

Dispatched transform values accepted by make_prior(...):

Enum Member	String	transform_kwargs
IDENTITY	"identity"	none
LOG	"log"	none
SOFTPLUS	"softplus"	none
LOGIT	"logit"	none
PROBIT	"probit"	none
AFFINE_LOGIT	"affine_logit"	low, high
AFFINE_PROBIT	"affine_probit"	low, high
LOWER_BOUNDED	"lower_bounded"	low
UPPER_BOUNDED	"upper_bounded"	high

Additional TransformMethod enum members currently not dispatched by make_prior(...):

Enum Member	String
SIMPLEX	"simplex"
CHOLESKY_COV	"cholesky_cov"
CHOLESKY_CORR	"cholesky_corr"

Example

from SymbolicDSGE.bayesian import make_prior

priors = {
    "beta": make_prior(
        distribution="beta", # (1)!
        parameters={"a": 100.0, "b": 5.0},
        transform="logit", # (2)!
    ),
    "psi_pi": make_prior(
        distribution="normal",
        parameters={"mean": 2.0, "std": 0.5},
        transform="log", # (3)!
    ),
    "rho_g": make_prior(
        distribution="normal",
        parameters={"mean": 0.5, "std": 0.5},
        transform="affine_logit",
        transform_kwargs={"low": 0.0, "high": 1.0}, # (4)!
    ),
}

1. Parameter-space distribution on (0, 1) via beta family.
2. Maps (0, 1) into (-inf, inf) for unconstrained optimization.
3. Maps positive parameter space into (-inf, inf).
4. Required kwargs for bounded affine transforms.