Parameter Priors

The parameter prior framework controls the distributions placed on real-valued model parameters: pairwise interactions, category thresholds, continuous-variable means, and the diagonal of the precision matrix. All priors inherit from BaseParameterPrior in src/priors/parameter_prior.h. The user-facing R-side constructors are documented on the Prior Constructors reference page.

BaseParameterPrior interface

class BaseParameterPrior {
  virtual double logp(double x) const = 0;
  virtual double grad(double x) const = 0;
  virtual std::unique_ptr<BaseParameterPrior> clone() const = 0;
};

Each prior provides a log-density logp(x) and gradient grad(x) evaluated at a single point \(x\); clone() produces an independent copy for parallel chain execution. The scale-family classes (Cauchy, Normal) additionally expose a scale() accessor, and GammaScalePrior exposes shape() and rate(). These accessors are what the samplers consult beyond plain density evaluation: the GGM’s Gibbs eligibility check and slab-variance formulas read scale(), the conjugate edge move and row-block Gibbs read the Gamma shape()/rate(), the Cauchy scale-mixture weights are refreshed against scale(), and the standardized eta frame resolves the diagonal rate from the slab’s scale().

Concrete classes

Class	Family	Hyperparameters	R constructor
CauchyPrior	Cauchy(0, scale)	scale	cauchy_prior()
NormalPrior	Normal(0, scale)	scale	normal_prior()
BetaPrimePrior	logit-Beta(\(\alpha\), \(\beta\))	alpha, beta	beta_prime_prior()
GammaScalePrior	Gamma(shape, rate) on positive support	shape, rate	gamma_prior(), exponential_prior()

BetaPrimePrior is used only for thresholds and has no scale accessor. GammaScalePrior is used only for the precision-matrix diagonal.

Factory dispatch

Two inline factories at the bottom of parameter_prior.h map a (type, hyperparameters) triple to the concrete class:

Factory	Type strings	Returns
create_parameter_prior(type, scale, alpha, beta)	"cauchy", "normal", "beta-prime"	unique_ptr<BaseParameterPrior>
create_scale_prior(type, shape, rate)	"gamma", "exponential"	unique_ptr<BaseParameterPrior> (GammaScalePrior)

The R-side unpack_parameter_prior() and unpack_scale_prior() helpers flatten each prior object into its (family, hyperparameters) representation; the C++ bridge then calls the matching factory.

Where the priors are used

Each model holds unique_ptr<BaseParameterPrior> members for the prior roles it needs:

Role	Used by	Default
Pairwise interactions	GGM, OMRF, mixed MRF	normal_prior(scale = 1)
Baseline pairwise interactions	bgmCompare	normal_prior(scale = 1)
Category thresholds	OMRF, mixed MRF, bgmCompare	beta_prime_prior(0.5, 0.5)
Continuous means	mixed MRF	normal_prior(scale = 1)
Precision-matrix diagonal	GGM, mixed MRF	exponential_prior(eta = 1)

The model’s logp_and_gradient() and Metropolis update functions call into the held priors at every iteration. This polymorphic dispatch is what allows the user to swap families without touching the C++ code.

The standardized eta frame

The diagonal’s Gamma-family rate can be given in two frames (the rate and eta arguments of gamma_prior()/exponential_prior()). In the raw frame the rate applies to \(\theta_{ii}/2\) as-is. In the standardized frame, eta is the rate in the coordinate system where the slab has unit scale: the R layer resolves the raw rate at fit time as eta / s, with s the slab’s scale(). Because graph and partial-correlation inference is invariant to a joint rescaling of slab and diagonal, fixing eta keeps the prior geometry — how far the prior mass sits from the positive-definite cone boundary — unchanged when the user widens or narrows the slab. This triple \((\delta, \eta, \alpha)\) at unit slab scale is what the engine pages call the standardized cell; it is the frame in which the Z-ratio constants and correction tables are built, which is why one table serves every slab scale.