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 logp(double x, double scale_factor) const;
  virtual double grad(double x) const = 0;
  virtual double grad(double x, double scale_factor) const;
  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 \(x\), plus optional (x, scale_factor) overloads that multiply the prior’s scale by a per-pair factor. The scaled overloads are used by the OMRF and mixed MRF when standardize = TRUE, where the prior scale on each pairwise interaction is adjusted by the score-product range of the variable pair (see the standardize argument of bgm()). Priors that have no natural scale (the beta-prime threshold prior) ignore the factor and delegate to the unscaled overload.

clone() produces an independent copy for parallel chain execution.

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()

CauchyPrior and NormalPrior implement both the unscaled and scaled overloads. BetaPrimePrior is used only for thresholds and ignores the scale factor. GammaScalePrior is used only for the precision-matrix diagonal where pair-specific scaling does not apply.

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, bgmCompare	cauchy_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	gamma_prior(shape = 1, rate = 1)

The model’s logp_and_gradient() and Metropolis update functions call into the held priors at every iteration. Replacing the inline R::dcauchy() / closed-form lambda calls used in earlier versions with this polymorphic dispatch is what allows the user to swap families without touching the C++ code.