ccm_distributions: Probability Distributions in CCMnet

In CCMnet: Congruence Class Models for Networks

Probability Distributions in CCMnet

Description

Details on the probability distributions implemented in the CCMnet. These distributions define the target distribution placed on network properties during the MCMC sampling process.

Details

By decoupling the probability distribution from the network property, CCMnet allows researchers to represent structural uncertainty. For example, one might target a specific degree distribution via "dirmult" while allowing the total edge count to follow a wide "gamma" distribution.

Supported Distributions

"poisson"

Requires list(lambda). Typically used for count-based statistics like "edges" or "triangles".

"gamma"

Requires list(shape, rate). Useful for continuous or skewed properties. The implementation uses the kernel x^{\alpha-1}e^{-\beta x}.

"dirmult"

Requires list(alphas). A Dirichlet-Multinomial implementation optimized for proportions. In CCMnet, the global normalizing constant is omitted to facilitate sampling in systems where the total count (e.g., total edges) is variable.

"normal"

Requires list(mean, sd). Standard Gaussian constraint.

"lognormal"

Requires list(log mean, log sd). Log-scale of standard Gaussian constraint.

"beta"

Requires list(shape1, shape2). Restricted to properties bounded in the interval [0,1], such as "density".

"uniform"

A flat distribution where the MCMC explores the congruence class without preference for specific statistic values.

See Also

ccm_properties, sample_ccm

Other ccm_core: ccm_properties, sample_ccm()

CCMnet documentation built on June 9, 2026, 9:07 a.m.