prior_pc: Penalized complexity (PC) prior

In tulpa: Templated Unified Library for Posterior Approximation in Bayesian Hierarchical Models

Penalized complexity (PC) prior

Description

Specify a PC prior for a positive parameter (typically a standard deviation). PC priors shrink toward simpler models by penalizing deviation from a base model.

Usage

prior_pc(U = 1, alpha = 0.01)

Arguments

U	Upper bound. P(x > U) = alpha.
alpha	Tail probability. Default 0.01.

Details

The PC prior is specified via: P(sigma > U) = alpha

• U is the upper bound you consider "large"

• alpha is the probability of exceeding it

This implies an exponential prior with rate = -log(alpha) / U.

Value

A tulpa_prior object

References

Simpson, D., Rue, H., Riebler, A., Martins, T. G., & Sorbye, S. H. (2017). Penalising model component complexity: A principled, practical approach to constructing priors. Statistical Science, 32(1), 1-28.

Examples

prior_pc(U = 1, alpha = 0.01)    # P(sigma > 1) = 0.01
prior_pc(U = 0.5, alpha = 0.05)  # Tighter, P(sigma > 0.5) = 0.05

tulpa documentation built on Oct. 19, 2026, 5:09 p.m.