Prior specification for tulpa models

Specify priors for model parameters. Supports both PC (penalized complexity) priors for variance components and standard distributions for other parameters.

A tulpa_priors object is what the simulation tools draw parameters from: prior_predict() and tulpa_simulate() with theta = NULL. The model fitters do not read one. tulpa() carries its own defaults, set per backend through its beta_prior, re_prior and hyperprior arguments:

• Fixed effects: prior_normal(0, 2.5) on every backend – the same default as beta here.

• Random-effect SDs: a PC prior with P(sigma > 3) = 0.01 (plus an LKJ(2) prior on a correlated block's correlations) on the routes that integrate or maximize over them (nested Laplace, re_cov_nested, mode = "eb"); half-Cauchy(2.5) on the samplers (re_prior$sigma_re_scale, and re_prior$prior_sigma_scale for mode = "gibbs"); an inverse-Wishart under control$re_cov = "gibbs".

The sigma, phi, rho_temporal and rho_spatial defaults below are therefore the simulation defaults, not the priors a fit ran under.

Usage

tulpa_priors(
  beta = NULL,
  sigma = NULL,
  phi = NULL,
  rho_temporal = NULL,
  rho_spatial = NULL
)

# S3 method for class 'tulpa_priors'
print(x, ...)

# S3 method for class 'tulpa_prior'
print(x, ...)

# S3 method for class 'tulpa_prior_normal'
format(x, indent = "", ...)

# S3 method for class 'tulpa_prior_half_normal'
format(x, indent = "", ...)

# S3 method for class 'tulpa_prior_half_cauchy'
format(x, indent = "", ...)

# S3 method for class 'tulpa_prior_gamma'
format(x, indent = "", ...)

# S3 method for class 'tulpa_prior_exponential'
format(x, indent = "", ...)

# S3 method for class 'tulpa_prior_beta'
format(x, indent = "", ...)

# S3 method for class 'tulpa_prior_pc'
format(x, indent = "", ...)

# S3 method for class 'tulpa_prior'
format(x, indent = "", ...)

Arguments

beta

Prior for fixed effects. Default: prior_normal(0, 2.5).

sigma

Prior for random effect SDs. Default: PC prior with P(sigma > 1) = 0.01.

phi

Prior for overdispersion parameter. Default: PC prior with P(phi > 10) = 0.01.

rho_temporal

Prior for temporal autocorrelation. Default: prior_beta(2, 2) centered at 0.5.

rho_spatial

Prior for spatial proportion (BYM2). Default: prior_beta(1, 1) (uniform).

x

A tulpa_priors specification, or a single prior built by a prior_*() constructor.

...

Ignored.

indent

String prefixed to each formatted line.

Value

A tulpa_priors object

format() returns the prior as a character string.

Details

PC priors (Simpson et al., 2017) provide principled regularization that:

• Favors simpler models (smaller variance components)

• Has interpretable parameters (tail probabilities)

• Prevents overfitting with sparse data

For other parameters, standard distributions are available via helper functions: prior_normal(), prior_half_normal(), prior_half_cauchy(), prior_gamma(), prior_beta(), prior_exponential().

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

# Default priors
tulpa_priors()

# Custom fixed effect prior
tulpa_priors(beta = prior_normal(0, 1))

# Tighter random effect prior
tulpa_priors(sigma = prior_pc(U = 0.5, alpha = 0.01))

# Half-Cauchy for random effect SD
tulpa_priors(sigma = prior_half_cauchy(2.5))

# Informative prior for temporal correlation
tulpa_priors(rho_temporal = prior_beta(5, 2))  # Prior mode at ~0.8