Prior sensitivity analysis

Test how different prior specifications affect identifiability and posterior concentration.

Usage

prior_sensitivity(spec, y, par, prior_scales = NULL)

Arguments

spec

A model_spec object

y

Numeric vector of observed data

par

Numeric vector of parameter values (point estimate or posterior mean)

prior_scales

Named list of scale factors for each parameter. Each element should be a numeric vector of scales to test. Scale 1 means use the original bounds; larger scales mean wider priors.

Value

An S3 object of class prior_sensitivity containing:

results

Data frame of identifiability results for each prior setting

baseline

Identifiability result with original bounds

most_informative

Prior setting with best identifiability

Details

This function examines how the effective prior (parameter bounds) affects the Fisher information and identifiability. Wider bounds (larger scales) represent more diffuse priors, while narrower bounds represent more informative priors.

Examples

spec <- model_spec(
  loglik_fn = function(y, mu, sigma) sum(dnorm(y, mu, sigma, log = TRUE)),
  par_names = c("mu", "sigma"),
  par_bounds = list(mu = c(-10, 10), sigma = c(0.1, 10)),
  name = "Normal"
)

set.seed(123)
y <- rnorm(30, mean = 5, sd = 2)

sens <- prior_sensitivity(spec, y, par = c(mu = 5, sigma = 2),
  prior_scales = list(mu = c(0.5, 1, 2), sigma = c(0.5, 1, 2)))
print(sens)