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Symbolic Fisher information

Source: R/symbolic.R
symbolic_fisher.Rd

Compute Fisher information using closed-form analytical formulas for standard distributions. Falls back to numerical computation if no analytical formula is available.

Usage

symbolic_fisher(spec, y, par, method = c("auto", "analytical", "numerical"))

Arguments

spec

A model_spec object

y

Numeric vector of observed data (used for numerical fallback and n)

par

Named numeric vector of parameter values

method

Character; "auto" tries analytical first, "analytical" requires closed-form, "numerical" forces numerical computation

Value

A fisher_info object containing the Fisher information matrix

Details

Analytical formulas are available for:

  • Normal (mu, sigma): I = diag(n/sigma^2, 2n/sigma^2)

  • Exponential (rate): I = n/rate^2

  • Poisson (lambda): I = n/lambda

  • Gamma (shape, rate): Closed-form involving digamma/trigamma

  • Binomial (prob): I = n/(prob * (1-prob))

  • Beta (shape1, shape2): Closed-form involving trigamma

  • Log-normal (mu, sigma): Similar to normal on log scale

The function attempts to detect the distribution from the model name.

Examples

spec <- model_spec_normal()
y <- rnorm(100, mean = 5, sd = 2)

# Analytical computation
info <- symbolic_fisher(spec, y, par = c(mu = 5, sigma = 2))
print(info)