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Compare Fisher information across observation schemes

Source: R/fisher_info.R
compare_fisher_info.Rd

For a given parameter configuration, computes the observed Fisher information under Scheme 0 (system only), Scheme 1 (periodic inspection), and Scheme 2 (complete component data) via simulation.

Usage

compare_fisher_info(
  shapes = NULL,
  scales = NULL,
  rates = NULL,
  n = 200L,
  delta = 1,
  n_rep = 50L,
  component = dfr_exponential()
)

Arguments

shapes

Numeric vector. Weibull shape parameters (Weibull only, or NULL for exponential).

scales

Numeric vector. Weibull scale parameters (Weibull only, or NULL for exponential).

rates

Numeric vector. Exponential rate parameters (exponential only, alternative to shapes/scales).

n

Integer. Sample size per replicate.

delta

Numeric scalar. Inspection interval width for Scheme 1.

n_rep

Integer. Number of Monte Carlo replicates.

component

A dfr_dist prototype (e.g. dfr_exponential() or dfr_weibull()) specifying the component family.

Value

A list with components:

scheme0_det

Numeric vector of Scheme 0 information determinants (length n_rep).

scheme1_det

Numeric vector of Scheme 1 information determinants.

scheme2_det

Numeric vector of Scheme 2 (complete data) information determinants.

median_det

Named numeric vector of median determinants across schemes.

efficiency_01

Ratio of median Scheme 0 to Scheme 1 determinant (< 1 means Scheme 1 is more informative).

efficiency_02

Ratio of median Scheme 0 to Scheme 2 determinant.

efficiency_12

Ratio of median Scheme 1 to Scheme 2 determinant.

n_valid

Named integer vector of valid (non-NA) replicate counts per scheme.

Details

The determinant of the observed information matrix is used as a scalar summary. Efficiency ratios indicate relative information content: a ratio less than 1 means the denominator scheme carries more information.

For Scheme 2 (complete data), the Fisher information is computed analytically:

  • Exponential: \(I_{jj} = n / \lambda_j^2\) (diagonal).

  • Weibull: Block-diagonal with per-component 2x2 Fisher information matrices using the standard Weibull FIM formulas.

For Schemes 0 and 1, the observed information is computed numerically via numDeriv::hessian of the negative log-likelihood evaluated at the true parameter values.

Examples

# \donttest{
set.seed(1)
result <- compare_fisher_info(rates = c(1, 2), n = 50, delta = 1.0, n_rep = 5)
result$median_det
#>   scheme0   scheme1   scheme2 
#>  120.7422 1093.5996  625.0000 
result$efficiency_01  # Scheme 0 vs Scheme 1
#> [1] 0.110408
# }