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Dual-Anchor Prior Calibration

Source: R/15_dual_anchor.R
DPprior_dual.Rd

Refines a K_J-calibrated prior to also satisfy weight constraints, implementing the dual-anchor framework from RN-06.

Usage

DPprior_dual(
  fit,
  w1_target,
  lambda = 0.5,
  max_iter = 100L,
  verbose = FALSE,
  M = .QUAD_NODES_DEFAULT,
  loss_type = c("relative", "adaptive", "absolute")
)

Arguments

fit

A DPprior_fit object from any K-based calibration method.

w1_target

List specifying the first-weight target. Options:

list(prob = list(threshold = 0.5, value = 0.3))

Constrain \(P(w_1 > 0.5) = 0.3\)

list(quantile = list(prob = 0.9, value = 0.4))

Constrain 90th percentile of \(w_1\) = 0.4

list(mean = 0.3)

Constrain \(E[w_1] = 0.3\)

lambda

Numeric value between 0 and 1; weight on K_J anchor. Default is 0.5 (balanced). lambda = 1 recovers K-only fit.

max_iter

Integer; maximum optimization iterations.

verbose

Logical; if TRUE, print progress.

M

Integer; quadrature nodes.

loss_type

Character; "relative" (default), "adaptive", or "absolute". See dual_anchor_loss for details.

Value

An S3 object of class "DPprior_fit".

Details

Critical Fix (2025-12-29)

The original implementation used absolute squared errors for L_K, causing severe scale mismatch. The optimizer would essentially ignore the weight constraint. Example improvement at lambda = 0.5:

  • ABSOLUTE (broken): 0.5 percent reduction in \(P(w_1 > 0.5)\)

  • RELATIVE (fixed): 9 percent reduction

  • ADAPTIVE: 18 percent reduction

Choosing loss_type

  • "relative": Good default. Both losses dimensionless.

  • "adaptive": More aggressive. Use when you want lambda = 0.5 to give significant weight reduction.

  • "absolute": Legacy, not recommended.

Examples

# K-only fit
fit_K <- DPprior_a2_newton(J = 50, mu_K = 5, var_K = 8)
cat("K-only P(w_1 > 0.5):", prob_w1_exceeds(0.5, fit_K$a, fit_K$b), "\n")
#> K-only P(w_1 > 0.5): 0.481478 

# Dual-anchor with relative loss (default)
fit_rel <- DPprior_dual(
  fit_K,
  w1_target = list(prob = list(threshold = 0.5, value = 0.3)),
  lambda = 0.5,
  loss_type = "relative"
)
cat("Relative P(w_1 > 0.5):", fit_rel$dual_anchor$w1_achieved$prob_gt_50, "\n")
#> Relative P(w_1 > 0.5): 0.4379077 

# Dual-anchor with adaptive loss (more aggressive)
fit_adp <- DPprior_dual(
  fit_K,
  w1_target = list(prob = list(threshold = 0.5, value = 0.3)),
  lambda = 0.5,
  loss_type = "adaptive"
)
cat("Adaptive P(w_1 > 0.5):", fit_adp$dual_anchor$w1_achieved$prob_gt_50, "\n")
#> Adaptive P(w_1 > 0.5): 0.3426554