Package index • DPprior

Core Elicitation

Main user-facing functions for prior elicitation

DPprior_fit(): Fit a Gamma Hyperprior for DP Concentration Parameter
DPprior_dual(): Dual-Anchor Prior Calibration

Approximation Algorithms

A1 closed-form and A2 Newton-based algorithms

DPprior_a1(): A1 Closed-Form Prior Elicitation
DPprior_a2_newton(): A2-MN Exact-Moment Newton Solver
DPprior_a2_kl(): A2-KL: KL Divergence Minimization for Prior Calibration

Stirling Numbers

Computation of unsigned Stirling numbers of the first kind

compute_log_stirling(): Compute Log Stirling Numbers (First Kind, Unsigned)

K Distribution (Conditional)

Antoniak distribution P(K | alpha)

pmf_K_given_alpha(): PMF of K Given Alpha (Antoniak Distribution)
log_pmf_K_given_alpha(): Log-PMF of K Given Alpha (Antoniak Distribution)
cdf_K_given_alpha(): CDF of K Given Alpha
mean_K_given_alpha(): Conditional Mean of K_J Given Alpha
var_K_given_alpha(): Conditional Variance of K_J Given Alpha
mode_K_given_alpha(): Mode of K Given Alpha
quantile_K_given_alpha(): Quantile of K Given Alpha
moments_K_given_alpha(): Conditional Mean and Variance of K_J Given Alpha
cv_K_given_alpha(): Coefficient of Variation for K Given Alpha
dispersion_K_given_alpha(): Dispersion Index for K Given Alpha

K Distribution (Marginal)

Marginal distribution of K under Gamma prior on alpha

pmf_K_marginal(): Marginal PMF of K_J under Gamma Hyperprior
cdf_K_marginal(): CDF of Marginal K Distribution
mode_K_marginal(): Mode of Marginal K Distribution
quantile_K_marginal(): Quantile of Marginal K Distribution
summary_K_marginal(): Summary Statistics for Marginal K Distribution
K_moments(): Convenience Wrapper for Marginal Moments
exact_K_moments(): Exact Marginal Moments of K_J under Gamma Prior

Weight Distribution (w1)

Distribution of the first stick-breaking / size-biased weight

mean_w1(): Mean of w₁
var_w1(): Variance of w₁
prob_w1_exceeds(): Survival Function of w₁
quantile_w1(): Quantile Function of w₁
density_w1(): Density of w₁
cdf_w1(): CDF of First Stick-Breaking Weight w₁
rw1(): Random Generation from w₁ Distribution
summary_w1(): Summary Statistics for w₁ Distribution
w1_grid(): Compute w₁ Distribution on Grid

Co-clustering Probability (rho)

Pairwise co-clustering probability functions

mean_rho(): Marginal Mean of rho
var_rho(): Marginal Variance of rho
mean_rho_given_alpha(): Conditional Mean of rho Given Alpha
var_rho_given_alpha(): Conditional Variance of rho Given Alpha
cv_rho(): Coefficient of Variation of rho
rrho(): Random Generation from rho Distribution
summary_rho(): Summary Statistics for rho Distribution
rho_conditional_grid(): Compute rho Conditional Moments on alpha Grid

Diagnostics

Prior validation and diagnostic tools

DPprior_diagnostics(): Comprehensive Prior Diagnostics
DPprior_error_bounds(): Compute A1 Approximation Error Bounds
check_dominance_risk(): Quick Dominance Risk Check
dual_anchor_diagnostics(): Dual-Anchor Diagnostic Comparison
compare_a1_a2(): Compare A1 vs A2 Accuracy

Visualization

Plotting functions

plot(<DPprior_fit>): Plot Method for DPprior_fit Objects
plot_alpha_prior(): Plot Prior Density of Alpha
plot_K_prior(): Plot Prior PMF of K_J
plot_w1_prior(): Plot Prior Density of w1
plot_prior_dashboard(): 4-Panel Prior Dashboard
plot_dual_comparison(): Plot Dual-Anchor Comparison Dashboard
plot_dual_dashboard(): Plot Dual-Anchor Extended Dashboard
plot_tradeoff_curve(): Plot Trade-off Curve
plot_tradeoff_dashboard(): Plot Trade-off Multi-Panel
DPprior_colors(): DPprior Color Palette
theme_DPprior(): Publication-Quality Theme for DPprior Plots

S3 Methods

Print, summary, and coercion methods

print(<DPprior_fit>): Print Method for DPprior_fit Objects
summary(<DPprior_fit>): Summary Method for DPprior_fit Objects
print(<summary.DPprior_fit>): Print Method for summary.DPprior_fit
as.data.frame(<DPprior_fit>): Coerce DPprior_fit to Data Frame
print(<DPprior_diagnostics>): Print Method for DPprior_diagnostics Objects
summary(<DPprior_diagnostics>): Summary Method for DPprior_diagnostics Objects
print(<DPprior_error_bounds>): Print Method for DPprior_error_bounds Objects
summary(<DPprior_error_bounds>): Summary Method for DPprior_error_bounds Objects
print(<w1_summary>): Print Method for w1_summary Objects
print(<rho_summary>): Print Method for rho_summary Objects

Numerical Utilities

Conversion, quadrature, and numerical helper functions

vif_to_variance(): Convert Variance Inflation Factor to Variance
confidence_to_vif(): Map a Qualitative Confidence Level to a Variance Inflation Factor (VIF)
cv_alpha_to_variance(): Convert CV(alpha) to Variance
integrate_gamma(): Integrate Function Against Gamma Distribution
build_gamma_quadrature(): Build Quadrature for Gamma(a, b) Integration
gauss_laguerre_nodes(): Gauss-Laguerre Quadrature Nodes and Weights
logsumexp(): Numerically Stable Log-Sum-Exp (Binary)
logsumexp_vec(): Vectorized Log-Sum-Exp
score_a(): Score Function with Respect to Shape Parameter a
score_b(): Score Function with Respect to Rate Parameter b

Computation

Lower-level computational functions

compute_weight_diagnostics(): Weight Distribution Diagnostics (w1)
compute_error_landscape(): Compute A1 Error Landscape
compute_tradeoff_curve(): Compute Pareto Trade-off Curve
compute_scaling_constant(): Compute Scaling Constant for A1 Mapping
a1_moment_error(): A1 Approximation Moment Errors
discretize_chisq(): Discretize Chi-Square to K_J Support
kl_divergence_K(): KL Divergence Between Target and Induced K_J PMFs
kl_divergence_pmf(): KL Divergence Between Two PMFs
moments_with_jacobian(): Compute Marginal Moments and Jacobian Simultaneously

Validation & Verification

Functions for verifying mathematical properties

validate_stirling(): Validate Stirling Number Computation
verify_jacobian(): Verify Jacobian Against Finite Differences
verify_underdispersion(): Verify Underdispersion Inequality