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)
get_log_stirling(): Get Single Log-Stirling Value with Bounds Checking
get_stirling_row(): Get Stirling Numbers for a Fixed J

K Distribution (Conditional)

Antoniak distribution P(K | α)

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
summary_K_given_alpha(): Summary of Conditional Moments
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 α

pmf_K_marginal(): Marginal PMF of K_J under Gamma Hyperprior
log_pmf_K_marginal(): Log 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 largest stick-breaking 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 (ρ)

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
mean_rho_sq(): Marginal Second Moment of rho
mean_rho_sq_given_alpha(): Conditional Second Moment 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_diagnostics(): Compare Diagnostics Across Multiple Fits
compare_a1_a2(): Compare A1 vs A2 Accuracy
compare_rho_w1(): Compare rho and w1 Distributions
compare_to_negbin(): Compare Exact Moments to NegBin Approximation

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 and summary 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

Utilities

Helper and conversion functions

vif_to_variance(): Convert Variance Inflation Factor to Variance
vif_to_variance_fit(): Convert VIF to Target Variance
confidence_to_vif(): Map a Qualitative Confidence Level to a Variance Inflation Factor (VIF)
confidence_to_vif_fit(): Convert Confidence Level to Variance Inflation Factor
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
log_rising_factorial(): Log Rising Factorial (Pochhammer Symbol)
logsumexp(): Numerically Stable Log-Sum-Exp (Binary)
logsumexp_vec(): Vectorized Log-Sum-Exp
softmax(): Numerically Stable Softmax

Internal Computation

Lower-level computational functions

compute_K_diagnostics(): K Distribution Diagnostics
compute_weight_diagnostics(): Weight Distribution Diagnostics (w1)
compute_alpha_diagnostics(): Alpha Distribution Diagnostics
compute_coclustering_diagnostics(): Co-Clustering Diagnostics (rho)
compute_error_landscape(): Compute A1 Error Landscape
compute_tradeoff_curve(): Compute Pareto Trade-off Curve
compute_linearization_bound(): Mean-Linearization Error Bound
compute_poissonization_bound(): Poissonization Error Bound (Chen-Stein / Le Cam Bound)
compute_total_tv_bound(): Total TV Error Bound (Conditional)
compute_scaling_constant(): Compute Scaling Constant for A1 Mapping
compute_sum_p_squared(): Poissonization Error Bound (Raw Sum of Squared Probabilities)
expected_tv_bound(): Expected TV Bound Under Gamma Prior

Validation & Verification

Internal testing and validation functions

verify_DPprior_fit(): Verify DPprior_fit Module
verify_a1_mapping_all(): Run All Module 10 Verification Tests
verify_a2_all(): Run All A2-MN Verification Tests
verify_a2_kl(): Verify A2-KL Optimization
verify_a2_kl_all(): Run All Module 12 Verification Tests
verify_cdf_properties(): Verify CDF Properties
verify_derivative(): Verify Derivative via Finite Difference
verify_diagnostics(): Verify Diagnostics Module
verify_dual_anchor(): Verify Dual-Anchor Module
verify_jacobian_all(): Run All Module 07 Verification Tests
verify_kl_divergence(): Verify KL Divergence Properties
verify_marginal_moments(): Verify Marginal Moments Properties
verify_moments_marginal_all(): Run All Module 05 Verification Tests
verify_pmf_all(): Run All PMF Verifications
verify_pmf_marginal_all(): Run All Module 06 Verification Tests
verify_pmf_marginal_convergence(): Verify Quadrature Convergence
verify_pmf_marginal_moments(): Verify Moments Consistency
verify_pmf_marginal_properties(): Verify Marginal PMF Properties
verify_pmf_moments(): Verify PMF Consistency with Moments
verify_pmf_normalization(): Verify PMF Normalization
verify_quadrature(): Verify Quadrature Accuracy Against Known Gamma Moments
verify_s3_methods(): Verify S3 Methods Module
verify_stirling_row_sum(): Verify Row Sum Identity for Stirling Numbers
verify_underdispersion(): Verify Underdispersion Inequality
verify_visualization(): Verify Visualization Module
verify_zero_probability(): Verify Zero Probability at K=0
validate_moments_conditional(): Validate Conditional Moments Computation
validate_stirling(): Validate Stirling Number Computation

Other Internal

Other internal helper functions

a1_moment_error(): A1 Approximation Moment Errors
construct_target_pmf(): Construct Target PMF from User Specification
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
summary_pmf_K_given_alpha(): Summary of Conditional PMF