DPprior 1.0.0
Initial CRAN Release
This is the first public release of the DPprior package, providing tools for principled prior elicitation on the concentration parameter α in Dirichlet Process (DP) mixture models.
Core Features
Elicitation Engine
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DPprior_fit(): Unified interface for K-based prior elicitation- Supports confidence levels (“low”, “medium”, “high”) for easy specification
- Direct variance specification for precise control
- Automatic algorithm selection (A1 closed-form or A2 Newton refinement)
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DPprior_a1(): Closed-form approximation using Negative Binomial proxy- Near-instantaneous computation
- Exploits asymptotic relationship K_J | α ~ Poisson(α log J)
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DPprior_a2_newton(): Exact moment matching via Newton iteration- Typically converges in 2-4 iterations
- Guaranteed accuracy to specified tolerance
Dual-Anchor Framework
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DPprior_dual(): Joint control of cluster counts AND weight concentration- Addresses “unintended prior” problem (Vicentini & Jermyn, 2025)
- Flexible weighting between K and w₁ targets via λ parameter
- Supports probability, quantile, and moment constraints on w₁
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prob_w1_exceeds(): Compute P(w₁ > threshold) for dominance risk assessment -
mean_w1(),var_w1(): First and second moments of largest weight -
quantile_w1(): Quantiles of w₁ distribution
Exact Computation
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compute_log_stirling(): Stable computation of unsigned Stirling numbers- Log-scale for numerical stability with large J
- Vectorized for efficiency
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pmf_K_given_alpha(): Exact Antoniak distribution P(K = k | α) -
mean_K_given_alpha(),var_K_given_alpha(): Conditional moments of K
Diagnostic Tools
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DPprior_diagnostics(): Comprehensive prior validation- Checks K, w₁, ρ, and α distributions
- Identifies dominance risk (high P(w₁ > 0.5))
- Computes effective sample sizes
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plot.DPprior_fit(): Four-panel diagnostic dashboard -
summary.DPprior_fit(): Detailed numerical summary
Utility Functions
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vif_to_variance(): Convert variance inflation factor to Var(K) -
confidence_to_vif(): Map confidence levels to VIF values -
integrate_gamma(): High-precision Gauss-Laguerre integration -
moments_K_marginal(): Marginal moments E[K] and Var(K) under Gamma prior
Documentation
Comprehensive vignettes organized into two tracks:
Applied Researchers Track: - Introduction: Why prior elicitation matters - Quick Start: Your first prior in 5 minutes - Applied Guide: Complete elicitation workflow - Dual-Anchor: Control counts AND weights - Diagnostics: Verify prior behavior - Case Studies: Multisite trials and meta-analysis
Methodological Researchers Track: - Theory Overview: Mathematical foundations - Stirling Numbers: Antoniak distribution details - Approximations: A1 closed-form theory - Newton Algorithm: A2 exact moment matching - Weight Distributions: w₁, ρ, and dual-anchor framework - API Reference: Complete function documentation
Methodological Foundation
This package implements the DORO 2.0 methodology, extending the original DORO approach (Dorazio, 2009) with:
A1 closed-form approximation: Instant initial estimates using the asymptotic Negative Binomial distribution of K_J under a Gamma prior on α (Zito et al., 2024)
A2 Newton refinement: Exact moment matching using numerically stable computation of Stirling numbers and Gauss-Laguerre quadrature
Dual-anchor extension: Joint control of K and w₁ distributions, addressing the sample-size-independent concerns raised by Vicentini & Jermyn (2025)
References
Dorazio, R. M. (2009). On selecting a prior for the precision parameter of Dirichlet process mixture models. Journal of Statistical Planning and Inference, 139(10), 3384–3390.
Lee, J., Che, J., Rabe-Hesketh, S., Feller, A., & Miratrix, L. (2025). Improving the estimation of site-specific effects and their distribution in multisite trials. Journal of Educational and Behavioral Statistics, 50(5), 731–764.
Vicentini, C., & Jermyn, I. H. (2025). Prior selection for the precision parameter of Dirichlet process mixtures. arXiv:2502.00864.
Zito, A., Rigon, T., & Dunson, D. B. (2024). Bayesian nonparametric modeling of latent partitions via Stirling-gamma priors. arXiv:2306.02360.