TKApprox News

Version 0.1.0 (2026-07-20)

Initial Release

Features

• Distribution-agnostic Bayesian estimation framework using Tierney-Kadane approximation
• Support for arbitrary univariate probability distributions (continuous or discrete)
• Multiple Bayesian loss functions:
  • Squared Error Loss (SEL) - posterior mean
  • LINEX Loss - asymmetric linear-exponential loss
  • General Entropy Loss (GEL) - generalized entropy loss
  • Precautionary Loss - conservative estimation
  • Weighted Squared Error Loss - inverse-variance weighting
  • Custom loss functions - user-defined

Censoring Support

• Complete (uncensored) data
• Right-censored data
• Left-censored data
• Interval-censored data
• Type-I censoring
• Type-II censoring
• Progressive Type-II censoring
• Hybrid censoring
• Doubly censored data

Prior Distributions

• Gamma prior
• Normal prior
• Beta prior
• Uniform prior
• Exponential prior
• Log-Normal prior
• Weibull prior
• Inverse Gamma prior
• User-defined priors (via custom functions)
• Independent priors for multiple parameters

Optimization

• Multiple backends: BFGS, L-BFGS-B, Nelder-Mead, nlminb, maxLik, trust
• Automatic fallback between optimization methods
• Convergence diagnostics and iteration tracking
• Support for parameter bounds

Numerical Differentiation

• Numerical gradients and Hessians via numDeriv
• Optional analytic derivative support with validation

Model Comparison

• AIC (Akaike Information Criterion)
• BIC (Bayesian Information Criterion)
• CAIC (Consistent AIC)
• HQIC (Hannan-Quinn Information Criterion)
• DIC (Deviance Information Criterion) approximation
• Expected log-posterior
• Negative log-likelihood

Visualization

• Posterior approximation plots (per parameter)
• Likelihood surface and profile likelihood plots
• Contour plots for two-parameter models
• Prior vs posterior comparison plots
• Convergence diagnostics
• Credible interval forest plots
• Residuals plots (Pearson and deviance)

Prior Sensitivity Analysis

• Systematic variation of prior hyperparameters
• Impact on estimates, bias, variance, and risk
• Sensitivity plots and tables

S3 Methods

• summary() - comprehensive model summary
• print() - concise output
• coef() - extract Bayes estimates
• vcov() - extract posterior covariance matrix
• logLik() - extract log-likelihood
• AIC() - compute AIC
• BIC() - compute BIC
• plot() - diagnostic plots
• predict() - generate predictions
• residuals() - compute residuals

Testing

• Comprehensive testthat test suite
• Tests for all censoring schemes
• Tests for multiple prior families
• Tests for loss functions
• Tests for optimization scenarios
• GitHub Actions CI/CD for cross-platform checking

Documentation

• roxygen2 documentation for all exported functions
• Runnable examples in documentation
• Comprehensive vignettes (planned)