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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)

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.