Package {TKApprox}

Title:	A General Framework for Bayesian Estimation Using the 'Tierney'-'Kadane' Approximation
Version:	0.1.0
Description:	Provides a distribution-independent framework for Bayesian estimation of arbitrary univariate probability models using the 'Tierney'-'Kadane' approximation ('Tierney' & 'Kadane', 1986 <doi:10.1080/01621459.1986.10478240>). Users specify the probability distribution, likelihood, prior distributions, and censoring mechanism, while the package automatically constructs the posterior distribution, computes posterior modes and Hessian matrices, approximates posterior expectations under several Bayesian loss functions, and returns Bayesian parameter estimates, posterior covariance matrices, credible intervals, diagnostic plots, and model comparison statistics. Supports complete, right-, left-, interval-, Type-I, Type-II, progressive Type-II, hybrid, and doubly censored data ('Lawless', 2003 <ISBN:978-0-471-37215-8>; 'Meeker' & 'Escobar', 1998 <ISBN:978-0-471-14328-4>; 'Balakrishnan' & 'Aggarwala', 2000 <ISBN:978-0-8176-4129-0>; 'Kundu' & 'Pradhan', 2009 <doi:10.1198/TECH.2009.0019>), making it a flexible tool for Bayesian reliability, survival, and lifetime data analysis.
License:	GPL (≥ 3)
Encoding:	UTF-8
RoxygenNote:	7.3.3
Depends:	R (≥ 4.0.0)
Imports:	checkmate, numDeriv, maxLik, rlang, stats, graphics, grDevices, utils, MASS
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown, pkgdown, ggplot2, gridExtra
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2026-07-30 23:21:30 UTC; shikhar tyagi
Author:	Shikhar Tyagi [aut, cre], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer:	Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository:	CRAN
Date/Publication:	2026-08-07 20:00:02 UTC

AIC Method for tkfit Objects

Description

Computes the Akaike Information Criterion.

Usage

## S3 method for class 'tkfit'
AIC(object, ...)

Arguments

Value

AIC value

BIC Method for tkfit Objects

Description

Computes the Bayesian Information Criterion.

Usage

## S3 method for class 'tkfit'
BIC(object, ...)

Arguments

Value

BIC value

Compute CAIC (Consistent AIC)

Description

Compute CAIC (Consistent AIC)

Usage

CAIC(object, ...)

## S3 method for class 'tkfit'
CAIC(object, ...)

Arguments

Value

Numeric scalar value of Consistent Akaike Information Criterion (CAIC).

Methods (by class)

• CAIC(tkfit): CAIC method for tkfit objects

Compute DIC (Deviance Information Criterion) Approximation

Description

Computes an approximation to the DIC using the TK framework.

Usage

DIC(object, ...)

## S3 method for class 'tkfit'
DIC(object, ...)

Arguments

Value

Numeric scalar value of Deviance Information Criterion (DIC) approximation.

Methods (by class)

• DIC(tkfit): DIC method for tkfit objects

Compute HQIC (Hannan-Quinn Information Criterion)

Description

Compute HQIC (Hannan-Quinn Information Criterion)

Usage

HQIC(object, ...)

## S3 method for class 'tkfit'
HQIC(object, ...)

Arguments

Value

Numeric scalar value of Hannan-Quinn Information Criterion (HQIC).

Methods (by class)

• HQIC(tkfit): HQIC method for tkfit objects

Coefficients Method for tkfit Objects

Description

Extracts the Bayes estimates from a tkfit object.

Usage

## S3 method for class 'tkfit'
coef(object, ...)

Arguments

Value

Named vector of Bayes estimates

Evaluate the Log-Posterior at Given Parameters

Description

Evaluates the log-posterior function created by tk_posterior.

Usage

eval_logposterior(log_post_fn, param)

Arguments

Value

Numeric value of the log-posterior

Compute Expected Log-Posterior

Description

Computes the expected log-posterior using the TK approximation.

Usage

expected_logposterior(object, ...)

## S3 method for class 'tkfit'
expected_logposterior(object, ...)

Arguments

Value

Numeric scalar value of expected log-posterior.

Methods (by class)

• expected_logposterior(tkfit): Expected log-posterior method for tkfit objects

Likelihood Construction for Censored Data

Description

Functions to construct log-likelihood contributions for various censoring schemes. These functions are used internally to build the complete log-likelihood from user-supplied density/mass functions and CDFs.

Value

Numeric value of the log-likelihood for the specified data and parameters.

Log-Likelihood Method for tkfit Objects

Description

Extracts the log-likelihood at the posterior mode.

Usage

## S3 method for class 'tkfit'
logLik(object, ...)

Arguments

Value

Log-likelihood value

Complete (Uncensored) Data Log-Likelihood

Description

Computes the log-likelihood for complete (uncensored) data.

Usage

loglik_complete(data, pdf, param)

Arguments

Value

Numeric value of the log-likelihood

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
loglik_complete(c(1.2, 2.3, 0.9), pdf_exp, c(1.0))

Generic Likelihood Dispatcher

Description

Dispatches to the appropriate likelihood function based on the censoring scheme.

Usage

loglik_dispatcher(data, censoring_scheme, pdf, cdf = NULL, param, ...)

Arguments

Value

Numeric value of the log-likelihood

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
loglik_dispatcher(c(1.2, 2.3), "complete", pdf_exp, cdf_exp, c(1.0))

Doubly Censored Data Log-Likelihood

Description

Computes the log-likelihood for doubly censored data.

Usage

loglik_doubly_censored(data, status, pdf, cdf, param)

Arguments

Value

Numeric value of the log-likelihood

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
loglik_doubly_censored(c(0.5, 1.2, 2.0), c(-1, 0, 1), pdf_exp, cdf_exp, c(1.0))

Hybrid Censored Data Log-Likelihood

Description

Computes the log-likelihood for hybrid censored data.

Usage

loglik_hybrid_censored(data, censoring_time, r, n, pdf, cdf, param)

Arguments

Value

Numeric value of the log-likelihood

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
loglik_hybrid_censored(c(0.5, 1.2), 2.0, 3, 5, pdf_exp, cdf_exp, c(1.0))

Interval-Censored Data Log-Likelihood

Description

Computes the log-likelihood for interval-censored data. Data should be a matrix or data.frame with columns: lower, upper.

Usage

loglik_interval_censored(data, pdf, cdf, param)

Arguments

Value

Numeric value of the log-likelihood

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
dat <- cbind(c(1, 2), c(1, 3))
loglik_interval_censored(dat, pdf_exp, cdf_exp, c(1.0))

Left-Censored Data Log-Likelihood

Description

Computes the log-likelihood for left-censored data. Status: 1 = observed, 0 = left-censored.

Usage

loglik_left_censored(data, status, pdf, cdf, param)

Arguments

Value

Numeric value of the log-likelihood

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
loglik_left_censored(c(1.2, 2.3), c(1, 0), pdf_exp, cdf_exp, c(1.0))

Progressive Type-II Censored Data Log-Likelihood

Description

Computes the log-likelihood for progressive Type-II censored data.

Usage

loglik_progressive_type2_censored(data, removals, n, pdf, cdf, param)

Arguments

Value

Numeric value of the log-likelihood

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
loglik_progressive_type2_censored(c(0.5, 1.2), c(1, 2), 5, pdf_exp, cdf_exp, c(1.0))

Right-Censored Data Log-Likelihood

Description

Computes the log-likelihood for right-censored data. Status: 1 = observed, 0 = right-censored.

Usage

loglik_right_censored(data, status, pdf, cdf, param)

Arguments

Value

Numeric value of the log-likelihood

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
loglik_right_censored(c(1.2, 2.3), c(1, 0), pdf_exp, cdf_exp, c(1.0))

Type-I Censored Data Log-Likelihood

Description

Computes the log-likelihood for Type-I (time) censored data.

Usage

loglik_type1_censored(data, censoring_time, pdf, cdf, param)

Arguments

Value

Numeric value of the log-likelihood

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
loglik_type1_censored(c(1.2, 2.0, 2.0), 2.0, pdf_exp, cdf_exp, c(1.0))

Type-II Censored Data Log-Likelihood

Description

Computes the log-likelihood for Type-II censored data.

Usage

loglik_type2_censored(data, n, r, pdf, cdf, param)

Arguments

Value

Numeric value of the log-likelihood

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
loglik_type2_censored(c(0.5, 1.2), 5, 2, pdf_exp, cdf_exp, c(1.0))

Generic Prior Function Dispatcher

Description

Dispatches to the appropriate prior function based on the prior family name.

Usage

logprior_dispatcher(param, prior_family, hyperparameters)

Arguments

Value

Numeric value of the log-prior density

Examples

logprior_dispatcher(c(2, 3), "gamma", list(shape = 2, rate = 1))

Independent Priors for Multiple Parameters

Description

Computes the log-prior density when each parameter has an independent prior.

Usage

logprior_independent(param, prior_spec)

Arguments

Value

Numeric value of the total log-prior density

Examples

param_spec <- c(alpha = 2, beta = 3)
prior_spec <- list(
  alpha = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)),
  beta = list(family = "normal", hyperparameters = list(mean = 0, sd = 10))
)
logprior_independent(param_spec, prior_spec)

Model Comparison Statistics for tkfit Objects

Description

Computes various model comparison statistics for a fitted tkfit object.

Value

Numeric value or data frame containing model comparison statistics.

Comprehensive Model Comparison Table

Description

Computes a comprehensive table of model comparison statistics.

Usage

model_comparison_table(object)

Arguments

Value

A data.frame containing model comparison statistics (Statistic, Value).

Compute Negative Log-Likelihood

Description

Compute Negative Log-Likelihood

Usage

neglogLik(object, ...)

## S3 method for class 'tkfit'
neglogLik(object, ...)

Arguments

Value

Numeric scalar value of negative log-likelihood at posterior mode.

Methods (by class)

• neglogLik(tkfit): Negative log-likelihood method for tkfit objects

Plot Method for tkfit Objects

Description

Creates diagnostic plots for a fitted tkfit object.

Usage

## S3 method for class 'tkfit'
plot(x, which = c(1, 2, 3, 4), ask = FALSE, ...)

Arguments

Value

Invisibly returns the input x object of class "tkfit", called for side effects.

Plot Method for tksensitivity Objects

Description

Creates plots showing the sensitivity of estimates to prior hyperparameters.

Usage

## S3 method for class 'tksensitivity'
plot(x, which = c(1, 2), ask = FALSE, ...)

Arguments

Value

Invisibly returns the input x object of class "tksensitivity", called for side effects.

Convergence Diagnostic Plot

Description

Plots optimization convergence diagnostics.

Usage

plot_convergence(fit, ...)

Arguments

Value

Invisibly returns NULL, called for side effects.

Credible Intervals Plot

Description

Plots credible intervals for each parameter.

Usage

plot_credible_intervals(fit, parameter_index = NULL, ...)

Arguments

Value

Invisibly returns NULL, called for side effects.

Likelihood Surface Plot

Description

Plots the likelihood surface or profile for model parameters.

Usage

plot_likelihood_surface(fit, n_points = 50, ...)

Arguments

Value

Invisibly returns NULL, called for side effects.

Posterior Approximation Plot

Description

Plots the approximate posterior distribution for each parameter.

Usage

plot_posterior_approximation(fit, parameter_index = NULL, n_points = 100, ...)

Arguments

Value

Invisibly returns NULL, called for side effects.

Prior vs Posterior Comparison Plot

Description

Compares the prior and posterior distributions.

Usage

plot_prior_posterior(fit, parameter_index = NULL, n_points = 100, ...)

Arguments

Value

Invisibly returns NULL, called for side effects.

Residuals Plot

Description

Plots residuals from the fitted model.

Usage

plot_residuals(fit, type = "pearson", ...)

Arguments

Value

Invisibly returns NULL, called for side effects.

Plot Sensitivity of Estimates

Description

Plot Sensitivity of Estimates

Usage

plot_sensitivity_estimates(sensitivity, ...)

Arguments

Value

Invisibly returns NULL, called for side effects.

Plot Sensitivity of Log-Posterior

Description

Plot Sensitivity of Log-Posterior

Usage

plot_sensitivity_logposterior(sensitivity, ...)

Arguments

Value

Invisibly returns NULL, called for side effects.

Plot Sensitivity of Risk

Description

Plot Sensitivity of Risk

Usage

plot_sensitivity_risk(sensitivity, ...)

Arguments

Value

Invisibly returns NULL, called for side effects.

Predict Method for tkfit Objects

Description

Generates predictions from a fitted tkfit object.

Usage

## S3 method for class 'tkfit'
predict(object, newdata = NULL, type = "density", ...)

Arguments

Value

Predicted values

Print Method for tkexpectation Objects

Description

Print Method for tkexpectation Objects

Usage

## S3 method for class 'tkexpectation'
print(x, ...)

Arguments

Value

Invisibly returns the input x object of class "tkexpectation", called for side effects.

Print Method for tkfit Objects

Description

Print Method for tkfit Objects

Usage

## S3 method for class 'tkfit'
print(x, ...)

Arguments

Value

Invisibly returns the input x object of class "tkfit", called for side effects.

Print Method for tkhessian Objects

Description

Print Method for tkhessian Objects

Usage

## S3 method for class 'tkhessian'
print(x, ...)

Arguments

Value

Invisibly returns the input x object of class "tkhessian", called for side effects.

Print Method for tkmode Objects

Description

Print Method for tkmode Objects

Usage

## S3 method for class 'tkmode'
print(x, ...)

Arguments

Value

Invisibly returns the input x object of class "tkmode", called for side effects.

Print Method for tksensitivity Objects

Description

Print Method for tksensitivity Objects

Usage

## S3 method for class 'tksensitivity'
print(x, ...)

Arguments

Value

Invisibly returns the input x object of class "tksensitivity", called for side effects.

Print Model Comparison Table

Description

Print Model Comparison Table

Usage

print_model_comparison(object, ...)

Arguments

Value

Invisibly returns NULL, called for side effects.

Prior Distribution Functions

Description

Functions for computing log-prior densities for various prior distributions. These functions are used internally by tk_posterior to construct the log-posterior.

Usage

logprior_gamma(param, hyperparameters)

logprior_normal(param, hyperparameters)

logprior_beta(param, hyperparameters)

logprior_uniform(param, hyperparameters)

logprior_exponential(param, hyperparameters)

logprior_lognormal(param, hyperparameters)

logprior_weibull(param, hyperparameters)

logprior_invgamma(param, hyperparameters)

Arguments

Value

Numeric value of the log-prior density

Functions

• logprior_gamma(): Gamma prior log-density

• logprior_normal(): Normal prior log-density

• logprior_beta(): Beta prior log-density

• logprior_uniform(): Uniform prior log-density

• logprior_exponential(): Exponential prior log-density

• logprior_lognormal(): Log-Normal prior log-density

• logprior_weibull(): Weibull prior log-density

• logprior_invgamma(): Inverse Gamma prior log-density

Residuals Method for tkfit Objects

Description

Computes residuals from a fitted tkfit object.

Usage

## S3 method for class 'tkfit'
residuals(object, type = "pearson", ...)

Arguments

Value

Residual values

Summary Method for tkfit Objects

Description

Summary Method for tkfit Objects

Usage

## S3 method for class 'tkfit'
summary(object, ...)

Arguments

Value

Invisibly returns the input object object of class "tkfit", called for side effects.

Tierney-Kadane Approximation of Posterior Expectations

Description

Computes the Tierney-Kadane approximation of E(g(theta) | x) for a given function g. This is the core computational engine for all Bayes estimators.

Usage

tk_expectation(
  log_post_fn,
  g,
  mode_result,
  hessian_result,
  initial_values_star = NULL,
  ...
)

Arguments

Value

An object of class "tkexpectation" (a list) containing:

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
log_post <- tk_posterior(data, "complete", pdf_exp, cdf_exp, prior_spec)
mode_result <- tk_mode(log_post, initial_values = c(1))
hessian_result <- tk_hessian(log_post, mode_result$mode)
g_fn <- function(param) param[1]
tk_exp <- tk_expectation(log_post, g_fn, mode_result, hessian_result)

Compute Multiple Expectations Efficiently

Description

Computes TK approximations for multiple functions g_i(theta) efficiently by reusing the posterior mode and Hessian.

Usage

tk_expectations(log_post_fn, g_list, mode_result, hessian_result, ...)

Arguments

Value

Named vector of expectations

Main Function for Bayesian Estimation via Tierney-Kadane Approximation

Description

Performs Bayesian parameter estimation for user-specified univariate probability distributions using the Tierney-Kadane approximation.

Usage

tk_fit(
  data,
  censoring_scheme,
  pdf,
  cdf = NULL,
  prior_spec = NULL,
  loglik = NULL,
  initial_values,
  lower_bounds = NULL,
  upper_bounds = NULL,
  loss_function = "sel",
  loss_params = NULL,
  custom_g = NULL,
  optimization_method = "BFGS",
  hessian_method = "Richardson",
  analytic_hessian = NULL,
  true_parameter = NULL,
  ...
)

Arguments

Value

An object of class "tkfit" (a list) containing:

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
fit <- tk_fit(data, "complete", pdf_exp, cdf_exp, prior_spec,
              initial_values = c(rate = 1), loss_function = "sel")
summary(fit)

Compute the Hessian and Posterior Covariance Matrix

Description

Computes the Hessian of the log-posterior at a given parameter value and derives the approximate posterior covariance matrix.

Usage

tk_hessian(
  log_post_fn,
  param,
  method = "Richardson",
  analytic_hessian = NULL,
  validate_analytic = TRUE
)

Arguments

Value

An object of class "tkhessian" (a list) containing:

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
log_post <- tk_posterior(data, "complete", pdf_exp, cdf_exp, prior_spec)
mode_result <- tk_mode(log_post, initial_values = c(1))
hess_result <- tk_hessian(log_post, mode_result$mode)

Bayes Estimators Under Various Loss Functions

Description

Computes Bayes estimators under different loss functions using the Tierney-Kadane approximation framework.

Dispatches to the appropriate loss function based on the loss type.

Usage

tk_loss(loss_type, log_post_fn, mode_result, hessian_result, ...)

Arguments

Value

Named numeric vector of Bayes parameter estimates under specified loss.

Bayes estimate(s) under the specified loss function

Custom Loss Function Estimator

Description

Computes a Bayes estimator for a user-specified loss function.

Usage

tk_loss_custom(
  log_post_fn,
  mode_result,
  hessian_result,
  g,
  parameter_index = NULL,
  ...
)

Arguments

Value

Bayes estimate(s) under custom loss

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
log_post <- tk_posterior(data, "complete", pdf_exp, cdf_exp, prior_spec)
mode_result <- tk_mode(log_post, initial_values = c(1))
hessian_result <- tk_hessian(log_post, mode_result$mode)
g_fn <- function(param) log(param[1])
custom_estimate <- tk_loss_custom(log_post, mode_result, hessian_result, g_fn)

General Entropy Loss (GEL) Estimator

Description

Computes the Bayes estimator under General Entropy Loss. Estimator: theta_hat = (E(theta^(-q) | x))^(-1/q)

Usage

tk_loss_gel(
  log_post_fn,
  mode_result,
  hessian_result,
  q = 0.5,
  parameter_index = NULL,
  ...
)

Arguments

Value

Bayes estimate(s) under GEL

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
log_post <- tk_posterior(data, "complete", pdf_exp, cdf_exp, prior_spec)
mode_result <- tk_mode(log_post, initial_values = c(1))
hessian_result <- tk_hessian(log_post, mode_result$mode)
gel_estimate <- tk_loss_gel(log_post, mode_result, hessian_result, q = 0.5)

LINEX Loss Estimator

Description

Computes the Bayes estimator under LINEX (Linear-Exponential) loss. Estimator: theta_hat = -(1/c) * log E(exp(-c * theta) | x)

Usage

tk_loss_linex(
  log_post_fn,
  mode_result,
  hessian_result,
  c = 0.5,
  parameter_index = NULL,
  ...
)

Arguments

Value

Bayes estimate(s) under LINEX loss

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
log_post <- tk_posterior(data, "complete", pdf_exp, cdf_exp, prior_spec)
mode_result <- tk_mode(log_post, initial_values = c(1))
hessian_result <- tk_hessian(log_post, mode_result$mode)
linex_estimate <- tk_loss_linex(log_post, mode_result, hessian_result, c = 0.5)

Precautionary Loss Estimator

Description

Computes the Bayes estimator under precautionary loss. Estimator: theta_hat = sqrt(E(theta^2 | x))

Usage

tk_loss_precautionary(
  log_post_fn,
  mode_result,
  hessian_result,
  parameter_index = NULL,
  ...
)

Arguments

Value

Bayes estimate(s) under precautionary loss

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
log_post <- tk_posterior(data, "complete", pdf_exp, cdf_exp, prior_spec)
mode_result <- tk_mode(log_post, initial_values = c(1))
hessian_result <- tk_hessian(log_post, mode_result$mode)
precautionary_estimate <- tk_loss_precautionary(log_post, mode_result, hessian_result)

Squared Error Loss (SEL) Estimator

Description

Computes the posterior mean (Bayes estimator under squared error loss).

Usage

tk_loss_sel(
  log_post_fn,
  mode_result,
  hessian_result,
  parameter_index = NULL,
  ...
)

Arguments

Value

Bayes estimate(s) under SEL

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
log_post <- tk_posterior(data, "complete", pdf_exp, cdf_exp, prior_spec)
mode_result <- tk_mode(log_post, initial_values = c(1))
hessian_result <- tk_hessian(log_post, mode_result$mode)
sel_estimate <- tk_loss_sel(log_post, mode_result, hessian_result)

Weighted Squared Error Loss Estimator

Description

Computes the Bayes estimator under weighted squared error loss. Estimator: theta_hat = 1 / E(theta^(-1) | x)

Usage

tk_loss_weighted_sel(
  log_post_fn,
  mode_result,
  hessian_result,
  parameter_index = NULL,
  ...
)

Arguments

Value

Bayes estimate(s) under weighted SEL

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
log_post <- tk_posterior(data, "complete", pdf_exp, cdf_exp, prior_spec)
mode_result <- tk_mode(log_post, initial_values = c(1))
hessian_result <- tk_hessian(log_post, mode_result$mode)
weighted_estimate <- tk_loss_weighted_sel(log_post, mode_result, hessian_result)

Find the Posterior Mode via Optimization

Description

Locates the posterior mode (MAP estimate) using numerical optimization. Supports multiple optimization backends with automatic fallback.

Usage

tk_mode(
  log_post_fn,
  initial_values,
  lower_bounds = NULL,
  upper_bounds = NULL,
  method = "BFGS",
  control = NULL,
  max_attempts = 3
)

Arguments

Value

An object of class "tkmode" (a list) containing:

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
log_post <- tk_posterior(data, "complete", pdf_exp, cdf_exp, prior_spec)
mode_result <- tk_mode(log_post, initial_values = c(1), method = "BFGS")

Visualization Functions for tkfit Objects

Description

Functions to create diagnostic and exploratory plots for Tierney-Kadane Bayesian estimation results.

Dispatches to plot.tkfit for graphical diagnostics.

Usage

tk_plot(x, ...)

Arguments

Value

Invisibly returns the input object or NULL, called for side effects.

Invisibly returns the input x object of class "tkfit", called for side effects.

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
fit <- tk_fit(data, "complete", pdf_exp, cdf_exp, prior_spec, initial_values = c(rate = 1))
tk_plot(fit, which = 1)

Construct the Log-Posterior Function

Description

Creates a function that computes the log-posterior density for a given parameter vector, combining the log-likelihood and log-prior.

Usage

tk_posterior(
  data,
  censoring_scheme,
  pdf,
  cdf = NULL,
  prior_spec = NULL,
  loglik = NULL,
  ...
)

Arguments

Value

A function that takes a parameter vector and returns the log-posterior h(theta) = (log L + log pi) / n

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
log_post <- tk_posterior(data, "complete", pdf_exp, cdf_exp, prior_spec)
log_post(c(1.5))

Prior Sensitivity Analysis

Description

Performs sensitivity analysis by varying prior hyperparameters and examining the impact on Bayes estimates, bias, variance, and risk.

Usage

tk_sensitivity(
  fit,
  parameter_name,
  hyperparameter_name,
  hyperparameter_values,
  loss_function = "sel",
  loss_params = NULL,
  ...
)

Arguments

Value

An object of class "tksensitivity" (a list) containing:

Examples

pdf_exp <- function(x, param) dexp(x, rate = param[1])
cdf_exp <- function(x, param) pexp(x, rate = param[1])
prior_spec <- list(rate = list(family = "gamma", hyperparameters = list(shape = 2, rate = 1)))
data <- c(1.2, 2.3, 1.8, 3.1, 0.9)
fit <- tk_fit(data, "complete", pdf_exp, cdf_exp, prior_spec, initial_values = c(rate = 1))
sensitivity <- tk_sensitivity(fit, "rate", "shape", c(1, 2, 5))

Variance-Covariance Method for tkfit Objects

Description

Extracts the approximate posterior covariance matrix from a tkfit object.

Usage

## S3 method for class 'tkfit'
vcov(object, ...)

Arguments

Value

Covariance matrix