{
  "_id": "6ab9031e99f7aa8c6aa39ad6",
  "Package": "TKApprox",
  "Title": "A General Framework for Bayesian Estimation Using the\n'Tierney'-'Kadane' Approximation",
  "Version": "0.1.0",
  "Authors@R": "c(\nperson(\"Shikhar\", \"Tyagi\", email = \"shikhar1093tyagi@gmail.com\",\nrole = c(\"aut\", \"cre\"),\ncomment = c(ORCID = \"0000-0003-1606-0844\")),\nperson(\"Arvind\", \"Pandey\", email = \"arvindmzu@gmail.com\", role = \"aut\"),\nperson(\"Bhupendra\", \"Singh\", email = \"bhupendra.rana@gmail.com\", role = \"aut\"),\nperson(\"Vrijesh\", \"Tripathi\", email = \"vrijesh.tripathi@uwi.edu\", role = \"aut\"))",
  "Description": "Provides a distribution-independent framework for Bayesian\nestimation of arbitrary univariate probability models using the\n'Tierney'-'Kadane' approximation ('Tierney' & 'Kadane', 1986\n<doi:10.1080/01621459.1986.10478240>). Users specify the\nprobability distribution, likelihood, prior distributions, and\ncensoring mechanism, while the package automatically constructs\nthe posterior distribution, computes posterior modes and\nHessian matrices, approximates posterior expectations under\nseveral Bayesian loss functions, and returns Bayesian parameter\nestimates, posterior covariance matrices, credible intervals,\ndiagnostic plots, and model comparison statistics. Supports\ncomplete, right-, left-, interval-, Type-I, Type-II,\nprogressive Type-II, hybrid, and doubly censored data\n('Lawless', 2003 <ISBN:978-0-471-37215-8>; 'Meeker' &\n'Escobar', 1998 <ISBN:978-0-471-14328-4>; 'Balakrishnan' &\n'Aggarwala', 2000 <ISBN:978-0-8176-4129-0>; 'Kundu' &\n'Pradhan', 2009 <doi:10.1198/TECH.2009.0019>), making it a\nflexible tool for Bayesian reliability, survival, and lifetime\ndata analysis.",
  "License": "GPL (>= 3)",
  "Encoding": "UTF-8",
  "RoxygenNote": "7.3.3",
  "VignetteBuilder": "knitr",
  "NeedsCompilation": "no",
  "Packaged": {
    "Date": "2026-09-27 11:47:09 UTC",
    "User": "root"
  },
  "Author": "Shikhar Tyagi [aut, cre] (ORCID:\n<https://orcid.org/0000-0003-1606-0844>), Arvind Pandey [aut],\nBhupendra Singh [aut], Vrijesh Tripathi [aut]",
  "Maintainer": "Shikhar Tyagi <shikhar1093tyagi@gmail.com>",
  "Repository": "https://shikhartyagi.r-universe.dev",
  "Date/Publication": "2026-08-07 20:00:02 UTC",
  "RemoteUrl": "https://github.com/cran/TKApprox",
  "RemoteRef": "HEAD",
  "RemoteSha": "238c54ce6fa41d40d88ed7d77202e7ec42cd01c9",
  "_user": "shikhartyagi",
  "_type": "src",
  "_file": "TKApprox_0.1.0.tar.gz",
  "_fileid": "https://r2.ropensci.org/475d15be175de08d9640e4fd0a7b3dff8b92ba85faddab325a9324020985c91c",
  "_filesize": 1826169,
  "_sha256": "475d15be175de08d9640e4fd0a7b3dff8b92ba85faddab325a9324020985c91c",
  "_expires": "2027-01-05T11:50:52.000Z",
  "_created": "2026-09-27T11:47:09.000Z",
  "_published": "2026-09-27T11:50:54.826Z",
  "_jobs": [
    {
      "job": 108613125152,
      "time": 145,
      "config": "linux-devel-x86_64",
      "r": "4.7.0",
      "check": "OK",
      "artifact": "10931256406"
    },
    {
      "job": 108613125122,
      "time": 186,
      "config": "linux-release-x86_64",
      "r": "4.6.1",
      "check": "OK",
      "artifact": "10930488727"
    },
    {
      "job": 108613125131,
      "time": 90,
      "config": "macos-oldrel-arm64",
      "r": "4.5.3",
      "check": "OK",
      "artifact": "10930338729"
    },
    {
      "job": 108613125123,
      "time": 79,
      "config": "macos-release-arm64",
      "r": "4.6.1",
      "check": "OK",
      "artifact": "10930453640"
    },
    {
      "job": 108612544742,
      "time": 230,
      "config": "source",
      "r": "4.6.1",
      "check": "OK",
      "artifact": "10931007179"
    },
    {
      "job": 108613125132,
      "time": 112,
      "config": "wasm-release",
      "r": "4.6.0",
      "check": "OK",
      "artifact": "10931311185"
    },
    {
      "job": 108613125135,
      "time": 71,
      "config": "windows-devel-x86_64",
      "r": "4.7.0",
      "check": "OK",
      "artifact": "10930868350"
    },
    {
      "job": 108613125162,
      "time": 71,
      "config": "windows-oldrel-x86_64",
      "r": "4.5.3",
      "check": "OK",
      "artifact": "10930937941"
    },
    {
      "job": 108613125229,
      "time": 79,
      "config": "windows-release-x86_64",
      "r": "4.6.1",
      "check": "OK",
      "artifact": "10930912962"
    }
  ],
  "_host": "GitHub-Actions",
  "_buildurl": "https://github.com/r-universe/shikhartyagi/actions/runs/36316646605",
  "_status": "success",
  "_upstream": "https://github.com/cran/TKApprox",
  "_commit": {
    "id": "238c54ce6fa41d40d88ed7d77202e7ec42cd01c9",
    "author": "Shikhar Tyagi <shikhar1093tyagi@gmail.com>",
    "committer": "cran-robot <csardi.gabor+cran@gmail.com>",
    "message": "version 0.1.0\n",
    "time": 1786132802
  },
  "_maintainer": {
    "name": "Shikhar Tyagi",
    "email": "shikhar1093tyagi@gmail.com",
    "login": "shikhartyagi",
    "description": "Lecturer, Department of Mathematics and Statistics, The University of the West Indies, Trinidad and Tobago. ",
    "uuid": 38758495,
    "orcid": "0000-0003-1606-0844"
  },
  "_distro": "resolute",
  "_registered": true,
  "_dependencies": [
    {
      "package": "R",
      "version": ">= 4.0.0",
      "role": "Depends"
    },
    {
      "package": "checkmate",
      "role": "Imports"
    },
    {
      "package": "numDeriv",
      "role": "Imports"
    },
    {
      "package": "maxLik",
      "role": "Imports"
    },
    {
      "package": "rlang",
      "role": "Imports"
    },
    {
      "package": "stats",
      "role": "Imports"
    },
    {
      "package": "graphics",
      "role": "Imports"
    },
    {
      "package": "grDevices",
      "role": "Imports"
    },
    {
      "package": "utils",
      "role": "Imports"
    },
    {
      "package": "MASS",
      "role": "Imports"
    },
    {
      "package": "testthat",
      "version": ">= 3.0.0",
      "role": "Suggests"
    },
    {
      "package": "knitr",
      "role": "Suggests"
    },
    {
      "package": "rmarkdown",
      "role": "Suggests"
    },
    {
      "package": "pkgdown",
      "role": "Suggests"
    },
    {
      "package": "ggplot2",
      "role": "Suggests"
    },
    {
      "package": "gridExtra",
      "role": "Suggests"
    }
  ],
  "_owner": "cran",
  "_selfowned": true,
  "_usedby": 0,
  "_updates": [
    {
      "week": "2026-32",
      "n": 1
    }
  ],
  "_tags": [
    {
      "name": "0.1.0",
      "date": "2026-08-07"
    }
  ],
  "_stars": 0,
  "_contributors": [
    {
      "user": "shikhartyagi",
      "count": 1,
      "uuid": 38758495
    }
  ],
  "_userbio": {
    "uuid": 38758495,
    "type": "user",
    "name": "shikhartyagi",
    "followers": 0,
    "description": "Lecturer, Department of Mathematics and Statistics, The University of the West Indies, Trinidad and Tobago. "
  },
  "_downloads": {
    "count": 237,
    "source": "https://cranlogs.r-pkg.org/downloads/total/last-month/TKApprox"
  },
  "_searchresults": 0,
  "_rbuild": "4.6.1",
  "_assets": [
    "extra/citation.cff",
    "extra/citation.html",
    "extra/citation.json",
    "extra/citation.txt",
    "extra/contents.json",
    "extra/manual.pdf",
    "extra/NEWS.html",
    "extra/NEWS.txt",
    "extra/readme.html",
    "extra/readme.md",
    "extra/TKApprox.html"
  ],
  "_realowner": "shikhartyagi",
  "_cranurl": false,
  "_releases": [
    {
      "version": "0.1.0",
      "date": "2026-08-07"
    }
  ],
  "_exports": [
    "CAIC",
    "DIC",
    "eval_logposterior",
    "expected_logposterior",
    "HQIC",
    "loglik_complete",
    "loglik_dispatcher",
    "loglik_doubly_censored",
    "loglik_hybrid_censored",
    "loglik_interval_censored",
    "loglik_left_censored",
    "loglik_progressive_type2_censored",
    "loglik_right_censored",
    "loglik_type1_censored",
    "loglik_type2_censored",
    "logprior_beta",
    "logprior_dispatcher",
    "logprior_exponential",
    "logprior_gamma",
    "logprior_independent",
    "logprior_invgamma",
    "logprior_lognormal",
    "logprior_normal",
    "logprior_uniform",
    "logprior_weibull",
    "model_comparison_table",
    "neglogLik",
    "plot_convergence",
    "plot_credible_intervals",
    "plot_likelihood_surface",
    "plot_posterior_approximation",
    "plot_prior_posterior",
    "plot_residuals",
    "plot_sensitivity_estimates",
    "plot_sensitivity_logposterior",
    "plot_sensitivity_risk",
    "print_model_comparison",
    "tk_expectation",
    "tk_expectations",
    "tk_fit",
    "tk_hessian",
    "tk_loss",
    "tk_loss_custom",
    "tk_loss_gel",
    "tk_loss_linex",
    "tk_loss_precautionary",
    "tk_loss_sel",
    "tk_loss_weighted_sel",
    "tk_mode",
    "tk_plot",
    "tk_posterior",
    "tk_sensitivity"
  ],
  "_help": [
    {
      "page": "AIC.tkfit",
      "title": "AIC Method for tkfit Objects",
      "topics": [
        "AIC.tkfit"
      ]
    },
    {
      "page": "BIC.tkfit",
      "title": "BIC Method for tkfit Objects",
      "topics": [
        "BIC.tkfit"
      ]
    },
    {
      "page": "CAIC",
      "title": "Compute CAIC (Consistent AIC)",
      "topics": [
        "CAIC",
        "CAIC.tkfit"
      ]
    },
    {
      "page": "coef.tkfit",
      "title": "Coefficients Method for tkfit Objects",
      "topics": [
        "coef.tkfit"
      ]
    },
    {
      "page": "DIC",
      "title": "Compute DIC (Deviance Information Criterion) Approximation",
      "topics": [
        "DIC",
        "DIC.tkfit"
      ]
    },
    {
      "page": "eval_logposterior",
      "title": "Evaluate the Log-Posterior at Given Parameters",
      "topics": [
        "eval_logposterior"
      ]
    },
    {
      "page": "expected_logposterior",
      "title": "Compute Expected Log-Posterior",
      "topics": [
        "expected_logposterior",
        "expected_logposterior.tkfit"
      ]
    },
    {
      "page": "HQIC",
      "title": "Compute HQIC (Hannan-Quinn Information Criterion)",
      "topics": [
        "HQIC",
        "HQIC.tkfit"
      ]
    },
    {
      "page": "likelihood",
      "title": "Likelihood Construction for Censored Data",
      "topics": [
        "likelihood"
      ]
    },
    {
      "page": "loglik_complete",
      "title": "Complete (Uncensored) Data Log-Likelihood",
      "topics": [
        "loglik_complete"
      ]
    },
    {
      "page": "loglik_dispatcher",
      "title": "Generic Likelihood Dispatcher",
      "topics": [
        "loglik_dispatcher"
      ]
    },
    {
      "page": "loglik_doubly_censored",
      "title": "Doubly Censored Data Log-Likelihood",
      "topics": [
        "loglik_doubly_censored"
      ]
    },
    {
      "page": "loglik_hybrid_censored",
      "title": "Hybrid Censored Data Log-Likelihood",
      "topics": [
        "loglik_hybrid_censored"
      ]
    },
    {
      "page": "loglik_interval_censored",
      "title": "Interval-Censored Data Log-Likelihood",
      "topics": [
        "loglik_interval_censored"
      ]
    },
    {
      "page": "loglik_left_censored",
      "title": "Left-Censored Data Log-Likelihood",
      "topics": [
        "loglik_left_censored"
      ]
    },
    {
      "page": "loglik_progressive_type2_censored",
      "title": "Progressive Type-II Censored Data Log-Likelihood",
      "topics": [
        "loglik_progressive_type2_censored"
      ]
    },
    {
      "page": "loglik_right_censored",
      "title": "Right-Censored Data Log-Likelihood",
      "topics": [
        "loglik_right_censored"
      ]
    },
    {
      "page": "loglik_type1_censored",
      "title": "Type-I Censored Data Log-Likelihood",
      "topics": [
        "loglik_type1_censored"
      ]
    },
    {
      "page": "loglik_type2_censored",
      "title": "Type-II Censored Data Log-Likelihood",
      "topics": [
        "loglik_type2_censored"
      ]
    },
    {
      "page": "logLik.tkfit",
      "title": "Log-Likelihood Method for tkfit Objects",
      "topics": [
        "logLik.tkfit"
      ]
    },
    {
      "page": "logprior_dispatcher",
      "title": "Generic Prior Function Dispatcher",
      "topics": [
        "logprior_dispatcher"
      ]
    },
    {
      "page": "logprior_independent",
      "title": "Independent Priors for Multiple Parameters",
      "topics": [
        "logprior_independent"
      ]
    },
    {
      "page": "model_comparison",
      "title": "Model Comparison Statistics for tkfit Objects",
      "topics": [
        "model_comparison"
      ]
    },
    {
      "page": "model_comparison_table",
      "title": "Comprehensive Model Comparison Table",
      "topics": [
        "model_comparison_table"
      ]
    },
    {
      "page": "neglogLik",
      "title": "Compute Negative Log-Likelihood",
      "topics": [
        "neglogLik",
        "neglogLik.tkfit"
      ]
    },
    {
      "page": "plot_convergence",
      "title": "Convergence Diagnostic Plot",
      "topics": [
        "plot_convergence"
      ]
    },
    {
      "page": "plot_credible_intervals",
      "title": "Credible Intervals Plot",
      "topics": [
        "plot_credible_intervals"
      ]
    },
    {
      "page": "plot_likelihood_surface",
      "title": "Likelihood Surface Plot",
      "topics": [
        "plot_likelihood_surface"
      ]
    },
    {
      "page": "plot_posterior_approximation",
      "title": "Posterior Approximation Plot",
      "topics": [
        "plot_posterior_approximation"
      ]
    },
    {
      "page": "plot_prior_posterior",
      "title": "Prior vs Posterior Comparison Plot",
      "topics": [
        "plot_prior_posterior"
      ]
    },
    {
      "page": "plot_residuals",
      "title": "Residuals Plot",
      "topics": [
        "plot_residuals"
      ]
    },
    {
      "page": "plot_sensitivity_estimates",
      "title": "Plot Sensitivity of Estimates",
      "topics": [
        "plot_sensitivity_estimates"
      ]
    },
    {
      "page": "plot_sensitivity_logposterior",
      "title": "Plot Sensitivity of Log-Posterior",
      "topics": [
        "plot_sensitivity_logposterior"
      ]
    },
    {
      "page": "plot_sensitivity_risk",
      "title": "Plot Sensitivity of Risk",
      "topics": [
        "plot_sensitivity_risk"
      ]
    },
    {
      "page": "plot.tkfit",
      "title": "Plot Method for tkfit Objects",
      "topics": [
        "plot.tkfit"
      ]
    },
    {
      "page": "plot.tksensitivity",
      "title": "Plot Method for tksensitivity Objects",
      "topics": [
        "plot.tksensitivity"
      ]
    },
    {
      "page": "predict.tkfit",
      "title": "Predict Method for tkfit Objects",
      "topics": [
        "predict.tkfit"
      ]
    },
    {
      "page": "print_model_comparison",
      "title": "Print Model Comparison Table",
      "topics": [
        "print_model_comparison"
      ]
    },
    {
      "page": "print.tkexpectation",
      "title": "Print Method for tkexpectation Objects",
      "topics": [
        "print.tkexpectation"
      ]
    },
    {
      "page": "print.tkfit",
      "title": "Print Method for tkfit Objects",
      "topics": [
        "print.tkfit"
      ]
    },
    {
      "page": "print.tkhessian",
      "title": "Print Method for tkhessian Objects",
      "topics": [
        "print.tkhessian"
      ]
    },
    {
      "page": "print.tkmode",
      "title": "Print Method for tkmode Objects",
      "topics": [
        "print.tkmode"
      ]
    },
    {
      "page": "print.tksensitivity",
      "title": "Print Method for tksensitivity Objects",
      "topics": [
        "print.tksensitivity"
      ]
    },
    {
      "page": "priors",
      "title": "Prior Distribution Functions",
      "topics": [
        "logprior_beta",
        "logprior_exponential",
        "logprior_gamma",
        "logprior_invgamma",
        "logprior_lognormal",
        "logprior_normal",
        "logprior_uniform",
        "logprior_weibull",
        "priors"
      ]
    },
    {
      "page": "residuals.tkfit",
      "title": "Residuals Method for tkfit Objects",
      "topics": [
        "residuals.tkfit"
      ]
    },
    {
      "page": "summary.tkfit",
      "title": "Summary Method for tkfit Objects",
      "topics": [
        "summary.tkfit"
      ]
    },
    {
      "page": "tk_expectation",
      "title": "Tierney-Kadane Approximation of Posterior Expectations",
      "topics": [
        "tk_expectation"
      ]
    },
    {
      "page": "tk_expectations",
      "title": "Compute Multiple Expectations Efficiently",
      "topics": [
        "tk_expectations"
      ]
    },
    {
      "page": "tk_fit",
      "title": "Main Function for Bayesian Estimation via Tierney-Kadane Approximation",
      "topics": [
        "tk_fit"
      ]
    },
    {
      "page": "tk_hessian",
      "title": "Compute the Hessian and Posterior Covariance Matrix",
      "topics": [
        "tk_hessian"
      ]
    },
    {
      "page": "tk_loss",
      "title": "Bayes Estimators Under Various Loss Functions",
      "topics": [
        "tk_loss"
      ]
    },
    {
      "page": "tk_loss_custom",
      "title": "Custom Loss Function Estimator",
      "topics": [
        "tk_loss_custom"
      ]
    },
    {
      "page": "tk_loss_gel",
      "title": "General Entropy Loss (GEL) Estimator",
      "topics": [
        "tk_loss_gel"
      ]
    },
    {
      "page": "tk_loss_linex",
      "title": "LINEX Loss Estimator",
      "topics": [
        "tk_loss_linex"
      ]
    },
    {
      "page": "tk_loss_precautionary",
      "title": "Precautionary Loss Estimator",
      "topics": [
        "tk_loss_precautionary"
      ]
    },
    {
      "page": "tk_loss_sel",
      "title": "Squared Error Loss (SEL) Estimator",
      "topics": [
        "tk_loss_sel"
      ]
    },
    {
      "page": "tk_loss_weighted_sel",
      "title": "Weighted Squared Error Loss Estimator",
      "topics": [
        "tk_loss_weighted_sel"
      ]
    },
    {
      "page": "tk_mode",
      "title": "Find the Posterior Mode via Optimization",
      "topics": [
        "tk_mode"
      ]
    },
    {
      "page": "tk_plot",
      "title": "Visualization Functions for tkfit Objects",
      "topics": [
        "tk_plot"
      ]
    },
    {
      "page": "tk_posterior",
      "title": "Construct the Log-Posterior Function",
      "topics": [
        "tk_posterior"
      ]
    },
    {
      "page": "tk_sensitivity",
      "title": "Prior Sensitivity Analysis",
      "topics": [
        "tk_sensitivity"
      ]
    },
    {
      "page": "vcov.tkfit",
      "title": "Variance-Covariance Method for tkfit Objects",
      "topics": [
        "vcov.tkfit"
      ]
    }
  ],
  "_readme": "https://github.com/cran/TKApprox/raw/HEAD/README.md",
  "_rundeps": [
    "backports",
    "checkmate",
    "digest",
    "generics",
    "lattice",
    "MASS",
    "maxLik",
    "miscTools",
    "numDeriv",
    "rlang",
    "sandwich",
    "zoo"
  ],
  "_vignettes": [
    {
      "source": "censoring-schemes.Rmd",
      "filename": "censoring-schemes.html",
      "title": "Censoring Schemes",
      "author": "Your Name",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Introduction",
        "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",
        "Comparing Censoring Schemes",
        "Tips for Working with Censored Data",
        "Next Steps"
      ],
      "created": "2026-08-07 20:00:02",
      "modified": "2026-08-07 20:00:02",
      "commits": 1
    },
    {
      "source": "defining-distributions.Rmd",
      "filename": "defining-distributions.html",
      "title": "Defining Custom Distributions",
      "author": "Your Name",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Introduction",
        "Required Functions",
        "Continuous Distributions",
        "Example 1: Log-Normal Distribution",
        "Example 2: Pareto Distribution",
        "Example 3: Burr Type XII Distribution",
        "Discrete Distributions",
        "Example 4: Poisson Distribution",
        "Example 5: Negative Binomial Distribution",
        "Using Custom Log-Likelihood Functions",
        "Tips for Defining Distributions",
        "Next Steps"
      ],
      "created": "2026-08-07 20:00:02",
      "modified": "2026-08-07 20:00:02",
      "commits": 1
    },
    {
      "source": "intro.Rmd",
      "filename": "intro.html",
      "title": "Introduction to TKApprox",
      "author": "Your Name",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Introduction",
        "Basic Workflow",
        "A Simple Example: Exponential Distribution",
        "Step 1: Define the Distribution",
        "Step 2: Specify Prior",
        "Step 3: Generate Data",
        "Step 4: Fit the Model",
        "Step 5: Examine Results",
        "Visualization",
        "Different Loss Functions",
        "Squared Error Loss (Posterior Mean)",
        "LINEX Loss",
        "General Entropy Loss",
        "Censored Data",
        "Prior Sensitivity Analysis",
        "Multi-Parameter Models",
        "Next Steps"
      ],
      "created": "2026-08-07 20:00:02",
      "modified": "2026-08-07 20:00:02",
      "commits": 1
    },
    {
      "source": "loss-functions.Rmd",
      "filename": "loss-functions.html",
      "title": "Loss Functions",
      "author": "Your Name",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Introduction",
        "Squared Error Loss (SEL)",
        "LINEX Loss",
        "LINEX Sensitivity Analysis",
        "General Entropy Loss (GEL)",
        "Precautionary Loss",
        "Weighted Squared Error Loss",
        "Custom Loss Functions",
        "Comparing All Loss Functions",
        "Choosing a Loss Function",
        "Multi-Parameter Models",
        "Next Steps"
      ],
      "created": "2026-08-07 20:00:02",
      "modified": "2026-08-07 20:00:02",
      "commits": 1
    },
    {
      "source": "prior-specification.Rmd",
      "filename": "prior-specification.html",
      "title": "Prior Specification",
      "author": "Your Name",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Introduction",
        "Standard Prior Families",
        "Gamma Prior",
        "Normal Prior",
        "Beta Prior",
        "Uniform Prior",
        "Exponential Prior",
        "Log-Normal Prior",
        "Weibull Prior",
        "Inverse Gamma Prior",
        "Independent Priors for Multiple Parameters",
        "Custom Prior Functions",
        "Non-Informative (Flat) Priors",
        "Prior Sensitivity Analysis",
        "Systematic Prior Sensitivity",
        "Choosing Prior Hyperparameters",
        "Conjugate Priors",
        "Weakly Informative Priors",
        "Informative Priors",
        "Tips for Prior Specification",
        "Next Steps"
      ],
      "created": "2026-08-07 20:00:02",
      "modified": "2026-08-07 20:00:02",
      "commits": 1
    },
    {
      "source": "real-data-example.Rmd",
      "filename": "real-data-example.html",
      "title": "Real Data Example",
      "author": "Your Name",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Introduction",
        "Dataset: Air Conditioning System Failure Times",
        "Exploratory Data Analysis",
        "Weibull Distribution Model",
        "Define the Distribution",
        "Specify Priors",
        "Fit the Model with Complete Data",
        "Examine Results",
        "Model Comparison Statistics",
        "Visualization",
        "Analysis with Different Loss Functions",
        "LINEX Loss",
        "General Entropy Loss",
        "Comparison of Loss Functions",
        "Analysis with Censored Data",
        "Create Right-Censored Data",
        "Fit with Right Censoring",
        "Compare Complete vs Censored",
        "Reliability Function Estimation",
        "Hazard Function Estimation",
        "Prior Sensitivity Analysis",
        "Prediction",
        "Model Diagnostics",
        "Comparison with Maximum Likelihood Estimation",
        "Summary and Interpretation",
        "Key Findings",
        "Practical Implications",
        "References",
        "Next Steps"
      ],
      "created": "2026-08-07 20:00:02",
      "modified": "2026-08-07 20:00:02",
      "commits": 1
    },
    {
      "source": "simulation-studies.Rmd",
      "filename": "simulation-studies.html",
      "title": "Simulation Studies",
      "author": "Your Name",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Introduction",
        "Basic Simulation Framework",
        "Example 1: Exponential Distribution with Complete Data",
        "Setup",
        "Simulation Function",
        "Run Simulations",
        "Compute Performance Metrics",
        "Display Results",
        "Visualize Results",
        "Example 2: Censoring Schemes Comparison",
        "Simulation Function for Right Censoring",
        "Compute Metrics",
        "Visualize",
        "Example 3: Prior Sensitivity Simulation",
        "Example 4: Coverage Probability",
        "Run Simulation",
        "Example 5: Multi-Parameter Model Simulation",
        "Parallel Simulation",
        "Tips for Simulation Studies",
        "Interpreting Simulation Results",
        "Bias",
        "Variance",
        "MSE",
        "Coverage Probability",
        "Next Steps"
      ],
      "created": "2026-08-07 20:00:02",
      "modified": "2026-08-07 20:00:02",
      "commits": 1
    },
    {
      "source": "tierney-kadane-derivation.Rmd",
      "filename": "tierney-kadane-derivation.html",
      "title": "Tierney-Kadane Approximation: Theory and Derivation",
      "author": "Your Name",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Introduction",
        "Problem Statement",
        "Laplace Approximation Background",
        "Tierney-Kadane Derivation",
        "Step 1: Posterior Mode",
        "Step 2: Modified Function for Expectation",
        "Step 3: TK Approximation Formula",
        "Properties of the TK Approximation",
        "Accuracy",
        "Requirements",
        "Advantages",
        "Limitations",
        "Implementation in TKApprox",
        "Function Structure",
        "Example: Computing Posterior Mean",
        "Connection to Loss Functions",
        "Squared Error Loss (Posterior Mean)",
        "LINEX Loss",
        "General Entropy Loss",
        "Precautionary Loss",
        "Weighted Squared Error Loss",
        "Numerical Considerations",
        "Optimization",
        "Numerical Differentiation",
        "Numerical Stability",
        "Comparison with Other Methods",
        "vs. MCMC",
        "vs. Variational Inference",
        "vs. Importance Sampling",
        "References",
        "Next Steps"
      ],
      "created": "2026-08-07 20:00:02",
      "modified": "2026-08-07 20:00:02",
      "commits": 1
    }
  ],
  "_score": 3.6020599913279625,
  "_indexed": true,
  "_nocasepkg": "tkapprox",
  "_universes": [
    "shikhartyagi"
  ],
  "_binaries": [
    {
      "r": "4.7.0",
      "os": "linux",
      "version": "0.1.0",
      "date": "2026-09-27T11:49:35.000Z",
      "distro": "resolute",
      "commit": "238c54ce6fa41d40d88ed7d77202e7ec42cd01c9",
      "fileid": "https://r2.ropensci.org/81e1a6fd727a2192f5daf8d3f090ad548172230e68a482d66ced4ddd5cfe56d3",
      "status": "success",
      "check": "OK",
      "buildurl": "https://github.com/r-universe/shikhartyagi/actions/runs/36316646605"
    },
    {
      "r": "4.6.1",
      "os": "linux",
      "version": "0.1.0",
      "date": "2026-09-27T11:50:16.000Z",
      "distro": "resolute",
      "commit": "238c54ce6fa41d40d88ed7d77202e7ec42cd01c9",
      "fileid": "https://r2.ropensci.org/bc503bc45dc693a6a44cdbfd5f28414aabcc85fbb06dedf2a24beda57326fe80",
      "status": "success",
      "check": "OK",
      "buildurl": "https://github.com/r-universe/shikhartyagi/actions/runs/36316646605"
    },
    {
      "r": "4.5.3",
      "os": "mac",
      "version": "0.1.0",
      "date": "2026-09-27T11:48:55.000Z",
      "commit": "238c54ce6fa41d40d88ed7d77202e7ec42cd01c9",
      "fileid": "https://r2.ropensci.org/206961809494bb3c8adec2c73228e86b22641794b0ac4a1ed729780f2b794d15",
      "status": "success",
      "check": "OK",
      "buildurl": "https://github.com/r-universe/shikhartyagi/actions/runs/36316646605"
    },
    {
      "r": "4.6.1",
      "os": "mac",
      "version": "0.1.0",
      "date": "2026-09-27T11:48:42.000Z",
      "commit": "238c54ce6fa41d40d88ed7d77202e7ec42cd01c9",
      "fileid": "https://r2.ropensci.org/0ff3f357d25b25e83090b6d0682d349b434d5ba799c2ab29e56723214bc3a013",
      "status": "success",
      "check": "OK",
      "buildurl": "https://github.com/r-universe/shikhartyagi/actions/runs/36316646605"
    },
    {
      "r": "4.6.0",
      "os": "wasm",
      "version": "0.1.0",
      "date": "2026-09-27T11:49:22.000Z",
      "commit": "238c54ce6fa41d40d88ed7d77202e7ec42cd01c9",
      "fileid": "https://r2.ropensci.org/b42ba2be75b7ae09cda03f8feef9dbf77fa7e9816545602219dfaa8ef440c5c8",
      "status": "success",
      "buildurl": "https://github.com/r-universe/shikhartyagi/actions/runs/36316646605"
    },
    {
      "r": "4.7.0",
      "os": "win",
      "version": "0.1.0",
      "date": "2026-09-27T11:48:17.000Z",
      "commit": "238c54ce6fa41d40d88ed7d77202e7ec42cd01c9",
      "fileid": "https://r2.ropensci.org/6b0b784ac209b48db34a3cb0f7af0f6d01b13f2e94914db5b7c2717ffefed157",
      "status": "success",
      "check": "OK",
      "buildurl": "https://github.com/r-universe/shikhartyagi/actions/runs/36316646605"
    },
    {
      "r": "4.5.3",
      "os": "win",
      "version": "0.1.0",
      "date": "2026-09-27T11:48:18.000Z",
      "commit": "238c54ce6fa41d40d88ed7d77202e7ec42cd01c9",
      "fileid": "https://r2.ropensci.org/b7298178e4d5bb1d02a5f061c79cccaa5865b7ed4420ccb93e7eef55dc4e27ed",
      "status": "success",
      "check": "OK",
      "buildurl": "https://github.com/r-universe/shikhartyagi/actions/runs/36316646605"
    },
    {
      "r": "4.6.1",
      "os": "win",
      "version": "0.1.0",
      "date": "2026-09-27T11:48:25.000Z",
      "commit": "238c54ce6fa41d40d88ed7d77202e7ec42cd01c9",
      "fileid": "https://r2.ropensci.org/c6408a271bd85475c5b38d9453eed491ffd684f4ce1bbde0d485f9eac5e5d38b",
      "status": "success",
      "check": "OK",
      "buildurl": "https://github.com/r-universe/shikhartyagi/actions/runs/36316646605"
    }
  ]
}