Importance Sampling Inference for Censored Univariate Data

Distribution-independent framework for importance-sampling inference with univariate observations subject to censoring or truncation. Users provide probability functions and a proposal over model parameters. Constructs observed-data likelihood contributions, computes numerically stable importance weights, and supplies posterior, likelihood, predictive, diagnostic, and model-comparison summaries. Covers complete, right, left, interval, Type-I, Type-II, progressive Type-II, first-failure, progressive first-failure, doubly Type-II, middle-censored, and left/right-truncated data. Methods for importance sampling and censoring schemes are described in Geweke (1989) , Hesterberg (1995) , Robert and Casella (2004, ISBN:978-0-387-21617-1), Kundu and Joarder (2006) , Banerjee and Kundu (2008) , Iyer, Jammalamadaka, and Kundu (2008) , Wu and Kus (2009) , Prajapati, Mitra, and Kundu (2019) , Mondal and Kundu (2020) , Balakrishnan and Aggarwala (2000, ISBN:980-1-4612-1334-5), Ding and Gui (2023) , Nagar, Kumar, and Krishna (2026) , Goel and Krishna (2026) , Yadav, Jaiswal, and Yadav (2026) , and Goel, Kumar, and Krishna (2026, "Estimation in power Lindley distributions using balanced joint progressively Type-II censored data").

UniIS

UniIS is a distribution-independent R package for importance-sampling inference with univariate complete, censored, and truncated data. Users supply the probability functions of a distribution and a proposal over its parameters; the package constructs the observed likelihood and all log-scale importance weights.

Implemented core

The initial release supports complete, left/right/interval-censored, Type-I, Type-II, progressive Type-II, first-failure, progressive first-failure, doubly Type-II, middle-censored, left-truncated, and right-truncated observations. It includes ordinary, self-normalized, defensive-mixture, and adaptive deterministic-mixture importance sampling, evidence estimation, ESS and weight diagnostics, S3 summaries, likelihood information criteria, predictive functionals, plotting, and generic simulation helpers. New schemes can be provided as a parser function returning exact values, censoring intervals, and truncation regions.

The package intentionally distinguishes implemented methods from planned extensions. Sequential Monte Carlo, bridge sampling, Pareto-smoothed weights, and specialised joint/hybrid censoring likelihoods belong to future releases, where their methods can be documented and validated rather than silently approximated by a different design.

Example

library(UniIS)

set.seed(2026)
x <- rexp(100, rate = 1.5)
fit <- is_fit(
  data = x,
  pdf = function(x, theta) dexp(x, rate = exp(theta[1])),
  cdf = function(x, theta) pexp(x, rate = exp(theta[1])),
  survival = function(x, theta) pexp(x, rate = exp(theta[1]), lower.tail = FALSE),
  theta0 = c(log_rate = log(1)),
  proposal = is_proposal_normal(log(1), 0.75),
  scheme = "complete",
  control = is_control(n_draws = 5000, method = "adaptive")
)

summary(fit)
exp(coef(fit))
is_predictive(fit, c(0.5, 1), "survival")

For a positive parameter, sampling its logarithm as above avoids invalid proposal draws. Include the relevant Jacobian in a prior or proposal density when you use a custom transformed parameterisation.