arXiv subjects

Junshan Shen

Publications and source records attributed to Junshan Shen.

4 recordsLinked to original sources

arXiv2025

On MCMC mixing for predictive inference under unidentified transformation models

Reliable Bayesian predictive inference has long been an open problem under unidentified transformation models, since the Markov Chain Monte Carlo (MCMC) chains of posterior predictive distribution (PPD) values are generally poorly mixed. We address the poorly mixed PPD value chains under unidentified transformation models through an adaptive scheme for prior adjustment. Specifically, we originate a conception of sufficient informativeness, which explicitly quantifies the information level provided by nonparametric priors, and assesses MCMC mixing by comparison with the within-chain MCMC variance. We formulate the prior information level by a set of hyperparameters induced from the nonparametric prior elicitation with an analytic expression, which is guaranteed by asymptotic theory for the posterior variance under unidentified transformation models. The analytic prior information level consequently drives a hyperparameter tuning procedure to achieve MCMC mixing. The proposed method is general enough to cover various data domains through a multiplicative error working model. Comprehensive simulations and real-world data analysis demonstrate that our method successfully achieves MCMC mixing and outperforms state-of-the-art competitors in predictive capability.

stat.ME↗

arXiv2023

Bayesian prediction via nonparametric transformation models

This article tackles the old problem of prediction via a nonparametric transformation model (NTM) in a new Bayesian way. Estimation of NTMs is known challenging due to model unidentifiability though appealing because of its robust prediction capability in survival analysis. Inspired by the uniqueness of the posterior predictive distribution, we achieve efficient prediction via the NTM aforementioned under the Bayesian paradigm. Our strategy is to assign weakly informative priors to nonparametric components rather than identify the model by adding complicated constraints in the existing literature. The Bayesian success pays tribute to i) a subtle cast of NTMs by an exponential transformation for the purpose of compressing spaces of infinite-dimensional parameters to positive quadrants considering non-negativity of the failure time; ii) a newly constructed weakly informative quantile-knots I-splines prior for the recast transformation function together with the Dirichlet process mixture model assigned to the error distribution. In addition, we provide a convenient and precise estimator for the identified parameter component subject to the general unit-norm restriction through posterior modification, enabling effective relative risks. Simulations and applications on real datasets reveal that our method is robust and outperforms the competing methods. An R package BuLTM is available to predict survival curves, estimate relative risks, and facilitate posterior checking.

stat.ME↗

arXiv2021

Dependent Dirichlet Processes for Analysis of a Generalized Shared Frailty Model

Bayesian paradigm takes advantage of well fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this chapter, we aim to display the latest tendency in Bayesian computing, in the sense of automating the posterior sampling, through Bayesian analysis of survival modeling for multivariate survival outcomes with complicated data structure. Motivated by relaxing the strong assumption of proportionality and the restriction of a common baseline population, we propose a generalized shared frailty model which includes both parametric and nonparametric frailty random effects so as to incorporate both treatment-wise and temporal variation for multiple events. We develop a survival-function version of ANOVA dependent Dirichlet process to model the dependency among the baseline survival functions. The posterior sampling is implemented by the No-U-Turn sampler in Stan, a contemporary Bayesian computing tool, automatically. The proposed model is validated by analysis of the bladder cancer recurrences data. The estimation is consistent with existing results. Our model and Bayesian inference provide evidence that the Bayesian paradigm fosters complex modeling and feasible computing in survival analysis and Stan relaxes the posterior inference.

stat.ME↗

arXiv2012

Empirical Likelihood for Right Censored Lifetime Data

This paper considers the empirical likelihood (EL) construction of confidence intervals for a linear functional based on right censored lifetime data. Many of the results in literature show that log EL has a limiting scaled chi-square distribution, where the scale parameter is a function of the unknown asymptotic variance. The scale parameter has to be estimated for the construction. Additional estimation would reduce the coverage accuracy for the parameter. This diminishes a main advantage of the EL method for censored data. By utilizing certain influence functions in an estimating equation, it is shown that under very general conditions, log EL converges weakly to a standard chi-square distribution and thereby eliminates the need for estimating the scale parameter. Moreover, a special way of employing influence functions eases the otherwise very demanding computations of the EL method. Our approach yields smaller asymptotic variance of the influence function than those comparable ones considered by Wang and Jing (2001) and Qin and Zhao (2007). Thus it is not surprising that confidence intervals using influence functions give a better coverage accuracy as demonstrated by simulations.

math.ST↗