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Bayesian survival analysis for adaptive Type-II progressive hybrid censored Hjorth data

COMPUTATIONAL STATISTICS 2021年第3期36卷 1965-1990页

作者： Elshahhat, Ahmed Nassar, Mazen Zagazig Univ Fac Technol & Dev Dept Accounting & Quantitat Informat Syst Zagazig Egypt King Abdulaziz Univ Fac Sci Dept Stat Jeddah Saudi Arabia

Adaptive Type-II progressive hybrid censoring scheme has been proposed to increase the efficiency of statistical analysis and save the total test time on a life-testing experiment. This article deals with the problem of estimating the parameters, survival and hazard rate functions of the two-parameter Hjorth distribution under adaptive Type-II progressive hybrid censoring scheme using maximum likelihood and Bayesian approaches. The two-sided approximate confidence intervals of the unknown quantities are constructed. Under the assumption of independent gamma priors, the Bayes estimators are obtained using squared error loss function. Since the Bayes estimators cannot be expressed in closed forms, Lindley's approximation and Markov chain Monte Carlo methods are considered and the highest posterior density credible intervals are also obtained. To study the behavior of the various estimators, a Monte Carlo simulation study is performed. The performances of the different estimators have been compared on the basis of their average root mean squared error and relative absolute bias. Finally, to show the applicability of the proposed estimators a data set of industrial devices has been analyzed.

关键词： Adaptive Type-II progressive hybrid censoring scheme Bayes estimator metropolis-hasting algorithm Hjorth distribution Lindley’ s approximation method Maximum likelihood estimator Reliability characteristics

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Weighted polynomial models and weighted sampling schemes for finite population

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ANNALS OF STATISTICS 1998年第5期26卷 1894-1915页

作者： Chen, SX NYU Stern Sch Business New York NY 10012 USA

This paper outlines a theoretical framework for finite population models with unequal sample probabilities, along with sampling schemes for drawing random samples from these models. We first present four exact weighted sampling schemes that can be used for any finite population model to satisfy such requirements as ordered/unordered samples, with/without replacement, and fixed/nonfixed sample size. We then introduce a new class of finite population models called weighted polynomial models or, in short, WPM. The probability density of a WPM is defined through a symmetric polynomial of the weights of the units in the sample. The WPM is shown to have been applied in many statistical analyses including survey sampling, logistic regression, case-control studies, lottery, DNA sequence alignment and MCMC simulations. We provide general strategies that can help improve the efficiency of the exact weighted sampling schemes for any given WPM. We show that under a mild condition, sampling from any WPM can be implemented within polynomial time. A metropolis-hasting-type scheme is proposed for approximate weighted sampling when the exact sampling schemes become intractable for moderate population and sample sizes. We show that under a mild condition, the average acceptance rate of the approximate sampling scheme for any WPM can be expressed in closed form using only the inclusion probabilities.

关键词： finite population metropolis-hasting algorithm polynomial theory survey sampling weighted sampling

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Bayesian marginal inference via candidate's formula

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STATISTICS AND COMPUTING 2004年第1期14卷 59-66页

作者： Hsiao, CK Huang, SY Chang, CW Natl Taiwan Univ Inst Epidemiol Div Biostat Taipei 100 Taiwan Acad Sinica Inst Stat Sci Taipei 115 Taiwan Natl Hlth Res Inst Div Biostat & Bioinformat Taipei 115 Taiwan

Computing marginal probabilities is an important and fundamental issue in Bayesian inference. We present a simple method which arises from a likelihood identity for computation. The likelihood identity, called Candidate's formula, sets the marginal probability as a ratio of the prior likelihood to the posterior density. Based on Markov chain Monte Carlo output simulated from the posterior distribution, a nonparametric kernel estimate is used to estimate the posterior density contained in that ratio. This derived nonparametric Candidate's estimate requires only one evaluation of the posterior density estimate at a point. The optimal point for such evaluation can be chosen to minimize the expected mean square relative error. The results show that the best point is not necessarily the posterior mode, but rather a point compromising between high density and low Hessian. For high dimensional problems, we introduce a variance reduction approach to ease the tension caused by data sparseness. A simulation study is presented.

关键词： Bayes factor Gibbs sampler kernel density estimation marginal likelihood marginal likelihood identity Markov chain Monte Carlo metropolis-hasting algorithm

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On a logistic regression model with random intercept: diagnostic analytics, simulation and biological application

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2020年第13期90卷 2354-2383页

作者： Tapia, Alejandra Leiva, Victor Galea, Manuel Werneck, Rachel Univ Catolica Maule Fac Basic Sci Curico Chile Pontificia Univ Catolica Valparaiso Sch Ind Engn Valparaiso Chile Pontificia Univ Catolica Chile Dept Stat Santiago Chile Univ Sao Paulo Inst Biosci Postgrad Program Ecol Sao Paulo Brazil Zool Res Museum Alexander Koenig Bonn Germany

This article proposes a methodology for diagnostics in a logistic regression with random intercept motivated by a biological study. The methodology includes local and global influence techniques allowing us to contrast the results of both types of influence. The proposed methodology is applied to a case study with real data to show its potential. This study corresponds to the reproduction of arachnids reporting how the local and global influence of atypical observations can modify the significance of parameters, and then the biological conclusions. The model fitting is evaluated through predictive indicators. The methodology is summarized in an algorithm and a demo example is implemented inRcode to facilitate its application. To evaluate the performance of the methodology, Monte Carlo simulations are conducted.

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Identifiability of PBPK models with applications to dimethylarsinic acid exposure

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JOURNAL OF PHARMACOKINETICS AND PHARMACODYNAMICS 2015年第6期42卷 591-609页

作者： Garcia, Ramon I. Ibrahim, Joseph G. Wambaugh, John F. Kenyon, Elaina M. Setzer, R. Woodrow Univ N Carolina Dept Biostat Chapel Hill NC 27599 USA US EPA Natl Hlth & Environm Effects Lab Res Triangle Pk NC 27711 USA US EPA Natl Ctr Computat Toxicol Res Triangle Pk NC 27711 USA

Any statistical model should be identifiable in order for estimates and tests using it to be meaningful. We consider statistical analysis of physiologically-based pharmacokinetic (PBPK) models in which parameters cannot be estimated precisely from available data, and discuss different types of identifiability that occur in PBPK models and give reasons why they occur. We particularly focus on how the mathematical structure of a PBPK model and lack of appropriate data can lead to statistical models in which it is impossible to estimate at least some parameters precisely. Methods are reviewed which can determine whether a purely linear PBPK model is globally identifiable. We propose a theorem which determines when identifiability at a set of finite and specific values of the mathematical PBPK model (global discete identifiability) implies identifiability of the statistical model. However, we are unable to establish conditions that imply global discrete identifiability, and conclude that the only safe approach to analysis of PBPK models involves Bayesian analysis with truncated priors. Finally, computational issues regarding posterior simulations of PBPK models are discussed. The methodology is very general and can be applied to numerous PBPK models which can be expressed as linear time-invariant systems. A real data set of a PBPK model for exposure to dimethyl arsinic acid (DMA(V)) is presented to illustrate the proposed methodology.

关键词： PBPK Models Identifiability Gibbs sampling metropolis-hasting algorithm Dimethyl arsinic acid

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Estimation and prediction for Chen distribution with bathtub shape under progressive censoring

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2017年第2期87卷 348-366页

作者： Kayal, Tanmay Tripathi, Yogesh Mani Singh, Devendra Pratap Rastogi, Manoj Kumar Indian Inst Technol Patna Dept Math Patna Bihar India Natl Inst Pharmaceut Educ & Res Dept Biostat Hajipur India

We consider estimation of the unknown parameters of Chen distribution [Chen Z. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statist Probab Lett. 2000;49:155-161] with bathtub shape using progressive-censored samples. We obtain maximum likelihood estimates by making use of an expectation-maximization algorithm. Different Bayes estimates are derived under squared error and balanced squared error loss functions. It is observed that the associated posterior distribution appears in an intractable form. So we have used an approximation method to compute these estimates. A metropolis-hasting algorithm is also proposed and some more approximate Bayes estimates are obtained. Asymptotic confidence interval is constructed using observed Fisher information matrix. Bootstrap intervals are proposed as well. Sample generated from MH algorithm are further used in the construction of HPD intervals. Finally, we have obtained prediction intervals and estimates for future observations in one- and two-sample situations. A numerical study is conducted to compare the performance of proposed methods using simulations. Finally, we analyse real data sets for illustration purposes.

关键词： Bayesian estimation Bayesian prediction bootstrapping EM algorithm Fisherinformation matrix metropolis-hasting algorithm

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Seasonal fluctuations of photosynthetic parameters for light use efficiency models and the impacts on gross primary production estimation

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AGRICULTURAL AND FOREST METEOROLOGY 2017年 236卷 22-35页

作者： Lin, Xiaofeng Chen, Baozhang Chen, Jing Zhang, Huifang Sun, Shaobo Xu, Guang Guo, Lifeng Ge, Mengyu Qu, Junfeng Li, Lijuan Kong, Yawen Chinese Acad Sci Inst Geog Sci & Nat Resources Res State Key Lab Resources & Environm Informat Syst 11ADatun Rd Beijing 100101 Peoples R China Univ Chinese Acad Sci 19AYuquan Rd Beijing 100049 Peoples R China China Univ Min & Technol Sch Environm Sci & Spatial Informat Xuzhou 221116 Peoples R China Beijing Meteorol Bur Meteorol Informat Ctr Beijing 44 Zizhuyuan Rd Beijing 100089 Peoples R China China Univ Geosci Fac Earth Sci & Resources Beijing 100083 Peoples R China

How parameterization improves Light-use efficiency (LUE) models by taking into account the seasonal variations of the maximum LUE (epsilon(max)) has been rarely investigated. The LUE models include two categories which are the one-leaf LUE model (SL-LUE) and the two-leaf LUE model (TL-LUE) with separation of sunlit and shaded leaves (epsilon(msu) and epsilon(msh)). In this study, the SL-LUE and TL-LUE models were parameterized for 46 towers (176 site-years data) representing eighteen typical plant functional types (PFTs) by using the metropolis-hasting algorithm at monthly time scales. The results indicate that the maximum LUE parameters varied seasonally for most PFTs having a significant positive linear correlation with leaf area index (LAI) and ambient temperature changes. The relationships of epsilon(msu) and epsilon(msh) with epsilon(max) can be well described by linear equations, indicating the existence of general patterns across biomes. And as expected, The LUE models with the seasonal fluctuations of epsilon(max), epsilon(msu) and epsilon(msh) significantly improved GPP estimation except for needleleaf evergreen forests in mid- and low- latitude regions. The improvements of both the SL-WE and TL-LUE models were most significant in summer for tropical and Mediterranean climate regions, while most evident in spring and winter for temperate and boreal climate regions. Even with seasonal parameters, both the LUE models still cannot well capture GPP dynamics in cold season for some PFTs in Mediterranean and tropical regions (e.g., Tropical-BEF, C3-C4 grass). This study suggests that further improvement of modelling GPP requires taking into account seasonal variations of the key parameters. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Light use efficiency (LUE) models Seasonal variations of maximum LUE parameters Capacity of gross primary production metropolis-hasting algorithm Eddy covariance

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Studying convergence of Markov chain Monte Carlo algorithms using coupled sample paths

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 1996年第433期91卷 154-166页

作者： Johnson, VE Associate Professor Institute of Statistics and Decision Sciences Duke University Durham NC 27708

I describe a simple procedure for investigating the convergence properties of Markov chain Monte Carlo sampling schemes. The procedure uses coupled chains from the same sampler, obtained by using the same sequence of random deviates for each run. By examining the distribution of the iteration at which all sample paths couple, convergence properties for the system can be established. The procedure also provides a simple diagnostic for detecting modes in multimodal posteriors. Several examples of the procedure are provided. In Ising models, the relation between the correlation parameter and the convergence rate of rudimentary Gibbs samplers is investigated. In another example, the effects of multiple modes on the convergence of coupled paths are explored using mixtures of bivariate normal distributions. The technique is also used to evaluate the convergence properties of a Gibbs sampling scheme applied to a model for rat growth rates.

关键词： Bayesian inference Gibbs sampling metropolis-hasting algorithm quadrature

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A change-time hazard rate model and its goodness of fit

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2022年第4期13卷 1903-1912页

作者： Singh, Bhupendra Rathi, Shubhi Singh, Gajraj Gupta, Puneet Kumar CCS Univ Dept Stat Meerut Uttar Pradesh India ICFAI Univ ICFAI Business Sch Dehra Dun Uttarakhand India

The study presents the estimation of the location of the change in the hazard-rate function of the survival times of patients who continue to live after a major life-threatening medical operation. The real data set that acts as a backbone for the present work is the Stanford heart transplantation data. On studying and interpreting, the non-parametric hazard rate plot, and cumulative hazard curve of the data, a suitable hazard rate model is proposed. The parameters involved in the proposed model have been assessed by the classical and Bayesian methods estimation. The likelihood-ratio test has been conducted to test the validity of the change time point in the data.

关键词： Change-time hazard-rate model Cumulative hazard function Survival function metropolis-hasting algorithm Gibbs sample

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Inferences on Non-Identical Stress and Generalized Augmented Strength Reliability Parameters Under Informative Priors

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INTERNATIONAL JOURNAL OF RELIABILITY QUALITY AND SAFETY ENGINEERING 2020年第4期27卷

作者： Chandra, N. Rathaur, V. K. Ramanujan Sch Math Sci Dept Stat Pondicherry 605014 India Manipal Acad Higher Educ Dept Commerce Manipal 576104 Karnataka India

In this paper, an attempt has been made to estimate the augmented strength reliability of a system for the generalized case of Augmentation Strategy Plan (ASP) by assuming that the strength (X) and common stress (Y) are independently but not identically distributed as gamma distribution with parameters (alpha(1), lambda(1)) and (alpha(2), lambda(2)), respectively. ASP deals with two important challenges (i) early failures in a newly manufactured system while first and subsequent use and (ii) frequent failures of used system. ASP has a significant role in enhancing the strength of a weaker (or poor) system for failure-free journey to achieve its mission life. The maximum likelihood (ML) and Bayes estimation of augmented strength reliability are considered. In Bayesian context, the informative types of priors (Gamma and Inverted gamma) are chosen under symmetric and asymmetric loss functions for better comprehension purpose. A comparison between the ML and Bayes estimators of the augmented strength reliability is carried out on the basis of their mean square errors (mse's) and absolute biases by simulating Monte-Carlo samples from posterior distribution through metropolis Hosting approximation. Real life data sets are also considered for illustration purpose.

关键词： Stress-strength reliability augmentation MLE Bayesian estimators MCMC metropolis-hasting algorithm

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