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Statistical inference for competing risks model with Type-II generalized hybrid censored of inverse Lomax distribution with applications

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ALEXANDRIA ENGINEERING JOURNAL 2025年 118卷 132-146页

作者： Ahmed, Samah M. Abdalla, Mohamed Farghal, Al-Wageh A. Sohag Univ Fac Sci Dept Math Sohag 82524 Egypt King Khalid Univ Coll Sci Math Dept Abha Saudi Arabia

This article considered statistical inference based on independent competing risks data from inverse Lomax (ILo) distribution using Type-II generalized hybrid censored dataset. Time-to-failure under many causes of failure, which might be dependent or independent, defines the competing risks model. The situation of independent observed reasons of failure competing risks model is the main topic of this work. With Type- II generalized hybrid censored competing risks, the maximum likelihood estimates (MLE) of the unknown model parameters and the life parameters (reliability and hazard rate functions) are derived using the Newton- Raphson method, and the bootstrap approach is studied. By utilizing the MLEs' asymptotic normality property and the observed Fisher information matrix, approximate confidence intervals are created. Bayes estimates and highest posterior density (HPD) credible interval also are calculated under gamma prior distribution with the application of the Markov chain Monte Carlo (MCMC) approach yields both loss functions that are symmetric and asymmetric. Furthermore, a Monte Carlo simulation is run to evaluate the efficacy of the proposed methods. A set of real-world data is examined to illustrate the feasibility and suitability of the proposed methods.

关键词： Competing risks model Inverse Lomax distribution Bayesian inference The symmetric and asymmetric loss functions metropolis-hastings algorithm Maximum likelihood estimation Bootstrap method Type-II generalized hybrid censored

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Inference on inverted exponentiated Rayleigh data from accelerated life testing with hybrid censoring

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QUALITY TECHNOLOGY AND QUANTITATIVE MANAGEMENT 2025年

作者： Yadav, Priya Kumar, Devendra Singh, Sukhdev Cent Univ Haryana Dept Stat Mahendragarh India Univ Delhi Fac Math Sci Dept Stat Delhi India Thapar Inst Engn & Technol Dept Math Patiala India

This paper addresses the problem of estimating unknown parameters of the inverted exponentiated Rayleigh distribution within the context of accelerated life testing. We consider lifetime data observed through step-stress and type-I hybrid censoring, and incorporate the cumulative exposure model assumptions to establish connections between the distribution at various stress levels. We then write the associated likelihood function based on the observed data and derive maximum likelihood estimators for the distribution's unknown parameters. Furthermore, employing a Bayesian approach, we initially adopt gamma priors and compute posterior distributions for the parameters. These posterior distributions are then utilized to calculate Bayesian estimates using the squared error loss function. To assess the performance of maximum likelihood and Bayesian estimates, we conduct a simulation study under various scenarios, considering both non-informative and informative priors. We also evaluate interval estimates and coverage percentages under both classical and Bayesian approaches. Finally, for illustrative purposes, we analyze two real data sets, demonstrating the practical application of our proposed methodology.

关键词： Accelerated life testing cumulative exposure model Bayesian estimates hybrid censoring inverted exponentiated Rayleigh distribution metropolis-hastings algorithm

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Entropy-Based Burn-in Time Analysis and Ranking for (A)MCMC algorithms in High Dimension

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SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION 2025年第1期13卷 251-277页

作者： Chauveau, Didier Vandekerkhove, Pierre Univ Orleans Inst Denis Poisson UMR 7013 Inst Denis PoissonCNRS Rue Chartres F-45067 Orleans 2 France Univ Gustave Eiffel LAMA CNRS UMR 8050 5 Blvd Descartes F-77454 Marne La Vallee France

Many recent and often (adaptive) Markov chain Monte Carlo (A)MCMC methods are associated in practice to unknown rates of convergence. We propose a simulation-based methodology to estimate and compare MCMC's performance in terms of shortest burn-in time, using a Kullback divergence criterion requiring an estimate of the entropy of the algorithm densities at each iteration, computed from i.i.d. simulated chains. In previous works, we proved some consistency results in an MCMC setup for an entropy estimate based on Monte Carlo integration of a kernel density estimate proposed in [L. Gyo"\rfi and E. C. Van Der Meulen, An entropy estimate based on a kernel 1989, pp. 229--240], and we investigate an alternative nearest neighbor (NN) entropy estimate from [L. Kozachenko and N. N. Leonenko, Problemy Peredachi Informatsii, 23 (1987), pp. 9--16]. This estimate has been used mostly in univariate situations until recently, when entropy estimation in higher dimensions has been considered in other fields like neuroscience or system biology. Unfortunately, in higher dimensions, both estimators converge slowly with a noticeable bias. The present work goes several steps further, with bias reduction and automatic (A)MCMC burn-in time analysis in mind. First, for bias reduction, we apply in our situation a ``crossed NN-type"" nonparametric estimate of the Kullback divergence between two densities, based on i.i.d. samples from each, introduced by [Q. Wang, S. R. Kulkarni, and S. Verdu'\, A nearest-neighbor approach to estimating divergence between continuous random vectors, in IEEE International Symposium on Information Theory, Seattle, WA, 2006, pp. 242--246], [Q. Wang, S. R. Kulkarni, and S. Verdu'\, IEEE Trans. Inform. Theory, 55 (2009), pp. 2392-2405]. We prove the consistency of these entropy estimates under recent uniform control conditions, for the successive densities of a generic class of MCMC algorithm to which most of the methods proposed in the recent literature belong. Sec

关键词： adaptive MCMC algorithms Bayesian model entropy Kullback divergence metropolis-hastings algorithm nearest neighbor estimation nonparametric statistic

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metropolis-hastings algorithms with acceptance ratios of nearly 1

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 2009年第4期61卷 949-967页

作者： Kamatani, Kengo Univ Tokyo Grad Sch Math Sci Meguro Ku Tokyo 1530041 Japan

We develop the results on polynomial ergodicity of Markov chains and apply to the metropolis-hastings algorithms based on a Langevin diffusion. When a prescribed distribution p has heavy tails, the metropolis-hastings algorithms based on a Langevin diffusion do not converge to p at any geometric rate. However, those Langevin based algorithms behave like the diffusion itself in the tail area, and using this fact, we provide sufficient conditions of a polynomial rate convergence. By the feature in the tail area, our results can be applied to a large class of distributions to which p belongs. Then, we show that the convergence rate can be improved by a transformation. We also prove central limit theorems for those algorithms.

关键词： metropolis-hastings algorithm Polynomial ergodicity Langevin diffusion metropolis adjusted Langevin algorithm

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Bayesian analysis of competing risk models with high dimensional covariates with an application to adenocarcinoma survival data

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Communications in Statistics Case Studies Data Analysis and Applications 2025年第1期11卷 31-55页

作者： Ranjan, Rakesh Bhattacharjee, Atanu Sen, Rijji Upadhyay, S.K. DST-CIMS Banaras Hindu University Varanasi India Leicester Real World Evidence Unit Leicester Diabetes Centre University of Leicester Leicester United Kingdom Department of Statistics Behala College University of Calcutta Kolkata India Department of Statistics Banaras Hindu University Varanasi India

This paper analyses competing risk models with high dimensional covariates when the number of observations is comparatively quite small. This gives rise to a very typical situation where most statistical estimates become unstable and non-unique. Thus dimension reduction by carrying out variable selection becomes a very imperative part of the study. This is performed using both classical and Bayesian tools. Lifetimes under each risk is assumed to follow either the Weibull or the exponential distribution and a total of four models is formed using a combination of these risks. Bayesian analysis of the resulting four models are performed via Markov chain Monte Carlo methods. A real life application is provided for adenocarcinoma micro-array data. Finally, model selection is carried out using deviance information criterion. © 2025 Taylor & Francis Group, LLC.

关键词： adenocarcinoma Akaike information criterion competing risk deviance information criterion Genomic data least absolute shrinkage and selection operator metropolis-hastings algorithm Survival data

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Smoothed Langevin proposals in metropolis-hastings algorithms

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STATISTICS & PROBABILITY LETTERS 2000年第4期49卷 345-354页

作者： Skare, O Benth, FE Frigessi, A Norwegian Comp Ctr N-0314 Oslo Norway Aarhus Univ Ctr Math Phys & Stochast DK-8000 Aarhus C Denmark

The metropolis Adjusted Langevin algorithm (MALA) samples from complex multivariate densities pi. The proposal density is based on a discretized version of a Langevin diffusion, and is well defined only for continuously differentiable densities pi. We propose a modified MALA algorithm when this condition is not fulfilled or when pi has very rapid variations. The algorithm is illustrated on the Strauss model, for which two different classes of smoothing are proposed. In these examples smoothing gives advantages in terms of reduced asymptotic variance. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： Langevin diffusions Markov chain Monte Carlo metropolis-hastings algorithm Strauss model

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Variance reduction of estimators arising from metropolis-hastings algorithms

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STATISTICS AND COMPUTING 2013年第5期23卷 577-587页

作者： Iliopoulos, George Malefaki, Sonia Univ Piraeus Dept Stat & Insurance Sci Piraeus 18534 Greece Univ Patras Dept Engn Sci Patras 26500 Greece

The metropolis-hastings algorithm is one of the most basic and well-studied Markov chain Monte Carlo methods. It generates a Markov chain which has as limit distribution the target distribution by simulating observations from a different proposal distribution. A proposed value is accepted with some particular probability otherwise the previous value is repeated. As a consequence, the accepted values are repeated a positive number of times and thus any resulting ergodic mean is, in fact, a weighted average. It turns out that this weighted average is an importance sampling-type estimator with random weights. By the standard theory of importance sampling, replacement of these random weights by their (conditional) expectations leads to more efficient estimators. In this paper we study the estimator arising by replacing the random weights with certain estimators of their conditional expectations. We illustrate by simulations that it is often more efficient than the original estimator while in the case of the independence metropolis-hastings and for distributions with finite support we formally prove that it is even better than the "optimal" importance sampling estimator.

关键词： metropolis-hastings algorithm Importance sampling Weighted estimators Variance reduction

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Scaling limits for the transient phase of local metropolis-hastings algorithms

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 2005年第2期67卷 253-268页

作者： Christensen, OF Roberts, GO Rosenthal, JS Univ Lancaster Fylde Coll Dept Math & Stat Lancaster LA1 4YF England Aarhus Univ DK-8000 Aarhus C Denmark Univ Toronto Toronto ON Canada

The paper considers high dimensional metropolis and Langevin algorithms in their initial transient phase. In stationarity, these algorithms are well understood and it is now well known how to scale their proposal distribution variances. For the random-walk metropolis algorithm, convergence during the transient phase is extremely regular-to the extent that the algo-rithm's sample path actually resembles a deterministic trajectory. In contrast, the Langevin algorithm with variance scaled to be optimal for stationarity performs rather erratically. We give weak convergence results which explain both of these types of behaviour and practical guidance on implementation based on our theory.

关键词： Markov chain Monte Carlo methods metropolis-hastings algorithm transient phase weak convergence

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SIMPLE CONDITIONS FOR THE CONVERGENCE OF THE GIBBS SAMPLER AND metropolis-hastings algorithmS

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STOCHASTIC PROCESSES AND THEIR APPLICATIONS 1994年第2期49卷 207-216页

作者： ROBERTS, GO SMITH, AFM UNIV CAMBRIDGE CAMBRIDGEENGLAND UNIV LONDON IMPERIAL COLL SCI TECHNOL & MED LONDON SW7 2AZENGLAND

Markov chain Monte Carlo (MCMC) simulation methods are being used increasingly in statistical computation to explore and estimate features of likelihood surfaces and Bayesian posterior distributions. This paper presents simple conditions which ensure the convergence of two widely used versions of MCMC, the Gibbs sampler and metropolis-hastings algorithms.

关键词： MARKOV CHAIN MONTE-CARLO GIBBS SAMPLER metropolis-hastings algorithm STATISTICAL COMPUTATION ERGODICITY LOWER SEMICONTINUITY

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Optimal design of the Barker proposal and other locally balanced metropolis-hastings algorithms

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BIOMETRIKA 2023年第3期110卷 579-595页

作者： Vogrinc, Jure Livingstone, Samuel Zanella, Giacomo Univ Warwick Dept Stat Coventry CV4 7AL England UCL Dept Stat Sci Gower St London WC1E 6BT England Bocconi Univ Dept Decis Sci via Roentgen 1 I-20136 Milan Italy

We study the class of first-order locally balanced metropolis-hastings algorithms introduced in Livingstone & Zanella (2022). To choose a specific algorithm within the class, the user must select a balancing function g : R+ -> R+ satisfying g(t) = tg(1/t) and a noise distribution for the proposal increment. Popular choices within the class are the metropolis-adjusted Langevin algorithm and the recently introduced Barker proposal. We first establish a general limiting optimal acceptance rate of 57% and scaling of n(-1/3), as the dimension n tends to infinity among all members of the class under mild smoothness assumptions on g and when the target distribution for the algorithm is of product form. In particular, we obtain an explicit expression for the asymptotic efficiency of an arbitrary algorithm in the class, as measured by expected squared jumping distance. We then consider how to optimize this expression under various constraints. We derive an optimal choice of noise distribution for the Barker proposal, an optimal choice of balancing function under a Gaussian noise distribution, and an optimal choice of first-order locally balanced algorithm among the entire class, which turns out to depend on the specific target distribution. Numerical simulations confirm our theoretical findings, and in particular, show that a bimodal choice of noise distribution in the Barker proposal gives rise to a practical algorithm that is consistently more efficient than the original Gaussian version.

关键词： Barker proposal Locally balanced algorithm Markov chain Monte Carlo metropolis-hastings algorithm Optimal scaling

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