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Bayesian non-parametric inference for Λ-coalescents: Posterior consistency and a parametric method

BERNOULLI 2018年第3期24卷 2122-2153页

作者： Koskela, Jere Jenkins, Paul A. Spano, Dario Tech Univ Berlin Inst Math Str 17 Juni 136 D-10623 Berlin Germany Univ Warwick Dept Stat Coventry CV4 7AL W Midlands England Univ Warwick Dept Comp Sci Coventry CV4 7AL W Midlands England

We investigate Bayesian non-parametric inference of the Lambda-measure of Lambda-coalescent processes with recurrent mutation, parametrised by probability measures on the unit interval. We give verifiable criteria on the prior for posterior consistency when observations form a time series, and prove that any non-trivial prior is inconsistent when all observations are contemporaneous. We then show that the likelihood given a data set of size n is an element of N is constant across Lambda-measures whose leading n - 2 moments agree, and focus on inferring truncated sequences of moments. We provide a large class of functionals which can be extremised using finite computation given a credible region of posterior truncated moment sequences, and a pseudo-marginal Metropolis-Hastings algorithm for sampling the posterior. Finally, we compare the efficiency of the exact and noisy pseudo-marginal algorithms with and without delayed acceptance acceleration using a simulation study.

关键词： Dirichlet mixture model prior Lambda-coalescent non-parametric inference posterior consistency pseudo-marginal MCMC

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non-parametric Bayesian inference of strategies in repeated games

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ECONOMETRICS JOURNAL 2018年第3期21卷 298-315页

作者： Kleiman-Weiner, Max Tenenbaum, Joshua B. Zhou, Penghui MIT Brain & Cognit Sci 77 Massachusetts Ave Cambridge MA 02139 USA MIT Dept Econ 77 Massachusetts Ave Cambridge MA 02139 USA

Inferring underlying cooperative and competitive strategies from human behaviour in repeated games is important for accurately characterizing human behaviour and understanding how people reason strategically. Finite automata, a bounded model of computation, have been extensively used to compactly represent strategies for these games and are a standard tool in game theoretic analyses. However, inference over these strategies in repeated games is challenging since the number of possible strategies grows exponentially with the number of repetitions yet behavioural data are often sparse and noisy. As a result, previous approaches start by specifying a finite hypothesis space of automata that does not allow for flexibility. This limitation hinders the discovery of novel strategies that may be used by humans but are not anticipated a priori by current theory. Here we present a new probabilistic model for strategy inference in repeated games by exploiting non-parametric Bayesian modelling. With simulated data, we show that the model is effective at inferring the true strategy rapidly and from limited data, which leads to accurate predictions of future behaviour. When applied to experimental data of human behaviour in a repeated prisoner's dilemma, we uncover strategies of varying complexity and diversity.

关键词： Bayesian inference Computational economics Finite-state automata non-parametric inference Repeated games

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A New Evaluation Strategy for Diagnostic Tests Under Umbrella or Tree Ordering

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INTERNATIONAL STATISTICAL REVIEW 2025年第0期

作者： To, Duc-Khanh Adimari, Gianfranco Chiogna, Monica Univ Sci Fac Math & Comp Sci Ho Chi Minh City Vietnam Vietnam Natl Univ Ho Chi Minh City Vietnam Univ Padua Dept Cardiac Thorac & Vasc Sci & Publ Hlth Unit Biostat Epidemiol & Publ Hlth Padua Italy Univ Bologna Dept Stat Sci Paolo Fortunati Bologna Italy

In medical research, diagnostic tests (or biomarkers) with continuous values are widely employed to attempt to distinguish between diseased and non-diseased subjects. The diagnostic accuracy of a test can be assessed by its receiver operating characteristic (ROC) curve. For diseases with multiclasses, an important category of scenarios assumes tree or umbrella ordering, where the test measurement for one particular class is lower or higher than those for the other classes. In this paper, we propose a new ROC framework for tree or umbrella ordering, together with a related evaluation strategy. Such a strategy is based on new ROC representations on the plane, denoted as LTROC and UTROC, and new summary indexes. Related statistical inference is also discussed. In particular, we propose simple estimation and interval estimation procedures, in a nonparametric setting. For these procedures, we provide theoretical justification and assess the behaviour in finite samples through simulation experiments. Finally, we illustrate the proposed approach with two real data examples.

关键词： empirical likelihood non-parametric inference overlapping area ROC analysis sensitivity specificity

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A novel lifetime analysis of repairable systems via Daubechies wavelets

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ANNALS OF OPERATIONS RESEARCH 2025年第1期349卷 287-314页

作者： Wu, Jingchi Dohi, Tadashi Okamura, Hiroyuki Hiroshima Univ Grad Sch Adv Sci & Engn 1-4-1 Kagamiyama Higashihiroshima Hiroshima 7398527 Japan

It is well-known that minimally repaired systems are characterized by non-homogeneous Poisson processes. When the underlying lifetime distribution function or its associated intensity function is completely known, the statistical inference of the cumulative number of failures/repairs is made through some standard techniques. On the other hand, when the parametric form of the lifetime distribution or the intensity function is not known, non-parametric inference techniques such as non-parametric maximum likelihood estimate (NPMLE) and kernel-based estimates are employed. Since these techniques are based on the underlying lifetime data, the resulting estimates of the cumulative number of failures/repairs with respect to the system operation time are discontinuous and troublesome in assessing the reliability measures such as reliability function and mean time to failure, etc. In this paper, we propose a novel lifetime analysis of the repairable systems via Daubechies wavelets. More specifically, we generalize the seminal Daubechies wavelet estimate by Kuhl and Bhairgond (Winter Simul Conf Proc 1:562-571, 2000) by combining the ideas on NPMLE and KMBs. In both simulation experiments and real data analyses, we investigate applicability of our Daubechies wavelet-based approaches and compare them with the conventional non-parametric methods.

关键词： Repairable systems non-homogeneous poisson processes non-parametric inference Daubechies wavelets Simulation experiments Real data analyses

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Improved semi-parametric inference for a mixture model of responses from a control versus treatment group trial

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STATISTICAL METHODS IN MEDICAL RESEARCH 2024年第3期33卷 515-531页

作者： Lubich, Bradley Jeske, Daniel R. Univ Calif Riverside Dept Stat Riverside CA USA Univ Calif Riverside Dept Stat Olmsted Hall900 Univ Ave Riverside CA 92521 USA

The mixture of a distribution of responses from untreated patients and a shift of that distribution is a useful model for the responses from a group of treated patients. The mixture model accounts for the fact that not all the patients in the treated group will respond to the treatment and consequently their responses follow the same distribution as the responses from untreated patients. The treatment effect in this context consists of both the fraction of the treated patients that are responders and the magnitude of the shift in the distribution for the responders. In this article, we introduce inference based on a pseudo-likelihood approach and compare it with an existing method of moment approach. An extensive simulation study is used to compare robust performance of the two approaches regarding point estimation, confidence regions, and confidence intervals. The methods are demonstrated on an illustrative blood pressure data set.

关键词： Randomized clinical trial mixture model responders non-parametric inference treatment effect pseudo-likelihood

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Modeling 3D NAND Flash with nonparametric inference on Regression Coefficients for Reliable Solid-State Storage

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FUTURE INTERNET 2023年第10期15卷 319-319页

作者： Borghesi, Michela Zambelli, Cristian Micheloni, Rino Bonnini, Stefano Univ Ferrara Dept Econ & Management I-44121 Ferrara Italy Univ Ferrara Dept Engn I-44122 Ferrara Italy Avaneidi Srl I-21047 Saronno Italy

Solid-state drives represent the preferred backbone storage solution thanks to their low latency and high throughput capabilities compared to mechanical hard disk drives. The performance of a drive is intertwined with the reliability of the memories;hence, modeling their reliability is an important task to be performed as a support for storage system designers. In the literature, storage developers devise dedicated parametric statistical approaches to model the evolution of the memory's error distribution through well-known statistical frameworks. Some of these well-founded reliability models have a deep connection with the 3D NAND flash technology. In fact, the more precise and accurate the model, the less the probability of incurring storage performance slowdowns. In this work, to avoid some limitations of the parametric methods, a non-parametric approach to test the model goodness-of-fit based on combined permutation tests is carried out. The results show that the electrical characterization of different memory blocks and pages tested provides an FBC feature that can be well-modeled using a multiple regression analysis.

关键词： non-parametric inference goodness-of-fit 3D NAND flash reliability

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One-shot device test data analysis using non-parametric and semi-parametric inferential methods and applications

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2022年第0期221卷 108319-108319页

作者： Zhu, Xiaojun Balakrishnan, N. Xian Jiaotong Liverpool Univ Dept Financial & Actuarial Math Suzhou 215123 Peoples R China McMaster Univ Dept Math & Stat Hamilton ON L8S 4K1 Canada

A one-shot device, such as an automobile airbag, electro-explosive unit or munition, is a product that can be used only once. Its actual lifetime is unobservable, rendering the corresponding reliability analysis quite challenging. In this paper, two non-parametric methodologies-maximum likelihood estimation via EM-algorithm and Nelson-Aalen based estimation are developed for identical testing environment on one-shot devices. The EM-algorithm is usually used for unobserved failure times under some specific parametric models. But, here the EM-algorithm is adopted for the number of failures in each time interval in a nonparametric manner. Next, a semi-parametric approach, based on proportional hazards assumption, is developed for nonidentical testing environments, such as under an accelerated life-test. A Monte Carlo simulation study is then carried out for evaluating the performance of the inferential methods developed here. Finally, two data sets are analyzed for illustrative purpose.

关键词： Accelerated life-test Expectation-Maximization algorithm Kaplan-Meier estimator Nelson-Aalen estimator non-parametric inference One-shot device test Proportional hazards model Semi-parametric inference

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Using ranked set sampling with binary outcomes in cluster randomized designs

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 2020年第3期48卷 342-365页

作者： Wang, Xinlei Wang, Mumu Lim, Johan Ahn, Soohyun Southern Methodist Univ Dept Stat Sci Dallas TX 75205 USA Seoul Natl Univ Dept Stat Seoul South Korea Ajou Univ Dept Math Suwon South Korea

We study the use of ranked set sampling (RSS) with binary outcomes in cluster-randomized designs (CRDs), where a generalized linear mixed model (GLMM) is used to model the hierarchical data structure involved. Under the GLMM-based framework, we propose three different approaches to estimate the treatment effect, including the non-parametric (NP), maximum likelihood (ML) and pseudo likelihood (PL) estimators. We investigate their asymptotic properties and examine their finite-sample performance via simulation. Based on these three RSS estimators, we further develop procedures for testing the existence of the treatment effect. We examine the power and size of our proposed RSS tests and compare them with existing tests based on simple random sampling (SRS). All the proposed RSS estimation and test methods are illustrated with two data examples, one for rare events and the other for non-extreme events. Throughout our investigations, we also consider the possible effect of imperfect ranking. Among the proposed methods, we provide recommendations on whether to use RSS rather than SRS with binary outcomes in CRDs and, if yes, when to use which RSS method. The Canadian Journal of Statistics;2019 (c) 2019 Statistical Society of Canada

关键词： Generalized linear mixed model likelihood inference non-parametric inference order statistics ranking error

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Application of Multivariate-Rank-Based Techniques in Clustering of Big Data

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Vikalpa 2018年第4期43卷 179-190页

作者： Guha, Pritha Institute of Management Nirma University India

Very large or complex data sets, which are difficult to process or analyse using traditional data handling techniques, are usually referred to as big data. The idea of big data is characterized by the three ‘v’s which are volume, velocity, and variety (Liu, McGree, Ge, & Xie, 2015) referring respectively to the volume of data, the velocity at which the data are processed and the wide varieties in which big data are available. Every single day, different sectors such as credit risk management, healthcare, media, retail, retail banking, climate prediction, DNA analysis and, sports generate petabytes of data (1 petabyte = 250 bytes). Even basic handling of big data, therefore, poses significant challenges, one of them being organizing the data in such a way that it can give better insights into analysing and decision-making. With the explosion of data in our life, it has become very important to use statistical tools to analyse them. © 2018 Indian Institute of Management, Ahmedabad.

关键词： Big Data Cluster Analysis Data Depth non-parametric inference Spatial Rank Function

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Wavelet estimation for derivative of a density in a GARCH-type model

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2017年第5期46卷 2396-2410页

作者： Rao, B. L. S. Prakasa CR Rao Adv Inst Math Stat & Comp Sci Univ Hyderabad Campus Hyderabad 500046 Telengana India

We consider the GARCH-type model S = sigma(2)Z where sigma(2) and Z are independent random variables. We assume that the density f(sigma 2) of sigma(2) is unknown with support [0, 1] but differentiable whereas the density f(S) of S is bounded. We will also assume that the probability density function of the random variable Z is known and has the same distribution as the.-fold product of independent random variables uniformly distributed on the interval [0, 1]. We want to estimate the derivative of the density of sigma(2) from n independent and identically distributed observations of S. We will construct adaptive and non adaptive wavelet estimators for the derivative of the density and obtain sharp upper bounds on their mean integrated squared errors.

关键词： Derivative of density estimation GARCH-type model Mean integrated squared error non-parametric inference Upper bound Wavelets

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