Australian & New Zealand Journal of Statistics最新文献_第7页

Global implicit function theorems and the online expectation–maximisation algorithm 全局隐函数定理和在线期望最大化算法

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2022-01-24 DOI: 10.1111/anzs.12356

Hien Duy Nguyen, Florence Forbes

{"title":"Global implicit function theorems and the online expectation–maximisation algorithm","authors":"Hien Duy Nguyen, Florence Forbes","doi":"10.1111/anzs.12356","DOIUrl":"10.1111/anzs.12356","url":null,"abstract":"The expectation–maximisation (EM) algorithm framework is an important tool for statistical computation. Due to the changing nature of data, online and mini‐batch variants of EM and EM‐like algorithms have become increasingly popular. The consistency of the estimator sequences that are produced by these EM variants often rely on an assumption regarding the continuous differentiability of a parameter update function. In many cases, the parameter update function is not in closed form and may only be defined implicitly, which makes the verification of the continuous differentiability property difficult. We demonstrate how a global implicit function theorem can be used to verify such properties in the cases of finite mixtures of distributions in the exponential family, and more generally, when the component‐specific distributions admit data augmentation schemes, within the exponential family. We then illustrate the use of such a theorem in the cases of mixtures of beta distributions, gamma distributions, fully visible Boltzmann machines and Student distributions. Via numerical simulations, we provide empirical evidence towards the consistency of the online EM algorithm parameter estimates in such cases.","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83582209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Sufficient dimension reduction for clustered data via finite mixture modelling 通过有限混合模型对聚类数据进行足够的降维

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2022-01-22 DOI: 10.1111/anzs.12349

F.K.C. Hui, L.H. Nghiem

{"title":"Sufficient dimension reduction for clustered data via finite mixture modelling","authors":"F.K.C. Hui, L.H. Nghiem","doi":"10.1111/anzs.12349","DOIUrl":"10.1111/anzs.12349","url":null,"abstract":"<div>\u0000 \u0000 <p>Sufficient dimension reduction (SDR) is an attractive approach to regression modelling. However, despite its rich literature and growing popularity in application, surprisingly little research has been done on how to perform SDR for clustered data, for example as is commonly arises in longitudinal studies. Indeed, current popular SDR methods have been mostly based on a marginal estimating equation approach. In this article, we propose a new approach to SDR for clustered data based on a combination of finite mixture modelling and mixed effects regression. Finite mixture models offer a flexible means of estimating the fixed effects central subspace, based on slicing the space up and probabilistically clustering observations to each slice (mixture component). Dimension reduction is achieved by having the mixing proportions vary only through the sufficient fixed effect predictors. We then incorporate random effects as a natural means of accounting for correlations within clusters. We employ a Monte Carlo expectation–maximisation algorithm to estimate the model parameters and fixed effects central subspace, and discuss methods for associated uncertainty quantification and prediction. Simulation studies demonstrate that our approach performs strongly against both estimating equation methods for estimating the fixed effects central subspace, and SDR methods which do not account for within-cluster correlation. Finally, we apply the proposed approach to a data set on air pollutant monitoring across 13 stations in the Eastern United States.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73971724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Bayesian credible intervals for population attributable risk from case–control, cohort and cross-sectional studies 来自病例对照、队列和横断面研究的人群归因风险的贝叶斯可信区间

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2022-01-17 DOI: 10.1111/anzs.12352

Sarah Pirikahu, Geoffrey Jones, Martin L. Hazelton

{"title":"Bayesian credible intervals for population attributable risk from case–control, cohort and cross-sectional studies","authors":"Sarah Pirikahu, Geoffrey Jones, Martin L. Hazelton","doi":"10.1111/anzs.12352","DOIUrl":"10.1111/anzs.12352","url":null,"abstract":"<div>\u0000 \u0000 <p>Population attributable risk (PAR) and population attributable fraction (PAF) are used in epidemiology to predict the impact of removing a risk factor from the population. Until recently, no standard approach for calculating confidence intervals or the variance for PAR in particular was available in the literature. Previously we outlined a fully Bayesian approach to provide credible intervals for the PAR and PAF from a cross-sectional study, where the data was presented in the form of a 2×2 table. However, extensions to cater for other frequently used study designs were not provided. In this paper we provide methodology to calculate credible intervals for the PAR and PAF for case–control and cohort studies. Additionally, we extend the cross-sectional example to allow for the incorporation of uncertainty that arises when an imperfect diagnostic test is used. In all these situations the model becomes over-parameterised, or non-identifiable, which can result in standard ‘off-the-shelf’ Markov Chain Monte Carlo (MCMC) updaters taking a long time to converge or even failing altogether. We adapt an importance sampling methodology to overcome this problem, and propose some novel MCMC samplers that take into consideration the shape of the posterior ridge to aid in the convergence of the Markov chain.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79829223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Measuring the values of cricket players 衡量板球运动员的价值

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2022-01-15 DOI: 10.1111/anzs.12353

Pranjal Chandrakar, Shubhabrata Das

{"title":"Measuring the values of cricket players","authors":"Pranjal Chandrakar, Shubhabrata Das","doi":"10.1111/anzs.12353","DOIUrl":"10.1111/anzs.12353","url":null,"abstract":"<div>\u0000 \u0000 <p>Sports franchises that participate in team sports can make better decisions regarding their players’ financial compensation, renewal of the contracts, bidding strategies during the auction, etc., if they can adequately assess the value or worth of their players. Evaluating the value of a player in a team sport is difficult because various team members play different roles. In this study, we resolve this by measuring the value of a player in terms of how his inclusion in the team affects the team's probability of winning. With this notion of value, we develop a technique to measure the worth of a cricket player for his franchise. To illustrate this technique, we evaluate the values of cricket players who play in the Indian Premier League. We also study the relationship between players’ values and their salaries. We find that a few popular players earn disproportionately more than others. This disproportionality in the income of popular players cannot be justified by their performance alone, as adjudged by their values in this work. We attribute the disproportionality in the income to the factors not captured via conventional yardsticks, including leadership or brand value.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74128017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Detection boundary for a sparse gamma scale mixture model 稀疏伽玛尺度混合模型的检测边界

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2022-01-11 DOI: 10.1111/anzs.12347

Michael I. Stewart

引用次数: 1

Odds-symmetry model for cumulative probabilities and decomposition of a conditional symmetry model in square contingency tables 平方列联表中累积概率的奇数-对称模型及条件对称模型的分解

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-12-06 DOI: 10.1111/anzs.12346

Shuji Ando

{"title":"Odds-symmetry model for cumulative probabilities and decomposition of a conditional symmetry model in square contingency tables","authors":"Shuji Ando","doi":"10.1111/anzs.12346","DOIUrl":"10.1111/anzs.12346","url":null,"abstract":"<div>\u0000 \u0000 <p>For the analysis of square contingency tables, it is necessary to estimate an unknown distribution with high confidence from an obtained observation. For that purpose, we need to introduce a statistical model that fits the data well and has parsimony. This study proposes asymmetry models based on cumulative probabilities for square contingency tables with the same row and column ordinal classifications. In the proposed models, the odds, for all <i>i</i><<i>j</i>, that an observation will fall in row category <i>i</i> or below, and column category <i>j</i> or above, instead of row category <i>j</i> or above, and column category <i>i</i> or below, depend on only row category <i>i</i> or column category <i>j</i>. This is notwithstanding that the odds are constant without relying on row and column categories under the conditional symmetry (CS) model. The proposed models constantly hold when the CS model holds. However, the converse is not necessarily true. This study also shows that it is necessary to satisfy the extended marginal homogeneity model, in addition to the proposed models, to satisfy the CS model. These decomposition theorems explain why the CS model does not hold. The proposed models provide a better fit for application to a single data set of real-world occupational data for father-and-son dyads.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77244237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Proportional inverse Gaussian distribution: A new tool for analysing continuous proportional data 比例反高斯分布:分析连续比例数据的新工具

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-11-23 DOI: 10.1111/anzs.12345

Pengyi Liu, Guo-Liang Tian, Kam Chuen Yuen, Chi Zhang, Man-Lai Tang

{"title":"Proportional inverse Gaussian distribution: A new tool for analysing continuous proportional data","authors":"Pengyi Liu, Guo-Liang Tian, Kam Chuen Yuen, Chi Zhang, Man-Lai Tang","doi":"10.1111/anzs.12345","DOIUrl":"10.1111/anzs.12345","url":null,"abstract":"<div>\u0000 \u0000 <p>Outcomes in the form of rates, fractions, proportions and percentages often appear in various fields. Existing beta and simplex distributions are frequently unable to exhibit satisfactory performances in fitting such continuous data. This paper aims to develop the normalised inverse Gaussian (N-IG) distribution proposed by Lijoi, Mena & Prünster (2005, Journal of the American Statistical Association, <b>100</b>, 1278–1291) as a new tool for analysing continuous proportional data in (0,1) and renames the N-IG as proportional inverse Gaussian (PIG) distribution. Our main contributions include: (i) To overcome the difficulty of an integral in the PIG density function, we propose a novel minorisation–maximisation (MM) algorithm via the continuous version of Jensen's inequality to calculate the maximum likelihood estimates of the parameters in the PIG distribution; (ii) We also develop an MM algorithm aided by the gradient descent algorithm for the PIG regression model, which allows us to explore the relationship between a set of covariates with the mean parameter; (iii) Both the comparative studies and the real data analyses show that the PIG distribution is better when comparing with the beta and simplex distributions in terms of the AIC, the Cramér–von Mises and the Kolmogorov–Smirnov tests. In addition, bootstrap confidence intervals and testing hypothesis on the symmetry of the PIG density are also presented. Simulation studies are conducted and the hospital stay data of Barcelona in 1988 and 1990 are analysed to illustrate the proposed methods.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87974708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

BNPdensity: Bayesian nonparametric mixture modelling in R bnp密度:贝叶斯非参数混合建模

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-11-17 DOI: 10.1111/anzs.12342

J. Arbel, G. Kon Kam King, A. Lijoi, L. Nieto-Barajas, I. Prünster

{"title":"BNPdensity: Bayesian nonparametric mixture modelling in R","authors":"J. Arbel, G. Kon Kam King, A. Lijoi, L. Nieto-Barajas, I. Prünster","doi":"10.1111/anzs.12342","DOIUrl":"10.1111/anzs.12342","url":null,"abstract":"<div>\u0000 \u0000 <p>Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability distributions or infinite vectors. In the Bayesian nonparametric approach, prior distributions are designed for these parameters, which provide a handle to manage the complexity of nonparametric models in practice. However, most modern Bayesian nonparametric models seem often out of reach to practitioners, as inference algorithms need careful design to deal with the infinite number of parameters. The aim of this work is to facilitate the journey by providing computational tools for Bayesian nonparametric inference. The article describes a set of functions available in the <span>R</span> package <span>BNPdensity</span> in order to carry out density estimation with an infinite mixture model, including all types of censored data. The package provides access to a large class of such models based on normalised random measures, which represent a generalisation of the popular Dirichlet process mixture. One striking advantage of this generalisation is that it offers much more robust priors on the number of clusters than the Dirichlet. Another crucial advantage is the complete flexibility in specifying the prior for the scale and location parameters of the clusters, because conjugacy is not required. Inference is performed using a theoretically grounded approximate sampling methodology known as the Ferguson & Klass algorithm. The package also offers several goodness-of-fit diagnostics such as QQ plots, including a cross-validation criterion, the conditional predictive ordinate. The proposed methodology is illustrated on a classical ecological risk assessment method called the species sensitivity distribution problem, showcasing the benefits of the Bayesian nonparametric framework.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90676545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Experimental design in practice: The importance of blocking and treatment structures 实践中的实验设计:阻塞和处理结构的重要性

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-11-08 DOI: 10.1111/anzs.12343

E.R. Williams, C.G. Forde, J. Imaki, K. Oelkers

引用次数: 1

Accelerating adaptation in the adaptive Metropolis–Hastings random walk algorithm 自适应Metropolis-Hastings随机漫步算法中的加速自适应

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-11-03 DOI: 10.1111/anzs.12344

Simon E.F. Spencer

引用次数: 6