Australian & New Zealand Journal of Statistics最新文献_第9页

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":"63 3","pages":"542-564"},"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

Variable selection using penalised likelihoods for point patterns on a linear network 使用惩罚似然对线性网络上的点模式进行变量选择

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-10-18 DOI: 10.1111/anzs.12341

Suman Rakshit, Greg McSwiggan, Gopalan Nair, Adrian Baddeley

{"title":"Variable selection using penalised likelihoods for point patterns on a linear network","authors":"Suman Rakshit, Greg McSwiggan, Gopalan Nair, Adrian Baddeley","doi":"10.1111/anzs.12341","DOIUrl":"10.1111/anzs.12341","url":null,"abstract":"<div>\u0000 \u0000 <p>Motivated by the analysis of a comprehensive database of road traffic accidents, we investigate methods of variable selection for spatial point process models on a linear network. The original data may include explanatory spatial covariates, such as road curvature, and ‘mark’ variables attributed to individual accidents, such as accident severity. The treatment of mark variables is new. Variable selection is applied to the canonical covariates, which may include spatial covariate effects, mark effects and mark-covariate interactions. We approximate the likelihood of the point process model by that of a generalised linear model, in such a way that spatial covariates and marks are both associated with canonical covariates. We impose a convex penalty on the log likelihood, principally the elastic-net penalty, and maximise the penalised loglikelihood by cyclic coordinate ascent. A simulation study compares the performances of the lasso, ridge regression and elastic-net methods of variable selection on their ability to select variables correctly, and on their bias and standard error. Standard techniques for selecting the regularisation parameter <i>γ</i> often yielded unsatisfactory results. We propose two new rules for selecting <i>γ</i> which are designed to have better performance. The methods are tested on a small dataset on crimes in a Chicago neighbourhood, and applied to a large dataset of road traffic accidents in Western Australia.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"63 3","pages":"417-454"},"PeriodicalIF":1.1,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90533201","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: 4

ECM algorithm for estimating vector ARMA model with variance gamma distribution and possible unbounded density 用ECM算法估计具有方差分布和可能无界密度的向量ARMA模型

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-10-18 DOI: 10.1111/anzs.12340

Thanakorn Nitithumbundit, Jennifer S.K. Chan

{"title":"ECM algorithm for estimating vector ARMA model with variance gamma distribution and possible unbounded density","authors":"Thanakorn Nitithumbundit, Jennifer S.K. Chan","doi":"10.1111/anzs.12340","DOIUrl":"https://doi.org/10.1111/anzs.12340","url":null,"abstract":"<div>\u0000 \u0000 <p>The simultaneous analysis of several financial time series is salient in portfolio setting and risk management. This paper proposes a novel alternating expectation conditional maximisation (AECM) algorithm to estimate the vector autoregressive moving average (VARMA) model with variance gamma (VG) error distribution in the multivariate skewed setting. We explain why the VARMA-VG model is suitable for high-frequency returns (HFRs) because VG distribution provides thick tails to capture the high kurtosis in the data and unbounded central density further captures the majority of near-zero HFRs. The distribution can also be expressed in normal-mean-variance mixtures to facilitate model implementation using the Bayesian or expectation maximisation (EM) approach. We adopt the EM approach to avoid the time-consuming Markov chain Monto Carlo sampling and solve the unbounded density problem in the classical maximum likelihood estimation. We conduct extensive simulation studies to evaluate the accuracy of the proposed AECM estimator and apply the models to analyse the dependency between two HFR series from the time zones that only differ by one hour.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"63 3","pages":"485-516"},"PeriodicalIF":1.1,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137538704","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

The Inverse G-Wishart distribution and variational message passing 逆G-Wishart分布与变分消息传递

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-10-07 DOI: 10.1111/anzs.12339

Luca Maestrini, Matt P. Wand

引用次数: 5

An adequacy approach for deciding the number of clusters for OTRIMLE robust Gaussian mixture-based clustering 基于OTRIMLE鲁棒高斯混合聚类的聚类数量决定的充分性方法

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-09-03 DOI: 10.1111/anzs.12338

Christian Hennig, Pietro Coretto

{"title":"An adequacy approach for deciding the number of clusters for OTRIMLE robust Gaussian mixture-based clustering","authors":"Christian Hennig, Pietro Coretto","doi":"10.1111/anzs.12338","DOIUrl":"10.1111/anzs.12338","url":null,"abstract":"<p>We introduce a new approach to deciding the number of clusters. The approach is applied to Optimally Tuned Robust Improper Maximum Likelihood Estimation (OTRIMLE; Coretto & Hennig, <i>Journal of the American Statistical Association</i> <b>111</b>, 1648–1659) of a Gaussian mixture model allowing for observations to be classified as ‘noise’, but it can be applied to other clustering methods as well. The quality of a clustering is assessed by a statistic <i>Q</i> that measures how close the within-cluster distributions are to elliptical unimodal distributions that have the only mode in the mean. This non-parametric measure allows for non-Gaussian clusters as long as they have a good quality according to <i>Q</i>. The simplicity of a model is assessed by a measure <i>S</i> that prefers a smaller number of clusters unless additional clusters can reduce the estimated noise proportion substantially. The simplest model is then chosen that is adequate for the data in the sense that its observed value of <i>Q</i> is not significantly larger than what is expected for data truly generated from the fitted model, as can be assessed by parametric bootstrap. The approach is compared with model-based clustering using the Bayesian information criterion (BIC) and the integrated complete likelihood (ICL) in a simulation study and on two real data sets.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"64 2","pages":"230-254"},"PeriodicalIF":1.1,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12338","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75692546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

What is the effective sample size of a spatial point process? 空间点过程的有效样本量是多少?

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-07-21 DOI: 10.1111/anzs.12337

Ian W. Renner, David I. Warton, Francis K.C. Hui

引用次数: 4

Anna Karenina and the two envelopes problem 安娜·卡列尼娜和两个信封的问题

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-07-21 DOI: 10.1111/anzs.12329

R. D. Gill

{"title":"Anna Karenina and the two envelopes problem","authors":"R. D. Gill","doi":"10.1111/anzs.12329","DOIUrl":"10.1111/anzs.12329","url":null,"abstract":"<div>\u0000 \u0000 <p>The Anna Karenina principle is named after the opening sentence in the eponymous novel: Happy families are all alike; every unhappy family is unhappy in its own way. The two envelopes problem (TEP) is a much-studied paradox in probability theory, mathematical economics, logic and philosophy. Time and again a new analysis is published in which an author claims finally to explain what actually goes wrong in this paradox. Each author (the present author included) emphasises what is new in their approach and concludes that earlier approaches did not get to the root of the matter. We observe that though a logical argument is only correct if every step is correct, an apparently logical argument which goes astray can be thought of as going astray at different places. This leads to a comparison between the literature on TEP and a successful movie franchise: it generates a succession of sequels, and even prequels, each with a different director who approaches the same basic premise in a personal way. We survey resolutions in the literature with a view to synthesis, correct common errors, and give a new theorem on order properties of an exchangeable pair of random variables, at the heart of most TEP variants and interpretations. A theorem on asymptotic independence between the amount in your envelope and the question whether it is smaller or larger shows that the pathological situation of improper priors or infinite expectation values has consequences as we merely approach such a situation.</p>\u0000 </div>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"63 1","pages":"201-218"},"PeriodicalIF":1.1,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/anzs.12329","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80260052","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

A Festschrift for Adrian Baddeley 阿德里安·巴德利的欢宴

IF 1.1 4区数学

Australian & New Zealand Journal of Statistics Pub Date : 2021-07-21 DOI: 10.1111/anzs.12322

Martin L. Hazelton, R. Turner

引用次数: 0