Probability and statistics: A tale of two worlds?

This comparative study of research productivity and publication habits in probability and statistics completes the paper that was published in this Journal at the end of 1997. It is based on a ten-year survey of eighteen international journals, half of which are specialized in probability theory and the other half in statistics. Paper, author and adjusted page counts yield cursory measures of productivity for countries and institutions that contributed to fundamental research in these two related fields during the period 1986-1995. These data also reveal significant cultural differences between probabilists and statisticians in the volume of research, the length of papers, coauthorship practices, etc. Canada is seen to be one of the strongest contributors to the development of these two disciplines.     

Communicating the risks arising from geohazards

Summary. Construction on, or in, the ground is affected by uncertainty. This includes the inherent variability of the ground itself, the effect of natural and human processes on the ground and the difficulties that are associated with the management and implementation of any construction works. The risk is considered to be in two parts: the probability of occurrence of a geohazard and the effect that this will have on the outcome of the project. Geohazards are determined as part of the ground investigation process, the principles of which are well established. Nevertheless uncertainty remains and communication between the professions and with the public is not always effective. Barriers are created by unfamiliar terminology and a lack of a forum for education and exchange of views. It is argued that the public must be continually involved—not only as recipients, but also as contributors.     

Impact of Model Choice on LR Assessment in Case of Rare Haplotype Match (Frequentist Approach)

The likelihood ratio (LR) measures the relative weight of forensic data regarding two hypotheses. Several levels of uncertainty arise if frequentist methods are chosen for its assessment: the assumed population model only approximates the true one, and its parameters are estimated through a limited database. Moreover, it may be wise to discard part of data, especially that only indirectly related to the hypotheses. Different reductions define different LRs. Therefore, it is more sensible to talk about ‘a’ LR instead of ‘the’ LR, and the error involved in the estimation should be quantified. Two frequentist methods are proposed in the light of these points for the ‘rare type match problem’, that is, when a match between the perpetrator's and the suspect's DNA profile, never observed before in the database of reference, is to be evaluated.     

A Bayesian approach to inference about a change point model with application to DNA copy number experimental data

In this paper, we study the change-point inference problem motivated by the genomic data that were collected for the purpose of monitoring DNA copy number changes. DNA copy number changes or copy number variations (CNVs) correspond to chromosomal aberrations and signify abnormality of a cell. Cancer development or other related diseases are usually relevant to DNA copy number changes on the genome. There are inherited random noises in such data, therefore, there is a need to employ an appropriate statistical model for identifying statistically significant DNA copy number changes. This type of statistical inference is evidently crucial in cancer researches, clinical diagnostic applications, and other related genomic researches. For the high-throughput genomic data resulting from DNA copy number experiments, a mean and variance change point model (MVCM) for detecting the CNVs is appropriate. We propose to use a Bayesian approach to study the MVCM for the cases of one change and propose to use a sliding window to search for all CNVs on a given chromosome. We carry out simulation studies to evaluate the estimate of the locus of the DNA copy number change using the derived posterior probability. These simulation results show that the approach is suitable for identifying copy number changes. The approach is also illustrated on several chromosomes from nine fibroblast cancer cell line data (array-based comparative genomic hybridization data). All DNA copy number aberrations that have been identified and verified by karyotyping are detected by our approach on these cell lines.     

Using the Diffusion of Innovation Concept to Explain the Factors That Contribute to the Adoption Rate of E-journal Publishing

This paper reports on the factors that contribute to the adoption rate of e-journal publishing based upon responses from 82 Malaysian journal publishers. Drawing upon the theory of innovation diffusion, the study examines the role of awareness, three organization variables (publication size, age of the journal, and experience of editors), and attributes of e-journals (relative advantage, compatibility, complexity, trialability and observability) as influences to the rate of e-journal publishing adoption. Findings show that only two attributes—complexity and trialability—emerge as significant contributors to e-journal adoption rates, and all three organization variables—journal's age, publication size, and editorial experience—are significant. Collectively, these five significant variables explained 57.8% of the variance in adoption rate. We discuss the results and implication of the findings with respect to the wider context of e-journal publishing.     

Conditional failure occurrence rates for semi-Markov chains*

ABSTRACT

In the present paper, we aim at providing plug-in-type empirical estimators that enable us to quantify the contribution of each operational or/and non-functioning state to the failures of a system described by a semi-Markov model. In the discrete-time and finite state space semi-Markov framework, we study different conditional versions of an important reliability measure for random repairable systems, the failure occurrence rate, which is based on counting processes. The identification of potential failure contributors through the conditional counterparts of the failure occurrence rate is of paramount importance since it could lead to corrective actions that minimize the occurrence of the more important failure modes and therefore improve the reliability of the system. The aforementioned estimators are characterized by appealing asymptotic properties such as strong consistency and asymptotic normality. We further obtain detailed analytical expressions for the covariance matrices of the random vectors describing the conditional failure occurrence rates. As particular cases we present the failure occurrence rates for hidden (semi-) Markov models. We illustrate our results by means of a simulated study. Different applications are presented based on wind, earthquake and vibration data.     

我国居民收入分布与财产分布的极化

本文利用CHIP和CFPS住户调查数据,讨论了我国居民收入和财产分布的极化特征。本文给出了收入分布和财产分布的总体极化特征,并对收入和财产分布的DER指数进行了分解分析。本文的研究结果表明,尽管收入分布的极化指标比较稳定,但财产分布的极化现象在2002年到2013年期间有所加剧;财产分布的极化程度比收入极化要更为严重;城乡组间贡献仍是收入和财产分布极化的主要贡献因素;从根据收入构成的分解结果来看,工资收入和经营收入是收入分布极化的主要来源,财产收入对于总收入的极化程度的影响在逐渐增强;财产分布极化按照分项财产的构成分解表明,房产净值和金融资产对于全部净财产极化程度具有非常重要的影响。     

Poisson approximation and dna sequence matching

The Poisson distribution is commonly used to model the number of occurrences of independent rare events. However, many instances arise where dependence exists, for example, in counting the length of long head runs in coin tossing, or matches between two DNA sequences. The Chen-Stein method of Poisson approximation yields bounds on the error incurred when approximating the number of occurrences of possibly dependent events by a Poisson random variable of the same mean. In addition to the problems related to the motivating examples from molecular biology involving runs and matches, the method may be applied to questions as varied as calculating probabilities involving extremes of sequences of random variables and approximating the probability of general birthday coincidences.     

Extreme shape analysis

Summary.  We consider the analysis of extreme shapes rather than the more usual mean- and variance-based shape analysis. In particular, we consider extreme shape analysis in two applications: human muscle fibre images, where we compare healthy and diseased muscles, and temporal sequences of DNA shapes from molecular dynamics simulations. One feature of the shape space is that it is bounded, so we consider estimators which use prior knowledge of the upper bound when present. Peaks-over-threshold methods and maximum-likelihood-based inference are used. We introduce fixed end point and constrained maximum likelihood estimators, and we discuss their asymptotic properties for large samples. It is shown that in some cases the constrained estimators have half the mean-square error of the unconstrained maximum likelihood estimators. The new estimators are applied to the muscle and DNA data, and practical conclusions are given.     

On binomial and circular binomial distributions of orderk forl-overlapping success runs of lengthk

The number ofl-overlapping success runs of lengthk inn trials, which was introduced and studied recently, is presently reconsidered in the Bernoulli case and two exact formulas are derived for its probability distribution function in terms of multinomial and binomial coefficients respectively. A recurrence relation concerning this distribution, as well as its mean, is also obtained. Furthermore, the number ofl-overlapping success runs of lengthk inn Bernoulli trials arranged on a circle is presently considered for the first time and its probability distribution function and mean are derived. Finally, the latter distribution is related to the first, two open problems regarding limiting distributions are stated, and numerical illustrations are given in two tables. All results are new and they unify and extend several results of various authors on binomial and circular binomial distributions of orderk.     

Inferences from DNA data: population histories, evolutionary processes and forensic match probabilities

Summary. We develop a flexible class of Metropolis–Hastings algorithms for drawing inferences about population histories and mutation rates from deoxyribonucleic acid (DNA) sequence data. Match probabilities for use in forensic identification are also obtained, which is particularly useful for mitochondrial DNA profiles. Our data augmentation approach, in which the ancestral DNA data are inferred at each node of the genealogical tree, simplifies likelihood calculations and permits a wide class of mutation models to be employed, so that many different types of DNA sequence data can be analysed within our framework. Moreover, simpler likelihood calculations imply greater freedom for generating tree proposals, so that algorithms with good mixing properties can be implemented. We incorporate the effects of demography by means of simple mechanisms for changes in population size and structure, and we estimate the corresponding demographic parameters, but we do not here allow for the effects of either recombination or selection. We illustrate our methods by application to four human DNA data sets, consisting of DNA sequences, short tandem repeat loci, single-nucleotide polymorphism sites and insertion sites. Two of the data sets are drawn from the male-specific Y-chromosome, one from maternally inherited mitochondrial DNA and one from the β -globin locus on chromosome 11.     

规模以上工业企业的行业税负研究

 规模以上工业企业是国家税收的主要承担者。本文基于近些年规模以上工业企业的相关资料,解读工业增加值、主营业务收入与应交增值税、主营业务税金之间关系。通过建立面板数据模型,讨论分析了工业企业的行业税负水平。研究认为：规模以上工业企业税负偏重是不争的事实,行业之间也存在着一定的不平衡。建议,适度减轻工业企业税负,均衡行业之间的税负差异,进一步贯彻结构调整战略,促进经济发展方式转型。     

Interdisciplinary research: the importance of learning other people’s language

Good interdisciplinary research requires genuine team work and appreciation of the different skills contributed by the partners involved. By the nature of our subject, statisticians are often very important contributors to this kind of research. This short note offers some brief reflection on the issues of communication which are usually present. The skills required and the need to promote these in undergraduate education and beyond have been well documented in the literature but are further emphasised here.     

Testing the equality of correlation matrices

We present results that extend an existing test of equality of correlation matrices. A new test statistic is proposed and is shown to be asymptotically distributed as a linear combination of independent x ² random variables. This new formulation allows us to find the power of the existing test and our extensions by deriving the distribution under the alternative using a linear combination of independent non-central x ² random variables. We also investigate the null and the alternative distribution of two related statistics. The first one is a quadratic form in deviations from a control group with which the remaining k-1 groups are to be compared. The second test is designed for comparing adjacent groups. Several approximations for the null and the alternative distribution are considered and two illustrative examples are provided.     

Single Attribute Control Charts for a Markovian-Dependent Process

In a production process, sequence of observations related to the quality of a process need not be independent. In such situations, control charts based on the assumption of independence of the observations are not appropriate. When the characteristic under study is qualitative, the Markovian model serves as a simple model to account for the dependency of the observations. In this article, we develop two attribute control charts for a Markovian dependent process: the first is based on controlling the error probabilities; the second is based on minimizing the average time to get a correct signal.

The charts are developed under uniform sampling. Under uniform sampling, the two consecutive samples are far enough apart, so that for all practical purposes, two consecutive samples can be considered as if they are being independent. Optimal values of the design parameters of both the control charts are obtained. A procedure to estimate the values of the in-control parameters is also described. The chart's performance is evaluated using the probability of detecting shift. When we implement the proposed charts for the data simulated under given manufacturing environments, the charts exhibit the desired properties of error probabilities and average time to signal.     

Random Convex Combinations of m-Generalized Order Statistics

The situation of identical distributions of a single m-generalized order statistic and a random convex combination of two neighboring m-generalized order statistics with beta-distributed weights is studied, and related characterizations of generalized Pareto distributions are shown.     

ON CONVERGENCE RATES FOR NONPARAMETRIC POSTERIOR DISTRIBUTIONS

Rates of convergence of Bayesian nonparametric procedures are expressed as the maximum between two rates: one is determined via suitable measures of concentration of the prior around the “true” density f₀, and the other is related to the way the mass is spread outside a neighborhood of f₀. Here we provide a lower bound for the former in terms of the usual notion of prior concentration and in terms of an alternative definition of prior concentration. Moreover, we determine the latter for two important classes of priors: the infinite–dimensional exponential family, and the Pólya trees.     

Quantification of symmetry for functional data with application to equine lameness classification

This paper presents a study on symmetry of repeated bi-phased data signals, in particular, on quantification of the deviation between the two parts of the signal. Three symmetry scores are defined using functional data techniques such as smoothing and registration. One score is related to the L ₂-distance between the two parts of the signal, whereas the other two are constructed to specifically measure differences in amplitude and phase. Moreover, symmetry scores based on functional principal component analysis (PCA) are examined. The scores are applied to acceleration signals from a study on equine gait. The scores turn out to be highly associated with lameness, and their applicability for lameness quantification and detection is investigated. Four classification approaches turn out to give similar results. The scores describing amplitude and phase variation turn out to outperform the PCA scores when it comes to the classification of lameness.