The Statistician : journal of the Institute of Statisticians最新文献

{"title":"Student Selection of Random Digits","authors":"P. Boland, K. Hutchinson","doi":"10.1111/1467-9884.00250","DOIUrl":"https://doi.org/10.1111/1467-9884.00250","url":null,"abstract":"The paper describes an investigation in which four groups of university students, of sizes 228, 111, 51 and 68, were asked to generate randomly a sequence of 25 digits from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Previous studies of this kind have suggested that people have tendencies to avoid repetition, to respond serially and to cycle. The aim of our investigation was to study further the nature and extent of people's biases. Particular emphasis was put on the frequency and spread of digits in a selection, as well as on aspects of repetition and clustering. The distribution of the number of clusters of size k was obtained, and our analysis includes the use of this distribution. Our results support previous research showing the very special (and less favoured) status of 0 but also show a strong tendency of students to balance selections and to avoid clustering and sequentially repeating digits.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"21 1","pages":"519-529"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87583098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Initial Stage Problem in Autoregressive Binary Regression","authors":"J. Chan","doi":"10.1111/1467-9884.00248","DOIUrl":"https://doi.org/10.1111/1467-9884.00248","url":null,"abstract":"When data are repeatedly measured over time, they are highly correlated. To account for serial correlation, we may use an autoregressive (AR) model, in particular the AR(1) model. However, when t= 1, the previous outcome y 0 is unobserved. To overcome such problems in binary regression, we may simply set Y 10 = 0 and the contribution of the possible errors from one or several such initial cases to the model is small when each time series is sufficiently long. Another approach is to model the initial cases separately by using a marginal model and the rest of the observations by using a conditional AR(1) model. We consider the Bayesian approach of modelling the outcomes Y i0 by a beta prior and the resulting model is a two-point mixture model such that the outcome Y i0 = k occurs with probability π k , k = 0, 1, and π 0 + π 1 = 1. These models are demonstrated and compared by using a methadone clinic data set. A simulation study reveals that the mixture model is better than the conditional AR(1) model as it gives smaller relative biases and mean-squared errors for most covariates. Also, the standard deviation to standard error ratios in the mixture model are closer to 1 than in the conditional AR(1) model for most covariates. The improvements are more profound when the time series for each patient is shorter. This demonstrates the importance of the mixture model when the sample size is small.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"34 1","pages":"495-502"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86468062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantifying expert opinion in the UK water industry: an experimental study","authors":"P. Garthwaite, A. O’Hagan","doi":"10.1111/1467-9884.00246","DOIUrl":"https://doi.org/10.1111/1467-9884.00246","url":null,"abstract":"This paper reports an experiment in which 32 experts at three water companies quantified their opinions about two problems: the cost of refurbishing specified pumping stations and the length of unrecorded S24 sewers in four towns. Medians and both unconditional and conditional assessments of quantiles were elicited and assessments were compared with reality and given scores. The quantiles that experts were asked to assess varied and the experts differed in the extent of their relevant background knowledge. The influences of these factors on standard deviations and scores are examined. The main focus is on modelling methods and ways of using the elicited assessments to form subjective probability distributions. We consider fitting log-normal distributions to model asymmetric distributions and also examine models to relate a quantity's assessed standard deviation and interquantile range to its size, finding that interquantile ranges can be modelled more accurately. In addition, different approaches to separating opinions about components of variance are evaluated and compared.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"5 1","pages":"455-477"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88936979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Prediction and retrospective analysis of soccer matches in a league","authors":"H. Rue, Ø. Salvesen","doi":"10.1111/1467-9884.00243","DOIUrl":"https://doi.org/10.1111/1467-9884.00243","url":null,"abstract":"A common discussion subject for the male part of the population in particular is the prediction of the next week-end's soccer matches, especially for the local team. Knowledge of offensive and defensive skills is valuable in the decision process before making a bet at a bookmaker. We take an applied statistician's approach to the problem, suggesting a Bayesian dynamic generalized linear model to estimate the time-dependent skills of all teams in a league, and to predict the next week-end's soccer matches. The problem is more intricate than it may appear at first glance, as we need to estimate the skills of all teams simultaneously as they are dependent. It is now possible to deal with such inference problems by using the Markov chain Monte Carlo iterative simulation technique. We show various applications of the proposed model based on the English Premier League and division 1 in 1997–1998: prediction with application to betting, retrospective analysis of the final ranking, the detection of surprising matches and how each team's properties vary during the season.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"46 1","pages":"399-418"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77267267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Analysis of Contingency Tables with One Factor as The Response: Round Two","authors":"J. Nelder","doi":"10.1111/1467-9884.00241","DOIUrl":"https://doi.org/10.1111/1467-9884.00241","url":null,"abstract":"For contingency tables with one factor as a response, log-linear models can be used provided that a minimal model, which constrains the predicted sample sizes of the response factor to equal the actual sizes, is fitted first. Only models that contain this minimal term make inferential sense. For response factors with two levels the results from fitting such log-linear models are identical with those from the corresponding logistic regression. The correspondence is illustrated with two examples from recent literature, both of which have been previously misanalysed.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"69 1","pages":"383-388"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86131894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Philosophy of Statistics","authors":"D. Lindley","doi":"10.1111/1467-9884.00238","DOIUrl":"https://doi.org/10.1111/1467-9884.00238","url":null,"abstract":"This paper puts forward an overall view of statistics. It is argued that statistics is the study of uncertainty. The many demonstrations that uncertainties can only combine according to the rules of the probability calculus are summarized. The conclusion is that statistical inference is firmly based on probability alone. Progress is therefore dependent on the construction of a probability model; methods for doing this are considered. It is argued that the probabilities are personal. The roles of likelihood and exchangeability are explained. Inference is only of value if it can be used, so the extension to decision analysis, incorporating utility, is related to risk and to the use of statistics in science and law. The paper has been written in the hope that it will be intelligible to all who are interested in statistics.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"23 1","pages":"293-337"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75161515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Estimating Standard Errors in Multilevel Analysis","authors":"N. Longford","doi":"10.1111/1467-9884.00242","DOIUrl":"https://doi.org/10.1111/1467-9884.00242","url":null,"abstract":"Standard errors of maximum likelihood estimators are commonly estimated from the inverse of the information matrix. When the information matrix is a function of parameters, some of which are estimated with little precision, the standard error may be estimated very poorly. This problem is discussed in the context of two-level (random-coefficient) models, and some remedies are proposed.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"13 1","pages":"389-398"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88292503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bayesian modelling of prehistoric corbelled domes","authors":"Yanan Fan, S. Brooks","doi":"10.1111/1467-9884.00239","DOIUrl":"https://doi.org/10.1111/1467-9884.00239","url":null,"abstract":"The field of archaeology provides a rich source of complex, non-standard problems ideally suited to Bayesian inference. We discuss the application of Bayesian methodology to prehistoric corbelled tomb data collected from a variety of sites around Europe. We show how the corresponding analyses may be carried out with the aid of reversible jump Markov chain Monte Carlo simulation techniques and, by calculating posterior model probabilities, we show how to distinguish between competing models. In particular, we discuss how earlier analyses of tomb data by Cavanagh and Laxton and by Buck and co-workers, where structural changes are anticipated in the shape of the tomb at different depths, can be extended and improved by considering a wider range of models. We also discuss the extent to which these analyses may be useful in addressing questions concerning the origin of tomb building technologies, particularly in distinguishing between corbelled domes built by different civilizations, as well as the processes involved in their construction.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"3 1","pages":"339-354"},"PeriodicalIF":0.0,"publicationDate":"2000-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88077350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inference for the poly-Weibull model","authors":"A. Davison, F. Louzada-Neto","doi":"10.1111/1467-9884.00229","DOIUrl":"https://doi.org/10.1111/1467-9884.00229","url":null,"abstract":"Summary. We consider inference for the poly-Weibull model, which arises in competing risk scenarios when the risks have independent Weibull distributions and it is not known which is responsible for the failure. Real and generated data sets illustrate our approaches to inference, which in addition to standard likelihood methods include Bayesian inference by Laplace's method for analytical approximation of integrals and sampling-importance resampling. The poly-Weibull distribution is that of the minimum of several independent Weibull random variables. This arises in scenarios of competing risks (Cox and Oakes (1984), chapter 7), where failure may be due to several causes, each supposed to follow a Weibull law. As we shall see, its advantage over the Weibull model is that it allows not only increasing, constant or decreasing hazard functions with zero or non-zero asymptotes but also non-monotone hazard functions, for example with a 'bathtub' shape. This is an attractive property because such hazards are not uncommon in practice; they correspond to an initial high failure rate a 'bum-in' period followed by lower odds of failure, which eventually increase. See Blackstone et al. (1986) for an application of such hazards in the context of survival after heart surgery. This paper discusses inference for the model, which deserves to be better known. We show by example that standard likelihood or Bayesian inference is straightforward, despite the assertion by Berger and Sun (1993) that a computation of the likelihood is 'typically not feasible', a belief that led them to apply Gibbs sampling for Bayesian inference. In fact the likelihood is so simply obtained that Markov chain simulation is unnecessary, and either Laplace approximation (Tiemey and Kadane, 1986) or the Bayesian bootstrap (Smith and Gelfand, 1992) may be applied; neither has the difficulties of assessing convergence that are associated with Markov chain methods. This reduces considerably the computational burden in obtaining posterior probabilities, densities or moments and widens the class of prior densities that can easily be used because they need not be chosen mainly for computational convenience. The chief difficulty in using the likelihood is possible non-identifiability of the model parameters, but we give some practical suggestions for detecting this.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"1 1","pages":"189-196"},"PeriodicalIF":0.0,"publicationDate":"2000-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83118853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sample size calculations for failure time random variables in non-randomized studies","authors":"M. Bernardo, S. Lipsitz, D. Harrington, P. Catalano","doi":"10.1111/1467-9884.00217","DOIUrl":"https://doi.org/10.1111/1467-9884.00217","url":null,"abstract":"Summary. In non-randomized studies, sample size calculations for failure time random variables are often computed on the basis of the unadjusted log-rank test which assumes that the variable designating group membership is independent of other patient covariates. We show that by extending the methods proposed by Lipsitz and Parzen to time-to-event random variabes the power derived from the unadjusted log-rank test overestimates the true power of the comparison when the variable of interest is correlated with other covariates. We model the hazards by using exponential regression and derive the sample size formulae for both censored and uncensored data. We also present results of a simulation study to assess the validity of the derived formulae when the intended method of analysis is the proportional hazards regression model and the data continue to have an exponential distribution. We apply the methods proposed to the non-Hodgkin's lymphoma prognostic factors project data set.","PeriodicalId":83973,"journal":{"name":"The Statistician : journal of the Institute of Statisticians","volume":"30 1","pages":"31-40"},"PeriodicalIF":0.0,"publicationDate":"2000-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90100939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}