Forecasting with serially correlated regression models

In this article we investigate the asymptotic and finite-sample properties of predictors of regression models with autocorrelated errors. We prove new theorems associated with the predictive efficiency of generalized least squares (GLS) and incorrectly structured GLS predictors. We also establish the form associated with their predictive mean squared errors as well as the magnitude of these errors relative to each other and to those generated from the ordinary least squares (OLS) predictor. A large simulation study is used to evaluate the finite-sample performance of forecasts generated from models using different corrections for the serial correlation.

The specification of vector autoregressive moving average models

In this paper we propose a new identification method based on the residual white noise autoregressive criterion (Pukkila et al. , 1990) to select the order of VARMA structures. Results from extensive simulation experiments based on different model structures with varying number of observations and number of component series are used to demonstrate the performance of this new procedure. We also use economic and business data to compare the model structures selected by this order selection method with those identified in other published studies.

Statistical modeling and projections of lung cancer mortality in 4 industrialized countries

The purpose of this work was to model lung cancer mortality as a function of past exposure to tobacco and to forecast age-sex-specific lung cancer mortality rates. A 3-factor age-period-cohort (APC) model, in which the period variable is replaced by the product of average tar content and adult tobacco consumption per capita, was estimated for the US, UK, Canada and Australia by the maximum likelihood method. Age- and sex-specific tobacco consumption was estimated from historical data on smoking prevalence and total tobacco consumption. Lung cancer mortality was derived from vital registration records. Future tobacco consumption, tar content and the cohort parameter were projected by autoregressive moving average (ARIMA) estimation. The optimal exposure variable was found to be the product of average tar content and adult cigarette consumption per capita, lagged for 2530 years for both males and females in all 4 countries. The coefficient of the product of average tar content and tobacco consumption per capita differs by age and sex. In all models, there was a statistically significant difference in the coefficient of the period variable by sex. In all countries, male age-standardized lung cancer mortality rates peaked in the 1980s and declined thereafter. Female mortality rates are projected to peak in the first decade of this century. The multiplicative models of age, tobacco exposure and cohort fit the observed data between 1950 and 1999 reasonably well, and time-series models yield plausible past trends of relevant variables. Despite a significant reduction in tobacco consumption and average tar content of cigarettes sold over the past few decades, the effect on lung cancer mortality is affected by the time lag between exposure and established disease. As a result, the burden of lung cancer among females is only just reaching, or soon will reach, its peak but has been declining for I to 2 decades in men. Future sex differences in lung cancer mortality are likely to be greater in North America than Australia and the UK due to differences in exposure patterns between the sexes. (c) 2005 Wiley-Liss, Inc.

Application of mixture models to detect differentially expressed genes

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local FDR (false discovery rate) is provided for each gene. An attractive feature of the mixture model approach is that it provides a framework for the estimation of the prior probability that a gene is not differentially expressed, and this probability can subsequently be used in forming a decision rule. The rule can also be formed to take the false negative rate into account. We apply this approach to a well-known publicly available data set on breast cancer, and discuss our findings with reference to other approaches.

Using mixture models to detect differentially expressed genes

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local false discovery rate is provided for each gene, and it can be implemented so that the implied global false discovery rate is bounded as with the Benjamini-Hochberg methodology based on tail areas. The latter procedure is too conservative, unless it is modified according to the prior probability that a gene is not differentially expressed. An attractive feature of the mixture model approach is that it provides a framework for the estimation of this probability and its subsequent use in forming a decision rule. The rule can also be formed to take the false negative rate into account.

Designs for generalized linear models with several variables and model uncertainty

Standard factorial designs sometimes may be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments that uses a criterion allowing for uncertainty in the link function, the linear predictor, or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications, and their advantages over factorial and central composite designs are demonstrated.

Mixture models for detecting differentially expressed genes in microarrays

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local FDR (false discovery rate) is provided for each gene. An attractive feature of the mixture model approach is that it provides a framework for the estimation of the prior probability that a gene is not differentially expressed, and this probability can subsequently be used in forming a decision rule. The rule can also be formed to take the false negative rate into account. We apply this approach to a well-known publicly available data set on breast cancer, and discuss our findings with reference to other approaches.

Optimal crossover designs for logistic regression models in pharmacodynamics

Pharmacodynamics (PD) is the study of the biochemical and physiological effects of drugs. The construction of optimal designs for dose-ranging trials with multiple periods is considered in this paper, where the outcome of the trial (the effect of the drug) is considered to be a binary response: the success or failure of a drug to bring about a particular change in the subject after a given amount of time. The carryover effect of each dose from one period to the next is assumed to be proportional to the direct effect. It is shown for a logistic regression model that the efficiency of optimal parallel (single-period) or crossover (two-period) design is substantially greater than a balanced design. The optimal designs are also shown to be robust to misspecification of the value of the parameters. Finally, the parallel and crossover designs are combined to provide the experimenter with greater flexibility.

Defining a role for the subthalamic nucleus within operative theoretical models of subcortical participation in language

Objective:To investigate the effects of bilateral, surgically induced functional inhibition of the subthalamic nucleus (STN) on general language, high level linguistic abilities, and semantic processing skills in a group of patients with Parkinson’s disease. Methods:Comprehensive linguistic profiles were obtained up to one month before and three months after bilateral implantation of electrodes in the STN during active deep brain stimulation (DBS) in five subjects with Parkinson’s disease (mean age, 63.2 years). Equivalent linguistic profiles were generated over a three month period for a non-surgical control cohort of 16 subjects with Parkinson’s disease (NSPD) (mean age, 64.4 years). Education and disease duration were similar in the two groups. Initial assessment and three month follow up performance profiles were compared within subjects by paired t tests. Reliability change indices (RCI), representing clinically significant alterations in performance over time, were calculated for each of the assessment scores achieved by the five STN-DBS cases and the 16 NSPD controls, relative to performance variability within a group of 16 non-neurologically impaired adults (mean age, 61.9 years). Proportions of reliable change were then compared between the STN-DBS and NSPD groups. Results:Paired comparisons within the STN-DBS group showed prolonged postoperative semantic processing reaction times for a range of word types coded for meanings and meaning relatedness. Case by case analyses of reliable change across language assessments and groups revealed differences in proportions of change over time within the STN-DBS and NSPD groups in the domains of high level linguistics and semantic processing. Specifically, when compared with the NSPD group, the STN-DBS group showed a proportionally significant (p

Elliptic Gaudin models and elliptic KZ equations

The Gaudin models based on the face-type elliptic quantum groups and the XYZ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik–Zamolodchikov equations and their solutions are given.

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Review of recent results on excursion set models

Many images consist of two or more 'phases', where a phase is a collection of homogeneous zones. For example, the phases may represent the presence of different sulphides in an ore sample. Frequently, these phases exhibit very little structure, though all connected components of a given phase may be similar in some sense. As a consequence, random set models are commonly used to model such images. The Boolean model and models derived from the Boolean model are often chosen. An alternative approach to modelling such images is to use the excursion sets of random fields to model each phase. In this paper, the properties of excursion sets will be firstly discussed in terms of modelling binary images. Ways of extending these models to multi-phase images will then be explored. A desirable feature of any model is to be able to fit it to data reasonably well. Different methods for fitting random set models based on excursion sets will be presented and some of the difficulties with these methods will be discussed.

Language policy spread: Learning from health and social policy models

Except for a few large scale projects, language planners have tended to talk and argue among themselves rather than to see language policy development as an inherently political process. A comparison with a social policy example, taken from the United States, suggests that it is important to understand the problem and to develop solutions in the context of the political process, as this is where decisions will ultimately be made.