Towards Enhancement of the Economy of a Thermal Power Generating System through Prediction of Plant Efficiency

The plant ‘Heat Rate’ (HR) is a measure of overall efficiency of a thermal power generating system. It depends on a large number of factors, some of which are non-measurable, while data relating to others are seldom available and recorded. However, coal quality (expressed in terms of ‘effective heat value’ (EHV) as kcal/kg) transpires to be one of the important factors that influences HR values and data on EHV are available in any thermal power generating system. In the present work, we propose a prediction interval of the HR values on the basis of only EHV, keeping in mind that coal quality is one of the important (but not the only) factors that have a pronounced effect on the combustion process and hence on HR. The underlying theory borrows the idea of providing simultaneous confidence interval (SCI) to the coefficients of a p-th p(≥1) order autoregressive model (AR(p)). The theory has been substantiated with the help of real life data from a power utility (after suitable base and scale transformation of the data to maintain the confidentiality of the classified document). Scope for formulating strategies to enhance the economy of a thermal power generating system has also been explored.     

Power of the Neyman Smooth Test for Evaluating Multivariate Forecast Densities

We compare and investigate Neyman's smooth test, its components, and the Kolmogorov-Smirnov (KS) goodness-of-fit test for testing the uniformity of multivariate forecast densities. Simulations indicate that the KS test lacks power when the forecast distributions are misspecified, especially for correlated sequences of random variables. Neyman's smooth test and its components work well in samples of size typically available, although there sometimes are size distortions. The components provide directed diagnosis regarding the kind of departure from the null. For illustration, the tests are applied to forecast densities obtained from a bivariate threshold model fitted to high-frequency financial data.     

Estimation of the Force of Infection from Current Status Data Using Generalized Linear Mixed Models

Based on sero-prevalence data of rubella, mumps in the UK and varicella in Belgium, we show how the force of infection, the age-specific rate at which susceptible individuals contract infection, can be estimated using generalized linear mixed models (McCulloch & Searle, 2001). Modelling the dependency of the force of infection on age by penalized splines, which involve fixed and random effects, allows us to use generalized linear mixed models techniques to estimate both the cumulative probability of being infected before a given age and the force of infection. Moreover, these models permit an automatic selection of the smoothing parameter. The smoothness of the estimated force of infection can be influenced by the number of knots and the degree of the penalized spline used. To determine these, a different number of knots and different degrees are used and the results are compared to establish this sensitivity. Simulations with a different number of knots and polynomial spline bases of different degrees suggest - for estimating the force of infection from serological data - the use of a quadratic penalized spline based on about 10 knots.     

H-likelihood: problems and solutions

In recent issues of this journal it has been asserted in two papers that the use of h-likelihood is wrong, in the sense of giving unsatisfactory estimates of some parameters for binary data (Kuk and Cheng, 1999; Waddington and Thompson, 2004) or theoretically unsound (Kuk and Cheng, 1999). We wish to refute both these assertions.     

A direct derivation of the REML likelihood function

The original derivation of the widely cited form of the REML likelihood function for mixed linear models is difficult and indirect. This paper derives it directly using familiar operations with matrices and determinants.     

密度分布非均匀的反馈控制Logistic单种群模型平衡态的稳定性

本文对种群密度在非均匀分布情形下,考虑了具反馈控制的滞后 Logistic 生态模型平衡位置的稳定性;分别给出了在常时滞和弱连续时滞以及强连续时滞情况下的稳定性条件;其结果是对 Gopalsamy 在密度均匀分布情形下相应结果的推广.     

A Trivariate Distribution for the Height,Weight, and Fat of Adult Men*

Using exploratory data analysis, probability plots, scatterplots, and computer animations to rotate and visualize the data, we fit a trivariate Normal distribution to data for the height, the natural logarithm of body weight, and the body fat for 646 men between the ages of 50 and 80 years as reported by the medical staff of the U.S. Veterans Administration's “Normative Aging Study” in Boston, MA. Although these data do not include any children, women, or young men, the measurements represent the best data that we could find through a 4-year search. We believe that these data are well measured and reliable for men in the specified age range and that these data reveal an interesting statistical pattern for use in probabilistic PBPK models.     

Expressing Estimators of Expected Quality Adjusted Survival as Functions of Nelson-Aalen Estimators

Quality adjusted survival has been increasingly advocated in clinical trials to be assessed as a synthesis of survival and quality of life. We investigate nonparametric estimation of its expectation for a general multistate process with incomplete follow-up data. Upon establishing a representation of expected quality adjusted survival through marginal distributions of a set of defined events, we propose two estimators for expected quality adjusted survival. Expressed as functions of Nelson-Aalen estimators, the two estimators are strongly consistent and asymptotically normal. We derive their asymptotic variances and propose sample-based variance estimates, along with evaluation of asymptotic relative efficiency. Monte Carlo studies show that these estimation procedures perform well for practical sample sizes. We illustrate the methods using data from a national, multicenter AIDS clinical trial.     

A Discrete Variable Chain Graph for Applicants for Credit

A bank offering unsecured personal loans may be interested in several related outcome variables, including defaulting on the repayments, early repayment or failing to take up an offered loan. Current predictive models used by banks typically consider such variables individually. However, the fact that they are related to each other, and to many interrelated potential predictor variables, suggests that graphical models may provide an attractive alternative solution. We developed such a model for a data set of 15 variables measured on a set of 14 000 applications for unsecured personal loans. The resulting global model of behaviour enabled us to identify several previously unsuspected relationships of considerable interest to the bank. For example, we discovered important but obscure relationships between taking out insurance, prior delinquency with a credit card and delinquency with the loan.     

Venezuelan Rainfall Data Analysed by Using a Bayesian Space–time Model

We consider a set of data from 80 stations in the Venezuelan state of Guárico consisting of accumulated monthly rainfall in a time span of 16 years. The problem of modelling rainfall accumulated over fixed periods of time and recorded at meteorological stations at different sites is studied by using a model based on the assumption that the data follow a truncated and transformed multivariate normal distribution. The spatial correlation is modelled by using an exponentially decreasing correlation function and an interpolating surface for the means. Missing data and dry periods are handled within a Markov chain Monte Carlo framework using latent variables. We estimate the amount of rainfall as well as the probability of a dry period by using the predictive density of the data. We considered a model based on a full second-degree polynomial over the spatial co-ordinates as well as the first two Fourier harmonics to describe the variability during the year. Predictive inferences on the data show very realistic results, capturing the typical rainfall variability in time and space for that region. Important extensions of the model are also discussed.