Modelling seasonally varying data: A case study for sudden infant death syndrome (SIDS)

Many time series are measured monthly, either as averages or totals, and such data often exhibit seasonal variability-the values of the series are consistently larger for some months of the year than for others. A typical series of this type is the number of deaths each month attributed to SIDS (Sudden Infant Death Syndrome). Seasonality can be modelled in a number of ways. This paper describes and discusses various methods for modelling seasonality in SIDS data, though much of the discussion is relevant to other seasonally varying data. There are two main approaches, either fitting a circular probability distribution to the data, or using regression-based techniques to model the mean seasonal behaviour. Both are discussed in this paper.

Design and optimisation of a large-area process-based model for annual crops

The formulation of a new process-based crop model, the general large-area model (GLAM) for annual crops is presented. The model has been designed to operate on spatial scales commensurate with those of global and regional climate models. It aims to simulate the impact of climate on crop yield. Procedures for model parameter determination and optimisation are described, and demonstrated for the prediction of groundnut (i.e. peanut; Arachis hypogaea L.) yields across India for the period 1966-1989. Optimal parameters (e.g. extinction coefficient, transpiration efficiency, rate of change of harvest index) were stable over space and time, provided the estimate of the yield technology trend was based on the full 24-year period. The model has two location-specific parameters, the planting date, and the yield gap parameter. The latter varies spatially and is determined by calibration. The optimal value varies slightly when different input data are used. The model was tested using a historical data set on a 2.5degrees x 2.5degrees grid to simulate yields. Three sites are examined in detail-grid cells from Gujarat in the west, Andhra Pradesh towards the south, and Uttar Pradesh in the north. Agreement between observed and modelled yield was variable, with correlation coefficients of 0.74, 0.42 and 0, respectively. Skill was highest where the climate signal was greatest, and correlations were comparable to or greater than correlations with seasonal mean rainfall. Yields from all 35 cells were aggregated to simulate all-India yield. The correlation coefficient between observed and simulated yields was 0.76, and the root mean square error was 8.4% of the mean yield. The model can be easily extended to any annual crop for the investigation of the impacts of climate variability (or change) on crop yield over large areas. (C) 2004 Elsevier B.V. All rights reserved.

An evaluation of different growth functions for describing the profile of live weight with time (age) in meat and egg strains of chicken

A total of 86 profiles from meat and egg strains of chickens (male and female) were used in this study. Different flexible growth functions were evaluated with regard to their ability to describe the relationship between live weight and age and were compared with the Gompertz and logistic equations, which have a fixed point of inflection. Six growth functions were used: Gompertz, logistic, Lopez, Richards, France, and von Bertalanffy. A comparative analysis was carried out based on model behavior and statistical performance. The results of this study confirmed the initial concern about the limitation of a fixed point of inflection, such as in the Gompertz equation. Therefore, consideration of flexible growth functions as an alternatives to the simpler equations (with a fixed point of inflection) for describing the relationship between live weight and age are recommended for the following reasons: they are easy to fit, they very often give a closer fit to data points because of their flexibility and therefore a smaller RSS value, than the simpler models, and they encompasses simpler models for the addition of an extra parameter, which is especially important when the behavior of a particular data set is not defined previously.

A parametric model for the interval censored survival times of Acacia mangium plantation in a spacing trial

Survival times for the Acacia mangium plantation in the Segaliud Lokan Project, Sabah, East Malaysia were analysed based on 20 permanent sample plots (PSPs) established in 1988 as a spacing experiment. The PSPs were established following a complete randomized block design with five levels of spacing randomly assigned to units within four blocks at different sites. The survival times of trees in years are of interest. Since the inventories were only conducted annually, the actual survival time for each tree was not observed. Hence, the data set comprises censored survival times. Initial analysis of the survival of the Acacia mangium plantation suggested there is block by spacing interaction; a Weibull model gives a reasonable fit to the replicate survival times within each PSP; but a standard Weibull regression model is inappropriate because the shape parameter differs between PSPs. In this paper we investigate the form of the non-constant Weibull shape parameter. Parsimonious models for the Weibull survival times have been derived using maximum likelihood methods. The factor selection for the parameters is based on a backward elimination procedure. The models are compared using likelihood ratio statistics. The results suggest that both Weibull parameters depend on spacing and block.

An on-line algorithm of uncertain time delay estimation in a continuous system

In this paper, we present an on-line estimation algorithm for an uncertain time delay in a continuous system based on the observational input-output data, subject to observational noise. The first order Pade approximation is used to approximate the time delay. At each time step, the algorithm combines the well known Kalman filter algorithm and the recursive instrumental variable least squares (RIVLS) algorithm in cascade form. The instrumental variable least squares algorithm is used in order to achieve the consistency of the delay parameter estimate, since an error-in-the-variable model is involved. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.

Acoustic trapped modes in a three-dimensional waveguide of slowly varying cross section

In this paper we develop an asymptotic scheme to approximate the trapped mode solutions to the time harmonic wave equation in a three-dimensional waveguide with a smooth but otherwise arbitrarily shaped cross section and a single, slowly varying `bulge', symmetric in the longitudinal direction. Extending the work in Biggs (2012), we first employ a WKBJ-type ansatz to identify the possible quasi-mode solutions which propagate only in the thicker region, and hence find a finite cut-on region of oscillatory behaviour and asymptotic decay elsewhere. The WKBJ expansions are used to identify a turning point between the cut-on and cut-on regions. We note that the expansions are nonuniform in an interior layer centred on this point, and we use the method of matched asymptotic expansions to connect the cut-on and cut-on regions within this layer. The behaviour of the expansions within the interior layer then motivates the construction of a uniformly valid asymptotic expansion. Finally, we use this expansion and the symmetry of the waveguide around the longitudinal centre, x = 0, to extract trapped mode wavenumbers, which are compared with those found using a numerical scheme and seen to be extremely accurate, even to relatively large values of the small parameter.

Time-dependent orientation coupling in equilibrium polymer melts

The motion in concentrated polymer systems is described by either the Rouse or the reptation model, which both assume that the relaxation of each polymer chain is independent of the surrounding chains. This, however, is in contradiction with several experiments. In this Letter, we propose a universal description of orientation coupling in polymer melts in terms of the time-dependent coupling parameter κ(t). We use molecular dynamics simulations to show that the coupling parameter increases with time, reaching about 50% at long times, independently of the chain length or blend composition. This leads to predictions of component dynamics in mixtures of different molecular weights from the knowledge of monodisperse dynamics for unentangled melts. Finally, we demonstrate that entanglements do not play a significant role in the observed coupling. © 2010 The American Physical Society

Bayesian model averaging and identification of structural breaks in time series

Bayesian Model Averaging (BMA) is used for testing for multiple break points in univariate series using conjugate normal-gamma priors. This approach can test for the number of structural breaks and produce posterior probabilities for a break at each point in time. Results are averaged over specifications including: stationary; stationary around trend and unit root models, each containing different types and number of breaks and different lag lengths. The procedures are used to test for structural breaks on 14 annual macroeconomic series and 11 natural resource price series. The results indicate that there are structural breaks in all of the natural resource series and most of the macroeconomic series. Many of the series had multiple breaks. Our findings regarding the existence of unit roots, having allowed for structural breaks in the data, are largely consistent with previous work.

Parameter estimation based on stacked regression and evolutionary algorithms

A new parameter-estimation algorithm, which minimises the cross-validated prediction error for linear-in-the-parameter models, is proposed, based on stacked regression and an evolutionary algorithm. It is initially shown that cross-validation is very important for prediction in linear-in-the-parameter models using a criterion called the mean dispersion error (MDE). Stacked regression, which can be regarded as a sophisticated type of cross-validation, is then introduced based on an evolutionary algorithm, to produce a new parameter-estimation algorithm, which preserves the parsimony of a concise model structure that is determined using the forward orthogonal least-squares (OLS) algorithm. The PRESS prediction errors are used for cross-validation, and the sunspot and Canadian lynx time series are used to demonstrate the new algorithms.

Sensitivity analysis of a cyanobacterial growth and movement model under two different flow regimes

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling cyanobacterial behaviour in freshwaters is an important tool for understanding their population dynamics and predicting the location and timing of the bloom events in lakes, reservoirs and rivers. A new deterministic–mathematical model was developed, which simulates the growth and movement of cyanobacterial blooms in river systems. The model focuses on the mathematical description of the bloom formation, vertical migration and lateral transport of colonies within river environments by taking into account the major factors that affect the cyanobacterial bloom formation in rivers including light, nutrients and temperature. A parameter sensitivity analysis using a one-at-a-time approach was carried out. There were two objectives of the sensitivity analysis presented in this paper: to identify the key parameters controlling the growth and movement patterns of cyanobacteria and to provide a means for model validation. The result of the analysis suggested that maximum growth rate and day length period were the most significant parameters in determining the population growth and colony depth, respectively.

Performance analysis of near-far resistant CDMA detectors-influence of system parameter estimation errors

Little has been reported on the performance of near-far resistant CDMA detectors in the presence of system parameter estimation errors (SPEEs). Starting with the general mathematical model of matched filters, the paper examines the effects of three classes of SPEEs, i.e., time-delay, carrier phase, and carrier frequency errors, on the performance (BER) of an emerging type of near-far resistant coherent DS/SSMA detector, i.e., the linear decorrelating detector. For comparison, the corresponding results for the conventional detector are also presented. It is shown that the linear decorrelating detector can still maintain a considerable performance advantage over the conventional detector even when some SPEEs exist.

A hybrid data assimilation scheme for model parameter estimation: application to morphodynamic modelling

We present a novel algorithm for joint state-parameter estimation using sequential three dimensional variational data assimilation (3D Var) and demonstrate its application in the context of morphodynamic modelling using an idealised two parameter 1D sediment transport model. The new scheme combines a static representation of the state background error covariances with a flow dependent approximation of the state-parameter cross-covariances. For the case presented here, this involves calculating a local finite difference approximation of the gradient of the model with respect to the parameters. The new method is easy to implement and computationally inexpensive to run. Experimental results are positive with the scheme able to recover the model parameters to a high level of accuracy. We expect that there is potential for successful application of this new methodology to larger, more realistic models with more complex parameterisations.

Model-based groupware solution for distributed real-time collaborative 4D planning via teamwork

Construction planning plays a fundamental role in construction project management that requires team working among planners from a diverse range of disciplines and in geographically dispersed working situations. Model-based four-dimensional (4D) computer-aided design (CAD) groupware, though considered a possible approach to supporting collaborative planning, is still short of effective collaborative mechanisms for teamwork due to methodological, technological and social challenges. Targeting this problem, this paper proposes a model-based groupware solution to enable a group of multidisciplinary planners to perform real-time collaborative 4D planning across the Internet. In the light of the interactive definition method, and its computer-supported collaborative work (CSCW) design analysis, the paper discusses the realization of interactive collaborative mechanisms from software architecture, application mode, and data exchange protocol. These mechanisms have been integrated into a groupware solution, which was validated by a planning team in a truly geographically dispersed condition. Analysis of the validation results revealed that the proposed solution is feasible for real-time collaborative 4D planning to gain a robust construction plan through collaborative teamwork. The realization of this solution triggers further considerations about its enhancement for wider groupware applications.