Maximum likelihood estimation of higher-order integer-valued autoregressive processes

In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 701–722] and develop a general framework for maximum likelihood (ML) analysis of higher-order integer-valued autoregressive processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is binomial. A recursive representation of the transition probability of the model is proposed. Based on this transition probability, we derive expressions for the score function and the Fisher information matrix, which form the basis for ML estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. Using the INAR(2) speci?cation with binomial thinning and Poisson innovations, we examine both the asymptotic e?ciency and ?nite sample properties of the ML estimator in relation to the widely used conditional least
squares (CLS) and Yule–Walker (YW) estimators. We conclude that, if the Poisson assumption can be justi?ed, there are substantial gains to be had from using ML especially when the thinning parameters are large.

Fronts, jumps and secondary introductions suggested as different invasion patterns in marine species, with an increase in spread rates over time

Not all introduced (invasive) species in a region will spread from a single point of introduction. Long-distance dispersal or further introductions can obscure the pattern of spread, but the regional importance of such processes is difficult to gauge. These difficulties are further compounded when information on the multiple scale process of invasive species range expansion is reduced to one-dimensional estimates of spread (e. g. km yr(-1)). We therefore compared the results of two different metrics of range expansion: maximum linear rate of spread and accumulation of occupied grid squares (50 x 50 km) over time. An analysis of records for 54 species of introduced marine macrophytes in the Mediterranean and northeast Atlantic revealed cases where the invasion process was probably missed (e. g. Atlantic Bonnemaisonia hamifera) and suggested cases of secondary introductions or erratic jump dispersal (Dasysiphonia sp. and Womersleyella setacea). A majority of species analysed showed evidence for an accumulation of invaded sites without a clear invasion front. Estimates of spread rate are increasing for more recent introductions. The increase is greater than can be accounted for by temporally varying search effort and implies a historical increase in vector efficiency and/or a decreased resistance of native communities to invasion.

Intertidal molluscan and algal species richness around the UK coast

Geographically referenced databases of species records are becoming increasingly available. Doubts over the heterogeneous quality of the underlying data may restrict analyses of such collated databases. We partitioned the spatial variation in species richness of littoral algae and molluscs from the UK National Biodiversity Network database into a smoothed mesoscale component and a local component. Trend surface analysis (TSA) was used to define the mesoscale patterns of species richness, leaving a local residual component that lacked spatial autocorrelation. The analysis was based on 10 km grid squares with 115035 records of littoral algae (729 species) and 66879 records of littoral molluscs (569 species). The TSA identified variation in algal and molluscan species richness with a characteristic length scale of approximately 120 km. Locations of the most species-rich grid squares were consistent with the southern and western bias of species richness in the UK marine flora and fauna. The TSA also identified areas which showed significant changes in the spatial pattern of species richness: breakpoints, which correspond to major headlands along the south coast of England. Patterns of algal and molluscan species richness were broadly congruent. Residual variability was strongly influenced by proxies of collection effort, but local environmental variables including length of the coastline and variability in wave exposure were also important. Relative to the underlying trend, local species richness hotspots occurred on all coasts. While there is some justification for scepticism in analyses of heterogeneous datasets, our results indicate that the analysis of collated datasets can be informative.

Modelling distributional trends to inform conservation strategies for endangered species

Aim: Species loss has increased significantly over the last 1000 years and is ultimately attributed to the direct and indirect consequences of increased human population growth across the planet. A growing number of species are becoming endangered and require human intervention to prevent their local extirpation or complete extinction. Management strategies aimed at mitigating a species loss can benefit greatly from empirical approaches that indicate the rate of decline of a species providing objective information on the need for immediate conservation actions, e.g. captive breeding; however, this is rarely employed. The current study used a novel method to examine the distributional trends of a model endangered species, the freshwater pearl mussel, Margaritifera margaritifera (L.).
Location: United Kingdom and Republic of Ireland.
Methods: Using species presence data within 10-km grid squares since records began three-parameter logistic regression curves were fitted to extrapolate an estimated date of regional extinction.
Results: This study has shown that freshwater pearl mussel distribution has contracted since known historical records and outlier populations were lost first. Within the United Kingdom and Republic of Ireland, distribution loss has been greatest in Scotland, Northern Ireland, Wales and England, respectively, with the Republic of Ireland containing the highest relative proportion of M. margaritifera distribution, in 1998.
Main conclusions: This study provides empirical evidence that this species could become extinct throughout countries within the United Kingdom within 170 years under the current trends and emphasizes that regionally specific management strategies need to be implemented to prevent extirpation of this species.

Two-stage RBF network construction based on particle swarm optimization

The conventional radial basis function (RBF) network optimization methods, such as orthogonal least squares or the two-stage selection, can produce a sparse network with satisfactory generalization capability. However, the RBF width, as a nonlinear parameter in the network, is not easy to determine. In the aforementioned methods, the width is always pre-determined, either by trial-and-error, or generated randomly. Furthermore, all hidden nodes share the same RBF width. This will inevitably reduce the network performance, and more RBF centres may then be needed to meet a desired modelling specification. In this paper we investigate a new two-stage construction algorithm for RBF networks. It utilizes the particle swarm optimization method to search for the optimal RBF centres and their associated widths. Although the new method needs more computation than conventional approaches, it can greatly reduce the model size and improve model generalization performance. The effectiveness of the proposed technique is confirmed by two numerical simulation examples.

Fast automatic two-stage nonlinear model identification based on the extreme learning machine

It is convenient and effective to solve nonlinear problems with a model that has a linear-in-the-parameters (LITP) structure. However, the nonlinear parameters (e.g. the width of Gaussian function) of each model term needs to be pre-determined either from expert experience or through exhaustive search. An alternative approach is to optimize them by a gradient-based technique (e.g. Newton’s method). Unfortunately, all of these methods still need a lot of computations. Recently, the extreme learning machine (ELM) has shown its advantages in terms of fast learning from data, but the sparsity of the constructed model cannot be guaranteed. This paper proposes a novel algorithm for automatic construction of a nonlinear system model based on the extreme learning machine. This is achieved by effectively integrating the ELM and leave-one-out (LOO) cross validation with our two-stage stepwise construction procedure [1]. The main objective is to improve the compactness and generalization capability of the model constructed by the ELM method. Numerical analysis shows that the proposed algorithm only involves about half of the computation of orthogonal least squares (OLS) based method. Simulation examples are included to confirm the efficacy and superiority of the proposed technique.

The Oscillations of Tau Pegasi

We present extensive spectroscopic time series observations of the multiperiodic, rapidly rotating, delta Scuti star tau Pegasi. Information about the oscillations is contained within the patterns of line-profile variation of the star's blended absorption-line spectrum. We introduce the new technique of Doppler deconvolution with which to extract these patterns by modeling the intrinsic stellar spectrum and the broadening functions for each spectrum in the time series. Frequencies and modes of oscillation are identified from the variations using the technique of Fourier-Doppler imaging and a two-dimensional least-squares cleaning algorithm. We find a rich mode spectrum with degrees up to l = 20 and with frequencies below about 35 cycles day-1. Those modes with the largest amplitudes have frequencies that lie within a narrow band. We conclude that the observed spectrum can be explained if the modes of tau Peg propagate in the prograde direction with l ~= |m| and with frequencies that are about equal in the corotating frame of the star. We discuss the implications of these results for the prospect of delta Scuti seismology.

Monitoring and population estimation of the European badger (Meles meles) in Northern Ireland

The estimation of animal abundance has a central role in wildlife management and research, including the role of badgers Meles meles in bovine tuberculosis transmission to cattle. This is the first study to examine temporal change in the badger population of Northern Ireland over amedium- to long-term time frame of 14-18 years by repeating a national survey first conducted during 1990-1993. A total of 212 1-km2 squares were surveyed during 2007-2008 and the number, type and activity of setts therein recorded. Badgers were widespread with 75% of squares containing at least one sett. The mean density of activemain setts,which was equivalent to badger social group density, was 0.56 (95%CI: 0.46-0.67) active main setts per km2 during 2007-2008. Social group density varied significantly among landclass groups and counties. The total number of social groups was estimated at 7,600 (95%CI: 6,200-9,000) and, not withstanding probable sources of error in estimating social group size, the total abundance of badgers was estimated to be 34,100 (95% CI: 26,200-42,000). There was no significant change in the badger population from that recorded during 1990-1993. A resource selection model provided a relative probability of sett construction at a spatial scale of 25m. Sett locations were negatively associated with elevation and positively associated with slope, aspect, soil sand content, the presence of cover, and the area of improved grassland and arable agriculture within 300 m.

Development of the kinetic model of platinum catalyzed ammonia oxidation in a microreactor

The ammonia oxidation reaction on supported polycrystalline platinum catalyst was investigated in an aluminum-based microreactor. An extensive set of reactions was included in the chemical reactor modeling to facilitate the construction of a kinetic model capable of satisfactory predictions for a wide range of conditions (NH3 partial pressure, 0.01-0.12 atm; O-2 partial pressure, 0.10-0.88 atm; temperature, 523-673 K; contact time, 0.3-0.7 ms). The elementary surface reactions used in developing the mechanism were chosen based on the literature data concerning ammonia oxidation on a Pt catalyst. Parameter estimates for the kinetic model were obtained using multi-response least squares regression analysis using the isothermal plug-flow reactor approximation. To evaluate the model, the behavior of a microstructured reactor was simulated by means of a complete Navier-Stokes model accounting for the reactions on the catalyst surface and the effect of temperature on the physico-chemical properties of the reacting mixture. In this way, the effect of the catalytic wall temperature non-uniformity and the effect of a boundary layer on the ammonia conversion and selectivity were examined. After further optimization of appropriate kinetic parameters, the calculated selectivities and product yields agree very well with the values actually measured in the microreactor. (C) 2002 Elsevier Science B.V. All rights reserved.

Non-radial pulsation, rotation and outburst in the Be star omega Orionis from the MuSiCoS 1998 campaign

omega Ori (HD37490, HR1934) is a Be star known to have presented variations. In order to investigate the nature and origin of its short-term and mid-term variability, a study is performed of several spectral lines (Halpha, Hdelta, HeI 4471, 4713, 4921, 5876, 6678, CII 4267, 6578, 6583, Mg II 4481, Si III 4553 and Si II 6347), based on 249 high signal-to-noise high-resolution spectra taken with 8 telescopes over 22 consecutive nights during the MuSiCoS (Multi SIte COntinuous Spectroscopy) campaign in November-December 1998. The stellar parameters are revisited and the projected rotational velocity (v sin i = 179 km s(-1)) is redetermined using several methods. With the MuSiCoS 98 dataset, a time series analysis of line-profile variations (LPVs) is performed using the Restricted Local Cleanest (RLC) algorithm and a least squares method. The behaviour of the velocity of the centroid of the lines, the equivalent widths and the apparent vsini for several lines, as well as Violet and Red components of photospheric lines affected by emission (red He i lines, Si II 6347, CII 6578, 6583) are analyzed. The non-radial pulsation (NRP) model is examined using phase diagrams and the Fourier-Doppler Imaging (FDI) method. The LPVs are consistent with a NRP mode with l = 2 or 3, \m\ = 2 with frequency 1.03 cd(-1). It is shown that an emission line outburst occurred in the middle of the campaign. Two scenarios are proposed to explain the behaviour of a dense cloud, temporarily orbiting around the star with a frequency 0.46 c d(-1), in relation to the outburst.

Regression analysis of spatial data

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

The prediction of intake potential and organic matter digestibility of grass silages by near infrared spectroscopy analysis of undried samples

A study was undertaken to examine a range of sample preparation and near infrared reflectance spectroscopy (NIPS) methodologies, using undried samples, for predicting organic matter digestibility (OMD g kg(-1)) and ad libitum intake (g kg(-1) W-0.75) of grass silages. A total of eight sample preparation/NIRS scanning methods were examined involving three extents of silage comminution, two liquid extracts and scanning via either external probe (1100-2200 nm) or internal cell (1100-2500 nm). The spectral data (log 1/R) for each of the eight methods were examined by three regression techniques each with a range of data transformations. The 136 silages used in the study were obtained from farms across Northern Ireland, over a two year period, and had in vivo OMD (sheep) and ad libitum intake (cattle) determined under uniform conditions. In the comparisons of the eight sample preparation/scanning methods, and the differing mathematical treatments of the spectral data, the sample population was divided into calibration (n = 91) and validation (n = 45) sets. The standard error of performance (SEP) on the validation set was used in comparisons of prediction accuracy. Across all 8 sample preparation/scanning methods, the modified partial least squares (MPLS) technique, generally minimized SEP's for both OMD and intake. The accuracy of prediction also increased with degree of comminution of the forage and with scanning by internal cell rather than external probe. The system providing the lowest SEP used the MPLS regression technique on spectra from the finely milled material scanned through the internal cell. This resulted in SEP and R-2 (variance accounted for in validation set) values of 24 (g/kg OM) and 0.88 (OMD) and 5.37 (g/kg W-0.75) and 0.77 (intake) respectively. These data indicate that with appropriate techniques NIRS scanning of undried samples of grass silage can produce predictions of intake and digestibility with accuracies similar to those achieved previously using NIRS with dried samples. (C) 1998 Elsevier Science B.V.

Investigation of the Human Brain Metabolome to Identify Potential Markers for Early Diagnosis and Therapeutic Targets of Alzheimer’s Disease

A study combining high resolution mass spectrometry (liquid chromatography-quadrupole time-of-flight-mass spectrometry, UPLC-QTof-MS) and chemometrics for the analysis of post-mortem brain tissue from subjects with Alzheimer’s disease (AD) (n = 15) and healthy age-matched controls (n = 15) was undertaken. The huge potential of this metabolomics approach for distinguishing AD cases is underlined by the correct prediction of disease status in 94–97% of cases. Predictive power was confirmed in a blind test set of 60 samples, reaching 100% diagnostic accuracy. The approach also indicated compounds significantly altered in concentration following the onset of human AD. Using orthogonal partial least-squares discriminant analysis (OPLS-DA), a multivariate model was created for both modes of acquisition explaining the maximum amount of variation between sample groups (Positive Mode-R2 = 97%; Q2 = 93%; root mean squared error of validation (RMSEV) = 13%; Negative Mode-R2 = 99%; Q2 = 92%; RMSEV = 15%). In brain extracts, 1264 and 1457 ions of interest were detected for the different modes of acquisition (positive and negative, respectively). Incorporation of gender into the model increased predictive accuracy and decreased RMSEV values. High resolution UPLC-QTof-MS has not previously been employed to biochemically profile post-mortem brain tissue, and the novel methods described and validated herein prove its potential for making new discoveries related to the etiology, pathophysiology, and treatment of degenerative brain disorders.

Population enumeration and assessing conservation status in a widespread amphibian: A case study of Rana temporaria in Ireland

Global amphibian declines are a major element of the current biodiversity crisis. Monitoring changes in the distribution and abundance of target species is a basic component in conservation decision making and requires robust and repeatable sampling. For EU member states, surveillance of designated species, including the common frog Rana temporaria, is a formal requirement of the 'EC Habitats & Species Directive'. We deployed established methods for estimating frog population density at local water bodies and extrapolated these to the national and ecoregion scale. Spawn occurred at 49.4% of water bodies and 70.1% of independent 500-m survey squares. Using spawn mat area, we estimated the number of adult breeding females and subsequently the total population assuming a sex ratio of 1:1. A negative binomial model suggested that mean frog density was 23.5 frogsha [95% confidence interval (CI) 14.9-44.0] equating to 196M frogs (95%CI 124M-367M) throughout Ireland. A total of 86% of frogs bred in drainage ditches, which were a notably common feature of the landscape. The recorded distribution of the species did not change significantly between the last Article 17 reporting period (1993-2006) and the current period (2007-2011) throughout the Republic of Ireland. Recording effort was markedly lower in Northern Ireland, which led to an apparent decline in the recorded distribution. We highlight the need to coordinate biological surveys between adjacent political jurisdictions that share a common ecoregion to avoid apparent disparities in the quality of distributional information. Power analysis suggested that a reduced sample of 40-50 survey squares is sufficient to detect a 30% decline (consistent with the International Union for Conservation of Nature Category of 'Vulnerable') at 80% power providing guidance for minimizing future survey effort. Our results provin assessments for R. temporaria and other clump-spawning amphibians. 2013 The Zoological Society of London.

Chemometric techniques in multivariate statistical modelling of process plant

The techniques of principal component analysis (PCA) and partial least squares (PLS) are introduced from the point of view of providing a multivariate statistical method for modelling process plants. The advantages and limitations of PCA and PLS are discussed from the perspective of the type of data and problems that might be encountered in this application area. These concepts are exemplified by two case studies dealing first with data from a continuous stirred tank reactor (CSTR) simulation and second a literature source describing a low-density polyethylene (LDPE) reactor simulation.