Rank regression for analysis of clustered data: A natural induced smoothing approach

We consider rank regression for clustered data analysis and investigate the induced smoothing method for obtaining the asymptotic covariance matrices of the parameter estimators. We prove that the induced estimating functions are asymptotically unbiased and the resulting estimators are strongly consistent and asymptotically normal. The induced smoothing approach provides an effective way for obtaining asymptotic covariance matrices for between- and within-cluster estimators and for a combined estimator to take account of within-cluster correlations. We also carry out extensive simulation studies to assess the performance of different estimators. The proposed methodology is substantially Much faster in computation and more stable in numerical results than the existing methods. We apply the proposed methodology to a dataset from a randomized clinical trial.

Weighted rank regression for clustered data analysis

We consider ranked-based regression models for clustered data analysis. A weighted Wilcoxon rank method is proposed to take account of within-cluster correlations and varying cluster sizes. The asymptotic normality of the resulting estimators is established. A method to estimate covariance of the estimators is also given, which can bypass estimation of the density function. Simulation studies are carried out to compare different estimators for a number of scenarios on the correlation structure, presence/absence of outliers and different correlation values. The proposed methods appear to perform well, in particular, the one incorporating the correlation in the weighting achieves the highest efficiency and robustness against misspecification of correlation structure and outliers. A real example is provided for illustration.

Rank-based regression for analysis of repeated measures

We consider rank-based regression models for repeated measures. To account for possible withinsubject correlations, we decompose the total ranks into between- and within-subject ranks and obtain two different estimators based on between- and within-subject ranks. A simple perturbation method is then introduced to generate bootstrap replicates of the estimating functions and the parameter estimates. This provides a convenient way for combining the corresponding two types of estimating function for more efficient estimation.

Standard errors and covariance matrices for smoothed rank estimators

A 'pseudo-Bayesian' interpretation of standard errors yields a natural induced smoothing of statistical estimating functions. When applied to rank estimation, the lack of smoothness which prevents standard error estimation is remedied. Efficiency and robustness are preserved, while the smoothed estimation has excellent computational properties. In particular, convergence of the iterative equation for standard error is fast, and standard error calculation becomes asymptotically a one-step procedure. This property also extends to covariance matrix calculation for rank estimates in multi-parameter problems. Examples, and some simple explanations, are given.

Management of plant invasions mediated by frugivore interactions

1. Some of the most damaging invasive plants are dispersed by frugivores and this is an area of emerging importance in weed management. It highlights the need for practical information on how frugivores affect weed population dynamics and spread, how frugivore populations are affected by weeds and what management recommendations are available. 2. Fruit traits influence frugivore choice. Fruit size, the presence of an inedible peel, defensive chemistry, crop size and phenology may all be useful traits for consideration in screening and eradication programmes. By considering the effect of these traits on the probability, quality and quantity of seed dispersal, it may be possible to rank invasive species by their desirability to frugivores. Fruit traits can also be manipulated with biocontrol agents. 3. Functional groups of frugivores can be assembled according to broad species groupings, and further refined according to size, gape size, pre- and post-ingestion processing techniques and movement patterns, to predict dispersal and establishment patterns for plant introductions. 4. Landscape fragmentation can increase frugivore dispersal of invasives, as many invasive plants and dispersers readily use disturbed matrix environments and fragment edges. Dispersal to particular landscape features, such as perches and edges, can be manipulated to function as seed sinks if control measures are concentrated in these areas. 5. Where invasive plants comprise part of the diet of native frugivores, there may be a conservation conflict between control of the invasive and maintaining populations of the native frugivore, especially where other threats such as habitat destruction have reduced populations of native fruit species. 6. Synthesis and applications. Development of functional groups of frugivore-dispersed invasive plants and dispersers will enable us to develop predictions for novel dispersal interactions at both population and community scales. Increasingly sophisticated mechanistic seed dispersal models combined with spatially explicit simulations show much promise for providing weed managers with the information they need to develop strategies for surveying, eradicating and managing plant invasions. Possible conservation conflicts mean that understanding the nature of the invasive plant-frugivore interaction is essential for determining appropriate management.

Valuation of reduced eutrophication in the Gulf of Finland : Choice experiment with attention to heterogeneous and discontinuous preferences and respondent uncertainty

Eutrophication of the Baltic Sea is a serious problem. This thesis estimates the benefit to Finns from reduced eutrophication in the Gulf of Finland, the most eutrophied part of the Baltic Sea, by applying the choice experiment method, which belongs to the family of stated preference methods. Because stated preference methods have been subject to criticism, e.g., due to their hypothetical survey context, this thesis contributes to the discussion by studying two anomalies that may lead to biased welfare estimates: respondent uncertainty and preference discontinuity. The former refers to the difficulty of stating one s preferences for an environmental good in a hypothetical context. The latter implies a departure from the continuity assumption of conventional consumer theory, which forms the basis for the method and the analysis. In the three essays of the thesis, discrete choice data are analyzed with the multinomial logit and mixed logit models. On average, Finns are willing to contribute to the water quality improvement. The probability for willingness increases with residential or recreational contact with the gulf, higher than average income, younger than average age, and the absence of dependent children in the household. On average, for Finns the relatively most important characteristic of water quality is water clarity followed by the desire for fewer occurrences of blue-green algae. For future nutrient reduction scenarios, the annual mean household willingness to pay estimates range from 271 to 448 and the aggregate welfare estimates for Finns range from 28 billion to 54 billion euros, depending on the model and the intensity of the reduction. Out of the respondents (N=726), 72.1% state in a follow-up question that they are either Certain or Quite certain about their answer when choosing the preferred alternative in the experiment. Based on the analysis of other follow-up questions and another sample (N=307), 10.4% of the respondents are identified as potentially having discontinuous preferences. In relation to both anomalies, the respondent- and questionnaire-specific variables are found among the underlying causes and a departure from standard analysis may improve the model fit and the efficiency of estimates, depending on the chosen modeling approach. The introduction of uncertainty about the future state of the Gulf increases the acceptance of the valuation scenario which may indicate an increased credibility of a proposed scenario. In conclusion, modeling preference heterogeneity is an essential part of the analysis of discrete choice data. The results regarding uncertainty in stating one s preferences and non-standard choice behavior are promising: accounting for these anomalies in the analysis may improve the precision of the estimates of benefit from reduced eutrophication in the Gulf of Finland.

Evaluation of the efficacy and economics of irrigation management, plant resistance and Brassica(spot)(TM) models for management of white blister on Brassica crops

Options for the integrated management of white blister (caused by Albugo candida) of Brassica crops include the use of well timed overhead irrigation, resistant cultivars, programs of weekly fungicide sprays or strategic fungicide applications based on the disease risk prediction model, Brassica(spot)(TM). Initial systematic surveys of radish producers near Melbourne, Victoria, indicated that crops irrigated overhead in the morning (0800-1200 h) had a lower incidence of white blister than those irrigated overhead in the evening (2000-2400 h). A field trial was conducted from July to November 2008 on a broccoli crop located west of Melbourne to determine the efficacy and economics of different practices used for white blister control, modifying irrigation timing, growing a resistant cultivar and timing spray applications based on Brassica(spot)(TM). Growing the resistant cultivar, 'Tyson', instead of the susceptible cultivar, 'Ironman', reduced disease incidence on broccoli heads by 99 %. Overhead irrigation at 0400 h instead of 2000 h reduced disease incidence by 58 %. A weekly spray program or a spray regime based on either of two versions of the Brassica(spot)(TM) model provided similar disease control and reduced disease incidence by 72 to 83 %. However, use of the Brassica(spot)(TM) models greatly reduced the number of sprays required for control from 14 to one or two. An economic analysis showed that growing the more resistant cultivar increased farm profit per ha by 12 %, choosing morning irrigation by 3 % and using the disease risk predictive models compared with weekly sprays by 15 %. The disease risk predictive models were 4 % more profitable than the unsprayed control.

Gene flow from transgenic plant populations: models and applications for risk assessment

The future use of genetically modified (GM) plants in food, feed and biomass production requires a careful consideration of possible risks related to the unintended spread of trangenes into new habitats. This may occur via introgression of the transgene to conventional genotypes, due to cross-pollination, and via the invasion of GM plants to new habitats. Assessment of possible environmental impacts of GM plants requires estimation of the level of gene flow from a GM population. Furthermore, management measures for reducing gene flow from GM populations are needed in order to prevent possible unwanted effects of transgenes on ecosystems. This work develops modeling tools for estimating gene flow from GM plant populations in boreal environments and for investigating the mechanisms of the gene flow process. To describe spatial dimensions of the gene flow, dispersal models are developed for the local and regional scale spread of pollen grains and seeds, with special emphasis on wind dispersal. This study provides tools for describing cross-pollination between GM and conventional populations and for estimating the levels of transgenic contamination of the conventional crops. For perennial populations, a modeling framework describing the dynamics of plants and genotypes is developed, in order to estimate the gene flow process over a sequence of years. The dispersal of airborne pollen and seeds cannot be easily controlled, and small amounts of these particles are likely to disperse over long distances. Wind dispersal processes are highly stochastic due to variation in atmospheric conditions, so that there may be considerable variation between individual dispersal patterns. This, in turn, is reflected to the large amount of variation in annual levels of cross-pollination between GM and conventional populations. Even though land-use practices have effects on the average levels of cross-pollination between GM and conventional fields, the level of transgenic contamination of a conventional crop remains highly stochastic. The demographic effects of a transgene have impacts on the establishment of trangenic plants amongst conventional genotypes of the same species. If the transgene gives a plant a considerable fitness advantage in comparison to conventional genotypes, the spread of transgenes to conventional population can be strongly increased. In such cases, dominance of the transgene considerably increases gene flow from GM to conventional populations, due to the enhanced fitness of heterozygous hybrids. The fitness of GM plants in conventional populations can be reduced by linking the selectively favoured primary transgene to a disfavoured mitigation transgene. Recombination between these transgenes is a major risk related to this technique, especially because it tends to take place amongst the conventional genotypes and thus promotes the establishment of invasive transgenic plants in conventional populations.

Cellular Automata Models of Traffic Behavior in Presence of Speed Breaking Structures

In this article, we study traffic flow in the presence of speed breaking structures. The speed breakers are typically used to reduce the local speed of vehicles near certain institutions such as schools and hospitals. Through a cellular automata model we study the impact of such structures on global traffic characteristics. The simulation results indicate that the presence of speed breakers could reduce the global flow under moderate global densities. However, under low and high global density traffic regime the presence of speed breakers does not have an impact on the global flow. Further the speed limit enforced by the speed breaker creates a phase distinction. For a given global density and slowdown probability, as the speed limit enforced by the speed breaker increases, the traffic moves from the reduced flow phase to maximum flow phase. This underlines the importance of proper design of these structures to avoid undesired flow restrictions.

Reduced incidence of foot-related hospitalisation and amputation amongst persons with diabetes in Queensland, Australia

Objective To determine trends in the incidence of foot-related hospitalisation and amputation amongst persons with diabetes in Queensland (Australia) between 2005 and 2010 that coincided with changes in state-wide ambulatory diabetic foot-related complication management. Methods All data from cases admitted for the principal reason of diabetes foot-related hospitalisation or amputation in Queensland from 2005–2010 were obtained from the Queensland Hospital Admitted Patient Data Collection dataset. Incidence rates for foot-related hospitalisation (admissions, bed days used) and amputation (total, minor, major) cases amongst persons with diabetes were calculated per 1,000 person-years with diabetes (diabetes population) and per 100,000 person-years (general population). Age-sex standardised incidence and age-sex adjusted Poisson regression models were also calculated for the general population. Results There were 4,443 amputations, 24,917 hospital admissions and 260,085 bed days used for diabetes foot-related complications in Queensland. Incidence per 1,000 person-years with diabetes decreased from 2005 to 2010: 43.0% for hospital admissions (36.6 to 20.9), 40.1% bed days (391 to 234), 40.0% total amputations (6.47 to 3.88), 45.0% major amputations (2.18 to 1.20), 37.5% minor amputations (4.29 to 2.68) (p < 0.01 respectively). Age-sex standardised incidence per 100,000 person-years in the general population also decreased from 2005 to 2010: 23.3% hospital admissions (105.1 to 80.6), 19.5% bed days (1,122 to 903), 19.3% total amputations (18.57 to 14.99), 26.4% major amputations (6.26 to 4.61), 15.7% minor amputations (12.32 to 10.38) (p < 0.01 respectively). The age-sex adjusted incidence rates per calendar year decreased in the general population (rate ratio (95% CI)); hospital admissions 0.949 (0.942–0.956), bed days 0.964 (0.962–0.966), total amputations 0.962 (0.946–0.979), major amputations 0.945 (0.917–0.974), minor amputations 0.970 (0.950–0.991) (p < 0.05 respectively). Conclusions There were significant reductions in the incidence of foot-related hospitalisation and amputation amongst persons with diabetes in the population of Queensland over a recent six-year period.

Spiral-Wave Turbulence and Its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control chemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation.

Inference on Cointegration in Vector Autoregressive Models (summary section only)

In the thesis we consider inference for cointegration in vector autoregressive (VAR) models. The thesis consists of an introduction and four papers. The first paper proposes a new test for cointegration in VAR models that is directly based on the eigenvalues of the least squares (LS) estimate of the autoregressive matrix. In the second paper we compare a small sample correction for the likelihood ratio (LR) test of cointegrating rank and the bootstrap. The simulation experiments show that the bootstrap works very well in practice and dominates the correction factor. The tests are applied to international stock prices data, and the .nite sample performance of the tests are investigated by simulating the data. The third paper studies the demand for money in Sweden 1970—2000 using the I(2) model. In the fourth paper we re-examine the evidence of cointegration between international stock prices. The paper shows that some of the previous empirical results can be explained by the small-sample bias and size distortion of Johansen’s LR tests for cointegration. In all papers we work with two data sets. The first data set is a Swedish money demand data set with observations on the money stock, the consumer price index, gross domestic product (GDP), the short-term interest rate and the long-term interest rate. The data are quarterly and the sample period is 1970(1)—2000(1). The second data set consists of month-end stock market index observations for Finland, France, Germany, Sweden, the United Kingdom and the United States from 1980(1) to 1997(2). Both data sets are typical of the sample sizes encountered in economic data, and the applications illustrate the usefulness of the models and tests discussed in the thesis.

Estimation of signals in colored non gaussian noise based on Gaussian Mixture models

Non-Gaussianity of signals/noise often results in significant performance degradation for systems, which are designed using the Gaussian assumption. So non-Gaussian signals/noise require a different modelling and processing approach. In this paper, we discuss a new Bayesian estimation technique for non-Gaussian signals corrupted by colored non Gaussian noise. The method is based on using zero mean finite Gaussian Mixture Models (GMMs) for signal and noise. The estimation is done using an adaptive non-causal nonlinear filtering technique. The method involves deriving an estimator in terms of the GMM parameters, which are in turn estimated using the EM algorithm. The proposed filter is of finite length and offers computational feasibility. The simulations show that the proposed method gives a significant improvement compared to the linear filter for a wide variety of noise conditions, including impulsive noise. We also claim that the estimation of signal using the correlation with past and future samples leads to reduced mean squared error as compared to signal estimation based on past samples only.

Distributed space-time codes with reduced decoding complexity

We address the problem of distributed space-time coding with reduced decoding complexity for wireless relay network. The transmission protocol follows a two-hop model wherein the source transmits a vector in the first hop and in the second hop the relays transmit a vector, which is a transformation of the received vector by a relay-specific unitary transformation. Design criteria is derived for this system model and codes are proposed that achieve full diversity. For a fixed number of relay nodes, the general system model considered in this paper admits code constructions with lower decoding complexity compared to codes based on some earlier system models.

Models of Dispersal and Diversification

Ecology and evolutionary biology is the study of life on this planet. One of the many methods applied to answering the great diversity of questions regarding the lives and characteristics of individual organisms, is the utilization of mathematical models. Such models are used in a wide variety of ways. Some help us to reason, functioning as aids to, or substitutes for, our own fallible logic, thus making argumentation and thinking clearer. Models which help our reasoning can lead to conceptual clarification; by expressing ideas in algebraic terms, the relationship between different concepts become clearer. Other mathematical models are used to better understand yet more complicated models, or to develop mathematical tools for their analysis. Though helping us to reason and being used as tools in the craftmanship of science, many models do not tell us much about the real biological phenomena we are, at least initially, interested in. The main reason for this is that any mathematical model is a simplification of the real world, reducing the complexity and variety of interactions and idiosynchracies of individual organisms. What such models can tell us, however, both is and has been very valuable throughout the history of ecology and evolution. Minimally, a model simplifying the complex world can tell us that in principle, the patterns produced in a model could also be produced in the real world. We can never know how different a simplified mathematical representation is from the real world, but the similarity models do strive for, gives us confidence that their results could apply. This thesis deals with a variety of different models, used for different purposes. One model deals with how one can measure and analyse invasions; the expanding phase of invasive species. Earlier analyses claims to have shown that such invasions can be a regulated phenomena, that higher invasion speeds at a given point in time will lead to a reduction in speed. Two simple mathematical models show that analysis on this particular measure of invasion speed need not be evidence of regulation. In the context of dispersal evolution, two models acting as proof-of-principle are presented. Parent-offspring conflict emerges when there are different evolutionary optima for adaptive behavior for parents and offspring. We show that the evolution of dispersal distances can entail such a conflict, and that under parental control of dispersal (as, for example, in higher plants) wider dispersal kernels are optimal. We also show that dispersal homeostasis can be optimal; in a setting where dispersal decisions (to leave or stay in a natal patch) are made, strategies that divide their seeds or eggs into fractions that disperse or not, as opposed to randomized for each seed, can prevail. We also present a model of the evolution of bet-hedging strategies; evolutionary adaptations that occur despite their fitness, on average, being lower than a competing strategy. Such strategies can win in the long run because they have a reduced variance in fitness coupled with a reduction in mean fitness, and fitness is of a multiplicative nature across generations, and therefore sensitive to variability. This model is used for conceptual clarification; by developing a population genetical model with uncertain fitness and expressing genotypic variance in fitness as a product between individual level variance and correlations between individuals of a genotype. We arrive at expressions that intuitively reflect two of the main categorizations of bet-hedging strategies; conservative vs diversifying and within- vs between-generation bet hedging. In addition, this model shows that these divisions in fact are false dichotomies.