Joint Regression and Association Models for Repeated Categorical Responses

The focus of this study is on statistical analysis of categorical responses, where the response values are dependent of each other. The most typical example of this kind of dependence is when repeated responses have been obtained from the same study unit. For example, in Paper I, the response of interest is the pneumococcal nasopharengyal carriage (yes/no) on 329 children. For each child, the carriage is measured nine times during the first 18 months of life, and thus repeated respones on each child cannot be assumed independent of each other. In the case of the above example, the interest typically lies in the carriage prevalence, and whether different risk factors affect the prevalence. Regression analysis is the established method for studying the effects of risk factors. In order to make correct inferences from the regression model, the associations between repeated responses need to be taken into account. The analysis of repeated categorical responses typically focus on regression modelling. However, further insights can also be gained by investigating the structure of the association. The central theme in this study is on the development of joint regression and association models. The analysis of repeated, or otherwise clustered, categorical responses is computationally difficult. Likelihood-based inference is often feasible only when the number of repeated responses for each study unit is small. In Paper IV, an algorithm is presented, which substantially facilitates maximum likelihood fitting, especially when the number of repeated responses increase. In addition, a notable result arising from this work is the freely available software for likelihood-based estimation of clustered categorical responses.

Integrating pest population models with biophysical crop models to better represent the farming system

Farming systems frameworks such as the Agricultural Production Systems simulator (APSIM) represent fluxes through the soil, plant and atmosphere of the system well, but do not generally consider the biotic constraints that function within the system. We designed a method that allowed population models built in DYMEX to interact with APSIM. The simulator engine component of the DYMEX population-modelling platform was wrapped within an APSIM module allowing it to get and set variable values in other APSIM models running in the simulation. A rust model developed in DYMEX is used to demonstrate how the developing rust population reduces the crop's green leaf area. The success of the linking process is seen in the interaction of the two models and how changes in rust population on the crop's leaves feedback to the APSIM crop modifying the growth and development of the crop's leaf area. This linking of population models to simulate pest populations and biophysical models to simulate crop growth and development increases the complexity of the simulation, but provides a tool to investigate biotic constraints within farming systems and further moves APSIM towards being an agro-ecological framework.

Mathematical models on the impact of noise and dyadic molecular structures on the properties of a cardiac myocyte

In cardiac myocytes (heart muscle cells), coupling of electric signal known as the action potential to contraction of the heart depends crucially on calcium-induced calcium release (CICR) in a microdomain known as the dyad. During CICR, the peak number of free calcium ions (Ca) present in the dyad is small, typically estimated to be within range 1-100. Since the free Ca ions mediate CICR, noise in Ca signaling due to the small number of free calcium ions influences Excitation-Contraction (EC) coupling gain. Noise in Ca signaling is only one noise type influencing cardiac myocytes, e.g., ion channels playing a central role in action potential propagation are stochastic machines, each of which gates more or less randomly, which produces gating noise present in membrane currents. How various noise sources influence macroscopic properties of a myocyte, how noise is attenuated and taken advantage of are largely open questions. In this thesis, the impact of noise on CICR, EC coupling and, more generally, macroscopic properties of a cardiac myocyte is investigated at multiple levels of detail using mathematical models. Complementarily to the investigation of the impact of noise on CICR, computationally-efficient yet spatially-detailed models of CICR are developed. The results of this thesis show that (1) gating noise due to the high-activity mode of L-type calcium channels playing a major role in CICR may induce early after-depolarizations associated with polymorphic tachycardia, which is a frequent precursor to sudden cardiac death in heart failure patients; (2) an increased level of voltage noise typically increases action potential duration and it skews distribution of action potential durations toward long durations in cardiac myocytes; and that (3) while a small number of Ca ions mediate CICR, Excitation-Contraction coupling is robust against this noise source, partly due to the shape of ryanodine receptor protein structures present in the cardiac dyad.

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.

Modeling Asymmetries in Financial Data with Multiplicative Error Models

This thesis addresses modeling of financial time series, especially stock market returns and daily price ranges. Modeling data of this kind can be approached with so-called multiplicative error models (MEM). These models nest several well known time series models such as GARCH, ACD and CARR models. They are able to capture many well established features of financial time series including volatility clustering and leptokurtosis. In contrast to these phenomena, different kinds of asymmetries have received relatively little attention in the existing literature. In this thesis asymmetries arise from various sources. They are observed in both conditional and unconditional distributions, for variables with non-negative values and for variables that have values on the real line. In the multivariate context asymmetries can be observed in the marginal distributions as well as in the relationships of the variables modeled. New methods for all these cases are proposed. Chapter 2 considers GARCH models and modeling of returns of two stock market indices. The chapter introduces the so-called generalized hyperbolic (GH) GARCH model to account for asymmetries in both conditional and unconditional distribution. In particular, two special cases of the GARCH-GH model which describe the data most accurately are proposed. They are found to improve the fit of the model when compared to symmetric GARCH models. The advantages of accounting for asymmetries are also observed through Value-at-Risk applications. Both theoretical and empirical contributions are provided in Chapter 3 of the thesis. In this chapter the so-called mixture conditional autoregressive range (MCARR) model is introduced, examined and applied to daily price ranges of the Hang Seng Index. The conditions for the strict and weak stationarity of the model as well as an expression for the autocorrelation function are obtained by writing the MCARR model as a first order autoregressive process with random coefficients. The chapter also introduces inverse gamma (IG) distribution to CARR models. The advantages of CARR-IG and MCARR-IG specifications over conventional CARR models are found in the empirical application both in- and out-of-sample. Chapter 4 discusses the simultaneous modeling of absolute returns and daily price ranges. In this part of the thesis a vector multiplicative error model (VMEM) with asymmetric Gumbel copula is found to provide substantial benefits over the existing VMEM models based on elliptical copulas. The proposed specification is able to capture the highly asymmetric dependence of the modeled variables thereby improving the performance of the model considerably. The economic significance of the results obtained is established when the information content of the volatility forecasts derived is examined.

Assessment of functional forms of crop yield loss models of invasive plant species applied in decision support tools and bioeconomic modelling

AbstractObjectives Decision support tools (DSTs) for invasive species management have had limited success in producing convincing results and meeting users' expectations. The problems could be linked to the functional form of model which represents the dynamic relationship between the invasive species and crop yield loss in the DSTs. The objectives of this study were: a) to compile and review the models tested on field experiments and applied to DSTs; and b) to do an empirical evaluation of some popular models and alternatives. Design and methods This study surveyed the literature and documented strengths and weaknesses of the functional forms of yield loss models. Some widely used models (linear, relative yield and hyperbolic models) and two potentially useful models (the double-scaled and density-scaled models) were evaluated for a wide range of weed densities, maximum potential yield loss and maximum yield loss per weed. Results Popular functional forms include hyperbolic, sigmoid, linear, quadratic and inverse models. Many basic models were modified to account for the effect of important factors (weather, tillage and growth stage of crop at weed emergence) influencing weed–crop interaction and to improve prediction accuracy. This limited their applicability for use in DSTs as they became less generalized in nature and often were applicable to a much narrower range of conditions than would be encountered in the use of DSTs. These factors' effects could be better accounted by using other techniques. Among the model empirically assessed, the linear model is a very simple model which appears to work well at sparse weed densities, but it produces unrealistic behaviour at high densities. The relative-yield model exhibits expected behaviour at high densities and high levels of maximum yield loss per weed but probably underestimates yield loss at low to intermediate densities. The hyperbolic model demonstrated reasonable behaviour at lower weed densities, but produced biologically unreasonable behaviour at low rates of loss per weed and high yield loss at the maximum weed density. The density-scaled model is not sensitive to the yield loss at maximum weed density in terms of the number of weeds that will produce a certain proportion of that maximum yield loss. The double-scaled model appeared to produce more robust estimates of the impact of weeds under a wide range of conditions. Conclusions Previously tested functional forms exhibit problems for use in DSTs for crop yield loss modelling. Of the models evaluated, the double-scaled model exhibits desirable qualitative behaviour under most circumstances.

Hazard Function Models to Estimate Mortality Rates Affecting Fish Populations with Application to the Sea Mullet (Mugil cephalus) Fishery on the Queensland Coast (Australia)

Fisheries management agencies around the world collect age data for the purpose of assessing the status of natural resources in their jurisdiction. Estimates of mortality rates represent a key information to assess the sustainability of fish stocks exploitation. Contrary to medical research or manufacturing where survival analysis is routinely applied to estimate failure rates, survival analysis has seldom been applied in fisheries stock assessment despite similar purposes between these fields of applied statistics. In this paper, we developed hazard functions to model the dynamic of an exploited fish population. These functions were used to estimate all parameters necessary for stock assessment (including natural and fishing mortality rates as well as gear selectivity) by maximum likelihood using age data from a sample of catch. This novel application of survival analysis to fisheries stock assessment was tested by Monte Carlo simulations to assert that it provided unbiased estimations of relevant quantities. The method was applied to the data from the Queensland (Australia) sea mullet (Mugil cephalus) commercial fishery collected between 2007 and 2014. It provided, for the first time, an estimate of natural mortality affecting this stock: 0.22±0.08 year −1 .

Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

Karnaugh map analysis and synthesis of threshold functions

A unate function can easily be identified on a Karnaugh map from the well-known property that it cons ist s only ofess en ti al prime implicante which intersect at a common implicant. The additional property that the plot of a unate function F(x, ... XII) on a Karnaugh map should possess in order that F may also be Ivrealizable (n';:; 6) has been found. It has been sh own that the I- realizability of a unate function F corresponds to the ' compac tness' of the plot of F. No resort to tho inequalities is made, and no pre-processing such as positivizing and ordering of the given function is required.

Threshold level of defocus to produce an accommodation response

To investigate the threshold level of defocus that induces a measurable objective change in accommodation response to a target at an intermediate distance.

Queuing Models for Estimating Aircraft Fleet Availability

The availability of a small fleet of aircraft in a flying-base, repair-depot combination is modeled and studied. First, a deterministic flow model relates parameters of interest and represents the state-of-the art in the planning of such systems. Second, a cyclic queue model shows the effect of the principal uncertainties in operation and repair and shows the consequent decrease in the availability of aircraft at the flying-base. Several options such as increasing fleet size, investments in additional repair facilities, or building reliability and maintainability into the individual aircraft during its life-cycle are open for increasing the availability. A life-cycle cost criterion brings out some of these features. Numerical results confirm Rose's prediction that there exists a minimal cost combination of end products and repair-depot capability to achieve a prescribed operational availability.

Evaluation of k-epsilon and RNG turbulence models for confined swirling and non-swirling flow

In a very recent study [1] the Renormalisation Group (RNG) turbulence model was used to obtain flow predictions in a strongly swirling quarl burner, and was found to perform well in predicting certain features that are not well captured using less sophisticated models of turbulence. The implication is that the RNG approach should provide an economical and reliable tool for the prediction of swirling flows in combustor and furnace geometries commonly encountered in technological applications. To test this hypothesis the present work considers flow in a model furnace for which experimental data is available [2]. The essential features of the flow which differentiate it from the previous study [1] are that the annular air jet entry is relatively narrow and the base wall of the cylindrical furnace is at 90 degrees to the inlet pipe. For swirl numbers of order 1 the resulting flow is highly complex with significant inner and outer recirculation regions. The RNG and standard k-epsilon models are used to model the flow for both swirling and non-swirling entry jets and the results compared with experimental data [2]. Near wall viscous effects are accounted for in both models via the standard wall function formulation [3]. For the RNG model, additional computations with grid placement extending well inside the near wall viscous-affected sublayer are performed in order to assess the low Reynolds number capabilities of the model.