Likelihood-Based Inference for Partially Observed Multi-Type Markov Branching Processes

Thesis (Ph.D.)--University of Washington, 2016-08

Asymptotic Change-Point Analysis of the Dependencies in Time Series

In recent papers, Wied and his coauthors have introduced change-point procedures to detect and estimate structural breaks in the correlation between time series. To prove the asymptotic distribution of the test statistic and stopping time as well as the change-point estimation rate, they use an extended functional Delta method and assume nearly constant expectations and variances of the time series. In this thesis, we allow asymptotically infinitely many structural breaks in the means and variances of the time series. For this setting, we present test statistics and stopping times which are used to determine whether or not the correlation between two time series is and stays constant, respectively. Additionally, we consider estimates for change-points in the correlations. The employed nonparametric statistics depend on the means and variances. These (nuisance) parameters are replaced by estimates in the course of this thesis. We avoid assuming a fixed form of these estimates but rather we use "blackbox" estimates, i.e. we derive results under assumptions that these estimates fulfill. These results are supplement with examples. This thesis is organized in seven sections. In Section 1, we motivate the issue and present the mathematical model. In Section 2, we consider a posteriori and sequential testing procedures, and investigate convergence rates for change-point estimation, always assuming that the means and the variances of the time series are known. In the following sections, the assumptions of known means and variances are relaxed. In Section 3, we present the assumptions for the mean and variance estimates that we will use for the mean in Section 4, for the variance in Section 5, and for both parameters in Section 6. Finally, in Section 7, a simulation study illustrates the finite sample behaviors of some testing procedures and estimates.

LARGE MOTION VISUALIZATION AND ESTIMATION FOR FLAPPING WING SYSTEMS

Studies of fluid-structure interactions associated with flexible structures such as flapping wings require the capture and quantification of large motions of bodies that may be opaque. Motion capture of a free flying insect is considered by using three synchronized high-speed cameras. A solid finite element representation is used as a reference body and successive snapshots in time of the displacement fields are reconstructed via an optimization procedure. An objective function is formulated, and various shape difference definitions are considered. The proposed methodology is first studied for a synthetic case of a flexible cantilever structure undergoing large deformations, and then applied to a Manduca Sexta (hawkmoth) in free flight. The three-dimensional motions of this flapping system are reconstructed from image date collected by using three cameras. The complete deformation geometry of this system is analyzed. Finally, a computational investigation is carried out to understand the flow physics and aerodynamic performance by prescribing the body and wing motions in a fluid-body code. This thesis work contains one of the first set of such motion visualization and deformation analyses carried out for a hawkmoth in free flight. The tools and procedures used in this work are widely applicable to the studies of other flying animals with flexible wings as well as synthetic systems with flexible body elements.

Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.

Dynamic-Data Driven Real-Time Identification for Electric Power Systems

Power system engineers face a double challenge: to operate electric power systems within narrow stability and security margins, and to maintain high reliability. There is an acute need to better understand the dynamic nature of power systems in order to be prepared for critical situations as they arise. Innovative measurement tools, such as phasor measurement units, can capture not only the slow variation of the voltages and currents but also the underlying oscillations in a power system. Such dynamic data accessibility provides us a strong motivation and a useful tool to explore dynamic-data driven applications in power systems. To fulfill this goal, this dissertation focuses on the following three areas: Developing accurate dynamic load models and updating variable parameters based on the measurement data, applying advanced nonlinear filtering concepts and technologies to real-time identification of power system models, and addressing computational issues by implementing the balanced truncation method. By obtaining more realistic system models, together with timely updated parameters and stochastic influence consideration, we can have an accurate portrait of the ongoing phenomena in an electrical power system. Hence we can further improve state estimation, stability analysis and real-time operation.

Pseudoneglect and visual attention networks

Pseudoneglect represents the tendency for healthy individuals to show a slight but consistent bias in favour of stimuli appearing in the left visual field. The bias is often measured using variants of the line bisection task. An accurate model of the functional architecture of the visuospatial attention system must account for this widely observed phenomenon, as well as for modulation of the direction and magnitude of the bias within individuals by a variety of factors relating to the state of the participant and/or stimulus characteristics. To date, the neural correlates of pseudoneglect remain relatively unmapped. In the current thesis, I employed a combination of psychophysical measurements, electroencephalography (EEG) recording and transcranial direct current stimulation (tDCS) in an attempt to probe the neural generator(s) of pseudoneglect. In particular, I wished to utilise and investigate some of the factors known to modulate the bias (including age, time-on-task and the length of the to-be-bisected line) in order to identify neural processes and activity that are necessary and sufficient for the lateralized bias to arise. Across four experiments utilising a computerized version of a perceptual line bisection task, pseudoneglect was consistently observed at baseline in healthy young participants. However, decreased line length (experiments 1, 2 and 3), time-on-task (experiment 1) and healthy aging (experiment 3) were all found to modulate the bias. Specifically, all three modulations induced a rightward shift in subjective midpoint estimation. Additionally, the line length and time-on-task effects (experiment 1) and the line length and aging effects (experiment 3) were found to have additive relationships. In experiment 2, EEG measurements revealed the line length effect to be reflected in neural activity 100 – 200ms post-stimulus onset over source estimated posterior regions of the right hemisphere (RH: temporo-parietal junction (TPJ)). Long lines induced a hemispheric asymmetry in processing (in favour of the RH) during this period that was absent in short lines. In experiment 4, bi-parietal tDCS (Left Anodal/Right Cathodal) induced a polarity-specific rightward shift in bias, highlighting the crucial role played by parietal cortex in the genesis of pseudoneglect. The opposite polarity (Left Cathodal/Right Anodal) did not induce a change in bias. The combined results from the four experiments of the current thesis provide converging evidence as to the crucial role played by the RH in the genesis of pseudoneglect and in the processing of visual input more generally. The reduction in pseudoneglect with decreased line length, increased time-on-task and healthy aging may be explained by a reduction in RH function, and hence contribution to task processing, induced by each of these modulations. I discuss how behavioural and neuroimaging studies of pseudoneglect (and its various modulators) can provide empirical data upon which accurate formal models of visuospatial attention networks may be based and further tested.

Mixture of time-dependent growth models with an application to blue swimmer crab length-frequency data

Understanding how aquatic species grow is fundamental in fisheries because stock assessment often relies on growth dependent statistical models. Length-frequency-based methods become important when more applicable data for growth model estimation are either not available or very expensive. In this article, we develop a new framework for growth estimation from length-frequency data using a generalized von Bertalanffy growth model (VBGM) framework that allows for time-dependent covariates to be incorporated. A finite mixture of normal distributions is used to model the length-frequency cohorts of each month with the means constrained to follow a VBGM. The variances of the finite mixture components are constrained to be a function of mean length, reducing the number of parameters and allowing for an estimate of the variance at any length. To optimize the likelihood, we use a minorization–maximization (MM) algorithm with a Nelder–Mead sub-step. This work was motivated by the decline in catches of the blue swimmer crab (BSC) (Portunus armatus) off the east coast of Queensland, Australia. We test the method with a simulation study and then apply it to the BSC fishery data.

Probabilistic approach of water residence time and connectivity using Markov Chains with application to tidal embayments

Markov Chain analysis was recently proposed to assess the time scales and preferential pathways into biological or physical networks by computing residence time, first passage time, rates of transfer between nodes and number of passages in a node. We propose to adapt an algorithm already published for simple systems to physical systems described with a high resolution hydrodynamic model. The method is applied to bays and estuaries on the Eastern Coast of Canada for their interest in shellfish aquaculture. Current velocities have been computed by using a 2 dimensional grid of elements and circulation patterns were summarized by averaging Eulerian flows between adjacent elements. Flows and volumes allow computing probabilities of transition between elements and to assess the average time needed by virtual particles to move from one element to another, the rate of transfer between two elements, and the average residence time of each system. We also combined transfer rates and times to assess the main pathways of virtual particles released in farmed areas and the potential influence of farmed areas on other areas. We suggest that Markov chain is complementary to other sets of ecological indicators proposed to analyse the interactions between farmed areas - e.g. depletion index, carrying capacity assessment. Markov Chain has several advantages with respect to the estimation of connectivity between pair of sites. It makes possible to estimate transfer rates and times at once in a very quick and efficient way, without the need to perform long term simulations of particle or tracer concentration.

Effects of Information and Time of Use Pricing on Irish Electricity Demand and Supply

In this dissertation I quantify residential behavior response to interventions designed to reduce electricity demand at different periods of the day. In the first chapter, I examine the effect of information provision coupled with bimonthly billing, monthly billing, and in-home displays, as well as a time-of-use (TOU) pricing scheme to measure consumption over each month of the Irish Consumer Behavior Trial. I find that time-of-use pricing with real time usage information reduces electricity usage up to 8.7 percent during peak times at the start of the trial but the effect decays over the first three months and after three months the in-home display group is indistinguishable from the monthly treatment group. Monthly and bi-monthly billing treatments are not found to be statistically different from another. These findings suggest that increasing billing reports to the monthly level may be more cost effective for electricity generators who wish to decrease expenses and consumption, rather than providing in-home displays. In the following chapter, I examine the response of residential households after exposure to time of use tariffs at different hours of the day. I find that these treatments reduce electricity consumption during peak hours by almost four percent, significantly lowering demand. Within the model, I find evidence of overall conservation in electricity used. In addition, weekday peak reductions appear to carry over to the weekend when peak pricing is not present, suggesting changes in consumer habit. The final chapter of my dissertation imposes a system wide time of use plan to analyze the potential reduction in carbon emissions from load shifting based on the Ireland and Northern Single Electricity Market. I find that CO2 emissions savings are highest during the winter months when load demand is highest and dirtier power plants are scheduled to meet peak demand. TOU pricing allows for shifting in usage from peak usage to off peak usage and this shift in load can be met with cleaner and cheaper generated electricity from imports, high efficiency gas units, and hydro units.

Cognitive and structural aspects of addiction: Relation between iris patterns, time perception, eyeblink rate, impulsivity and cigarette addiction

Objectif : Le but de ce travail est d'étudier les corrélations existantes entre les patterns de l'iris, la perception du temps et la fréquence de clignement des paupières (eye blink rate) et ceci en relation avec l'addiction à la cigarette. Méthodologie: Revue de la littérature existante. Expériences sur une cohorte d'au moins trente sujets fumeurs/non-fumeurs. Analyses statistiques. Résultats: Nos résultats confirment qu'il existe des relations entre l'impulsivité, les patterns d'iris, l'eye blink rate spontané et la perception du temps. Nous observons également que l'addiction à la cigarette et son niveau de dépendance ont une influence sur ces différentes mesures. En effet, les sujets fumeurs tendent à avoir une personnalité plus impulsive par rapport aux sujets contrôles. On remarque également une nette diminution de l'eye blink rate dans le groupe des fumeurs et une tendance à la sur-estimation du temps qui passe. Conclusion : Ce travail nous permet de mieux comprendre les différentes corrélations qui existent entre les différentes variables que nous avons mesurées (patterns d'iris, score d'impulsivité et eye blink rate) ainsi que leur relation à l'addiction à la cigarette. Dès lors qu'il est avéré que les fumeurs peuvent avoir une perception du temps altérée par rapport au groupe contrôle, il serait intéressant d'en étudier l'évolution sur le long terme (aggravation avec la durée du tabagisme actif) ainsi que les conséquences qui en découlent écologiquement au moyen d'études longitudinales et de terrain.

Developing an index of dietary estimation of fermentable carbohydrate to allow dietary analysis for epidemiological studies

It has been proposed that long-term consumption of diets rich in non-digestible carbohydrates (NDCs), such as cereals, fruit and vegetables might protect against several chronic diseases, however, it has been difficult to fully establish their impact on health in epidemiology studies. The wide range properties of the different NDCs may dilution their impact when they are combined in one category for statistical comparisons in correlations or multivariate analysis. Several mechanisms have been suggested to explain the protective effects of NDCs, including increased stool bulk, dilution of carcinogens in the colonic lumen, reduced transit time, lowering pH, and bacterial fermentation to short chain fatty acids (SCFA) in the colon. However, it is very difficult to measure SCFA in humans in vivo with any accuracy, so epidemiological studies on the impact of SCFA are not feasible. Most studies use dietary fibre (DF) or Non-Starch Polysaccharides (NSP) intake to estimate the levels, but not all fibres or NSP are equally fermentable. It has been proposed that long-term consumption of diets rich in non-digestible carbohydrates (NDCs), such as cereals, fruit and vegetables might protect against several chronic diseases, however, it has been difficult to fully establish their impact on health in epidemiology studies. The wide range properties of the different NDCs may dilution their impact when they are combined in one category for statistical comparisons in correlations or multivariate analysis. Several mechanisms have been suggested to explain the protective effects of NDCs, including increased stool bulk, dilution of carcinogens in the colonic lumen, reduced transit time, lowering pH, and bacterial fermentation to short chain fatty acids (SCFA) in the colon. However, it is very difficult to measure SCFA in humans in vivo with any accuracy, so epidemiological studies on the impact of SCFA are not feasible. Most studies use dietary fibre (DF) or Non-Starch Polysaccharides (NSP) intake to estimate the levels, but not all fibres or NSP are equally fermentable. The first aim of this thesis was the development of the equations used to estimate the amount of FC that reaches the human colon and is fermented fully to SCFA by the colonic bacteria. Therefore, several studies were examined for evidence to determine the different percentages of each type of NDCs that should be included in the final model, based on how much NDCs entered the colon intact and also to what extent they were fermented to SCFA in vivo. Our model equations are FC-DF or NSP$ 1: 100 % Soluble + 10 % insoluble + 100 % NDOs¥ + 5 % TS** FC-DF or NSP 2: 100 % Soluble + 50 % insoluble + 100 % NDOs + 5 % TS FC-DF* or NSP 3: 100 % Soluble + 10 % insoluble + 100 % NDOs + 10 % TS FC-DF or NSP 4: 100 % Soluble + 50 % insoluble + 100 % NDOs + 10 % TS *DF: Dietary fibre; **TS: Total starch; $NSP: non-starch polysaccharide; ¥NDOs: non-digestible oligosaccharide The second study of this thesis aimed to examine all four predicted FC-DF and FC-NSP equations developed, to estimate FC from dietary records against urinary colonic NDCs fermentation biomarkers. The main finding of a cross-sectional comparison of habitual diet with urinary excretion of SCFA products, showed weak but significant correlation between the 24 h urinary excretion of SCFA and acetate with the estimated FC-DF 4 and FC-NSP 4 when considering all of the study participants (n = 122). Similar correlations were observed with the data for valid participants (n = 78). It was also observed that FC-DF and FC-NSP had positive correlations with 24 h urinary acetate and SCFA compared with DF and NSP alone. Hence, it could be hypothesised that using the developed index to estimate FC in the diet form dietary records, might predict SCFA production in the colon in vivo in humans. The next study in this thesis aimed to validate the FC equations developed using in vitro models of small intestinal digestion and human colon fermentation. The main findings in these in vitro studies were that there were several strong agreements between the amounts of SCFA produced after actual in vitro fermentation of single fibre and different mixtures of NDCs, and those predicted by the estimated FC from our developed equation FC-DF 4. These results which demonstrated a strong relationship between SCFA production in vitro from a range of fermentations of single fibres and mixtures of NDCs and that from the predicted FC equation, support the use of the FC equation for estimation of FC from dietary records. Therefore, we can conclude that the newly developed predicted equations have been deemed a valid and practical tool to assess SCFA productions for in vitro fermentation.

Indirect child mortality estimation technique to identify trends of under-five mortality in Ethiopia.

Background: In sub-Saharan African countries, the chance of a child dying before the age of five years is high. The problem is similar in Ethiopia, but it shows a decrease over years. Methods: The 2000; 2005 and 2011 Ethiopian Demographic and Health Survey results were used for this work. The purpose of the study is to detect the pattern of under-five child mortality overtime. Indirect child mortality estimation technique is adapted to examine the under-five child mortality trend in Ethiopia. Results: From the result, it was possible to see the trend of under-five child mortality in Ethiopia. The under-five child mortality shows a decline in Ethiopia. Conclusion: From the study, it can be seen that there is a positive correlation between mother and child survival which is almost certain in any population. Therefore, this study shows the trend of under-five mortality in Ethiopia and decline over time.

Change-point detection in environmental time series based on the informational approach

In this study, the Schwarz Information Criterion (SIC) is applied in order to detect change-points in the time series of surface water quality variables. The application of change-point analysis allowed detecting change-points in both the mean and the variance in series under study. Time variations in environmental data are complex and they can hinder the identification of the so-called change-points when traditional models are applied to this type of problems. The assumptions of normality and uncorrelation are not present in some time series, and so, a simulation study is carried out in order to evaluate the methodology’s performance when applied to non-normal data and/or with time correlation.

Age estimation in common sole Solea solea larvae: validation of daily increments and evaluation of a pattern recognition technique

Close similarities have been found between the otoliths of sea-caught and laboratory-reared larvae of the common sole Solea solea (L.), given appropriate temperatures and nourishment of the latter. But from hatching to mouth formation. and during metamorphosis, sole otoliths have proven difficult to read because the increments may be less regular and low contrast. In this study, the growth increments in otoliths of larvae reared at 12 degrees C were counted by light microscopy to test the hypothesis of daily deposition, with some results verified using scanning electron microscopy (SEM), and by image analysis in order to compare the reliability of the 2 methods in age estimation. Age was first estimated (in days posthatch) from light micrographs of whole mounted otoliths. Counts were initiated from the increment formed at the time of month opening (Day 4). The average incremental deposition rate was consistent with the daily hypothesis. However, the light-micrograph readings tended to underestimate the mean ages of the larvae. Errors were probably associated with the low-contrast increments: those deposited after the mouth formation during the transition to first feeding, and those deposited from the onset of eye migration (about 20 d posthatch) during metamorphosis. SEM failed to resolve these low-contrast areas accurately because of poor etching. A method using image analysis was applied to a subsample of micrograph-counted otoliths. The image analysis was supported by an algorithm of pattern recognition (Growth Demodulation Algorithm, GDA). On each otolith, the GDA method integrated the growth pattern of these larval otoliths to averaged data from different radial profiles, in order to demodulate the exponential trend of the signal before spectral analysis (Fast Fourier Transformation, FFT). This second method both allowed more precise designation of increments, particularly for low-contrast areas, and more accurate readings but increased error in mean age estimation. The variability is probably due to a still rough perception of otolith increments by the GDA method, counting being achieved through a theoretical exponential pattern and mean estimates being given by FFT. Although this error variability was greater than expected, the method provides for improvement in both speed and accuracy in otolith readings.

A space-time hybrid hourly rainfall model for derived flood frequency analysis

For derived flood frequency analysis based on hydrological modelling long continuous precipitation time series with high temporal resolution are needed. Often, the observation network with recording rainfall gauges is poor, especially regarding the limited length of the available rainfall time series. Stochastic precipitation synthesis is a good alternative either to extend or to regionalise rainfall series to provide adequate input for long-term rainfall-runoff modelling with subsequent estimation of design floods. Here, a new two step procedure for stochastic synthesis of continuous hourly space-time rainfall is proposed and tested for the extension of short observed precipitation time series. First, a single-site alternating renewal model is presented to simulate independent hourly precipitation time series for several locations. The alternating renewal model describes wet spell durations, dry spell durations and wet spell intensities using univariate frequency distributions separately for two seasons. The dependence between wet spell intensity and duration is accounted for by 2-copulas. For disaggregation of the wet spells into hourly intensities a predefined profile is used. In the second step a multi-site resampling procedure is applied on the synthetic point rainfall event series to reproduce the spatial dependence structure of rainfall. Resampling is carried out successively on all synthetic event series using simulated annealing with an objective function considering three bivariate spatial rainfall characteristics. In a case study synthetic precipitation is generated for some locations with short observation records in two mesoscale catchments of the Bode river basin located in northern Germany. The synthetic rainfall data are then applied for derived flood frequency analysis using the hydrological model HEC-HMS. The results show good performance in reproducing average and extreme rainfall characteristics as well as in reproducing observed flood frequencies. The presented model has the potential to be used for ungauged locations through regionalisation of the model parameters.