In developing an understanding of real-world problems, researchers develop mathematical and statistical models. Various model selection methods exist which can be used to obtain a mathematical model that best describes the real-world situation in some or other sense. These methods aim to assess the merits of competing models by concentrating on a particular criterion. Each selection method is associated with its own criterion and is named accordingly. The better known ones include Akaike's Information Criterion, Mallows' Cp and cross-validation, to name a few. The value of the criterion is calculated for each model and the model corresponding to the minimum value of the criterion is then selected as the "best" model. / Mathematical Sciences / M. Sc. (Statistics)

In developing an understanding of real-world problems, researchers develop mathematical and statistical models. Various model selection methods exist which can be used to obtain a mathematical model that best describes the real-world situation in some or other sense. These methods aim to assess the merits of competing models by concentrating on a particular criterion. Each selection method is associated with its own criterion and is named accordingly. The better known ones include Akaike's Information Criterion, Mallows' Cp and cross-validation, to name a few. The value of the criterion is calculated for each model and the model corresponding to the minimum value of the criterion is then selected as the "best" model. / Mathematical Sciences / M. Sc. (Statistics)

The aim of this thesis is to carry out economic analysis of Aero Vodochody, to analyze its current development and see whether the methods of analysis reflect the negative trend in the past. This should be reflected in values, which will be applied the method to acquire. The operational objective of this thesis is also to try to apply the method of Harry Pollak, which belongs to the methods of comprehensive evaluation of the business entity. It is an assessment of the vitality of the enterprise. This method is substantially subjective and relatively young, which explains the fact that it is somewhat less widespread.

Indiana University-Purdue University Indianapolis (IUPUI) / Useful medical indices pose important roles in predicting medical outcomes. Medical indices, such as the well-known Body Mass Index (BMI), Charleson Comorbidity Index, etc., have been used extensively in research and clinical practice, for the quantification of risks in individual patients. However, the development of these indices is challenged; and primarily based on heuristic arguments. Statistically, most medical indices can be expressed as a function of a linear combination of individual variables and fitted by single-index model. Single-index model represents a way to retain latent nonlinear features of the data without the usual complications that come with increased dimensionality. In my dissertation, I propose a single-index model approach to analytically derive indices from observed data; the resulted index inherently correlates with specific health outcomes of interest. The first part of this dissertation discusses the derivation of an index function for the prediction of one outcome using longitudinal data. A cubic-spline estimation scheme for partially linear single-index mixed effect model is proposed to incorporate the within-subject correlations among outcome measures contributed by the same subject. A recursive algorithm based on the optimization of penalized least square estimation equation is derived and is shown to work well in both simulated data and derivation of a new body mass measure for the assessment of hypertension risk in children. The second part of this dissertation extends the single-index model to a multivariate setting. Specifically, a multivariate version of single-index model for longitudinal data is presented. An important feature of the proposed model is the accommodation of both correlations among multivariate outcomes and among the repeated measurements from the same subject via random effects that link the outcomes in a unified modeling structure. A new body mass index measure that simultaneously predicts systolic and diastolic blood pressure in children is illustrated. The final part of this dissertation shows existence, root-n strong consistency and asymptotic normality of the estimators in multivariate single-index model under suitable conditions. These asymptotic results are assessed in finite sample simulation and permit joint inference for all parameters.

Einleitung Studierende der Veterinärmedizin müssen neben umfangreichem theoretischem Wissen zahlreiche praktische Fertigkeiten erlernen. Da jeder Einzelne in seinem eigenen Tempo lernt, besteht ein großer Bedarf an Trainingsmöglichkeiten. Kadaver und lebende Tiere sind selten in ausreichender Menge verfügbar und lebende Tiere sind zudem aus Gründen des Tierwohls nur eingeschränkt zu verwenden. Simulationsmodelle (Modelle von Organismen / Körperteilen) können hier Abhilfe schaffen. Kommerziell erhältliche Modelle sind sehr kostenintensiv und für die Tiermedizin noch nicht flächendeckend erhältlich. Zunehmend werden selbst entwickelte low-fidelity Modelle in der Tiermedizin verwendet. Aufgrund des Mangels an publizierten Daten zu ihrem Einsatz besteht intensiver Forschungsbedarf. Ziele der Untersuchungen In dieser Arbeit sollte untersucht werden, ob einfache, selbst entwickelte Simulationsmodelle (low-fidelity Modelle) erfolgreich in der Lehre eingesetzt werden können. Dazu wurden zwei selbst entwickelte und gebaute Simulationsmodelle evaluiert (Studie 1) und ihr Einsatz in Kombination mit anderen Lehrmedien untersucht (Studie 2). Materialien und Methoden In Studie 1 wurden zwei low-fidelity Modelle zur kaninen Intubation und Katheterisierung entwickelt und evaluiert. Es wurde ein Studiendesign genutzt, das die erworbenen Fertigkeiten zweier Übungsgruppen und einer Kontrollgruppe in einer praktischen Prüfung (OSCE = objective structured clinical examination) am toten Hund vergleicht. Achtundfünfzig Studierende (4. FS) erhielten eine theoretische Einführung zur Intubation und wurden randomisiert auf drei Gruppen aufgeteilt. Gruppe 1 (high-fidelity) übte am kommerziell erhältlichen Intubation Training Manikin, Gruppe 2 (low-fidelity) am entwickelten low-fidelity Modell und die Textgruppe las einen Text, der die Intubation beim Hund beschreibt. Siebenundvierzig Studierende (10. FS) durchliefen dasselbe Studiendesign zum Thema Katheterisierung der Hündin. Sie nutzten das kommerziell erhältliche Female Urinary Catheter Training Manikin, das selbst entwickelte low-fidelity Modell und Lehrtexte. In Studie 2 wurde die Vermittlung zweier spezifischer Fertigkeiten mit Hilfe von Potcasts und Simulationstraining evaluiert. Zwei anleitende Potcasts zu Intubation und Katheterisierung und die oben beschriebenen Modelle wurden innerhalb eines crossover-Studiendesigns genutzt. In dieser Studie sind Potcasts audio-visuell aufbereitete Animationen mit Schritt für Schritt – Anleitungen und Informationen. Die erworbenen praktischen Fertigkeiten zweier Übungsgruppen, die sich in der Art der theoretischen Vorbereitung unterschieden, wurden in einer praktischen Prüfung (OSCE) am toten Hund verglichen. Ein Fragebogen erfasste das Feedback der Teilnehmer. Sechzig Studierende (2. FS) wurden randomisiert auf eine Potcast- und eine Textgruppe aufgeteilt. Die Potcastgruppe sah sich das anleitende Potcast an, die Textgruppe bereitete sich anhand eines Lehrtextes vor. Im Anschluss hatten beide Gruppen separate Übungseinheiten an den low-fidelity Modellen ohne Betreuung durch Lehrende. Ergebnisse In Studie 1 schnitten alle Übungsgruppen signifikant besser ab als die Textgruppen. Gruppe 1 (high-fidelity) und Gruppe 2 (low-fidelity) unterschieden sich weder bei der Intubation noch bei der Katheterisierung signifikant in ihren Leistungen. In Studie 2 schnitt die Potcastgruppe beim Thema Intubation signifikant besser ab als die Textgruppe, beim Thema Katheterisierung ergaben sich keine signifikanten Unterschiede. Insgesamt hatte das Simulationstraining den Studierenden Spaß gemacht, das Lernen ohne Betreuer wurde jedoch als Herausforderung empfunden. Schlussfolgerungen Es ist davon auszugehen, dass low-fidelity Modelle genauso geeignet für das Training klinischer Fertigkeiten sein können wie high-fidelity Modelle. Das Training klinischer Fertigkeiten mit Hilfe von Potcasts und low-fidelity Modellen sollte durch Betreuer ergänzt werden, anstatt als alleiniges Lehrmedium für Studierende des ersten Studienjahres Verwendung zu finden. Eigenständiges Lernen klinischer Fertigkeiten, angeleitet durch Potcasts bietet eine Möglichkeit für vertiefendes und wiederholendes Training höherer Semester. Der Einsatz von Simulationsmodellen in der veterinärmedizinischen Ausbildung wächst seit wenigen Jahren stetig. Diese Arbeit leistet einen zeitgerechten Beitrag bei der Evaluierung von Simulationstraining. / Introduction Students of veterinary medicine are expected to acquire various practical skills in addition to a wide range of theoretical knowledge. There is a strong demand for training opportunities, as every individual learns and acquires practical skills at individual pace. For reasons of animal welfare concerns and availability, live animals and cadavers cannot always be used for clinical skills training. Simulation models, which are models of organisms or body parts can be a considerable alternative for clinical skills training. Models that are commercially produced often have a high price and are not available for all skills. Self-made models are increasingly used in veterinary education. Because there is few published data regarding their use, more scientific research is required. Aims of the Investigation The objective of this study was to determine, if self-made low-fidelity models can be successfully used in veterinary medical education. For this purpose, two self-made low-fidelity models were evaluated (study 1) and their use in combination with other teaching tools was analyzed (study 2). Materials and Methods In study 1, two self-made low-fidelity models for simulation of canine intubation and canine female urinary catheterization were developed and evaluated. We used a study design that compares acquired skills of two intervention groups and one control group in a practical examination (OSCE = objective structured clinical examination). Fifty-eight second-year veterinary medicine students received a theoretical introduction to intubation and were randomly divided into three groups. Group 1 (high-fidelity) was then trained on a commercially available Intubation Training Manikin, group 2 (low-fidelity) was trained on our low-fidelity model, and the text group read a text describing intubation of the dog. Forty-seven fifth-year veterinary medicine students followed the same procedure for training urinary catheterization using the commercially available Female Urinary Catheter Training Manikin, our self-made model, and text. Outcomes were assessed in a practical examination on a cadaver using an OSCE checklist. In study 2 we evaluated the teaching of two specific clinical skills using potcasts and low-fidelity simulation training. Two instructional potcasts describing intubation and catheterization and both low-fidelity models described above were used. In our study, potcasts are audio-visual animations that provide the learner with step by step information and instruction on a clinical skill. We used a crossover study design and compared the acquired practical skills of two intervention groups after a different theoretical preparation. A survey captured the participants’ feedback. Sixty first year veterinary medicine students were randomly allocated to two groups, a potcast group and a text group. The potcast group watched a potcast while the text group read an instructional text for preparation. Then both groups had separate self-directed training sessions on low-fidelity models. Outcomes were assessed in practical examinations on a cadaver using an objective structured clinical examination (OSCE) checklist. Results In study 1 all intervention groups performed significantly better than the text groups. Group I (high-fidelity) and group II (low-fidelity) for both intubation and catheterization showed no significant differences. In study 2 the potcast group performed significantly better than the text group in study intubation but no significant differences were observed in study catheterization. Overall, participants enjoyed clinical skills training but experienced self-directed learning as challenging. Conclusion Low-fidelity models can be as effective as high-fidelity models for clinical skills training. Clinical skills training using potcasts and self-directed low-fidelity simulation training should be complemented by supervisor or peer instruction rather than used as exclusive tool for teaching first year veterinary students. We assume though, that self-directed learning instructed by our potcasts can be a valuable chance for deepening and repetitive training of higher semesters. The use of simulation models in veterinary education has been consistently increasing in the past few years. This study is an important, timely contribution to the evaluation of simulation based education.

Since the turn of the millennium, a large number of computational models of visual salience have been put forward. How best to evaluate a given model's ability to predict where human observers fixate in images of real-world scenes remains an open research question. Assessing the role of spatial biases is a challenging issue; this is particularly true when we consider the tendency for high-salience items to appear in the image center, combined with a tendency to look straight ahead (“central bias”). This problem is further exacerbated in the context of model comparisons, because some—but not all—models implicitly or explicitly incorporate a center preference to improve performance. To address this and other issues, we propose to combine a-priori parcellation of scenes with generalized linear mixed models (GLMM), building upon previous work. With this method, we can explicitly model the central bias of fixation by including a central-bias predictor in the GLMM. A second predictor captures how well the saliency model predicts human fixations, above and beyond the central bias. By-subject and by-item random effects account for individual differences and differences across scene items, respectively. Moreover, we can directly assess whether a given saliency model performs significantly better than others. In this article, we describe the data processing steps required by our analysis approach. In addition, we demonstrate the GLMM analyses by evaluating the performance of different saliency models on a new eye-tracking corpus. To facilitate the application of our method, we make the open-source Python toolbox “GridFix” available.

Indiana University-Purdue University Indianapolis (IUPUI) / Riparian buffers have well documented capacity to remove nitrate (NO3-) from runoff and subsurface flow paths, but information on field-scale N2O emission from these buffers is lacking. This study monitored N2O fluxes at two agricultural riparian buffers in the White River watershed (Indiana) from December 2009 to May 2011 to assess the impact of landscape and hydrogeomorphologic factors on emission. Soil chemical and biochemical properties were measured and environmental variables (soil temperature and moisture) were monitored in an attempt to identify key drivers of N2O emission. The study sites included a mature riparian forest (WR) and a riparian grass buffer (LWD); adjacent corn fields were also monitored for land-use comparison. With the exception of net N mineralization, most soil properties (particle size, bulk density, pH, denitrification potential, organic carbon, C:N) showed little correlation with N2O emission. Analysis of variance (ANOVA) identified season, land-use (riparian buffer vs. crop field), and site geomorphology as major drivers of N2O emission. At both study sites, N2O emission showed strong seasonal variability; the largest emission peaks in the riparian buffers (up to 1,300 % increase) and crop fields (up to 3,500 % increase) occurred in late spring/early summer as a result of flooding, elevated soil moisture and N-fertilization. Nitrous oxide emission was found to be significantly higher in crop fields than in riparian buffers at both LWD (mean: 1.72 and 0.18 mg N2O-N m-2 d-1) and WR (mean: 0.72 and 1.26 mg N2O-N m-2 d-1, respectively). Significant difference (p=0.02) in N2O emission between the riparian buffers was detected, and this effect was attributed to site geomorphology and the greater potential for flooding at the WR site (no flooding occurred at LWD). More than previously expected, the study results demonstrate that N2O emission in riparian buffers is largely driven by landscape geomorphology and land-stream connection (flood potential).

Indiana University-Purdue University Indianapolis (IUPUI) / Magnetic resonance (MR) spectroscopy is a neuroimaging technique. It is widely used to quantify the concentration of important metabolites in a brain tissue. Imbalance in concentration of brain metabolites has been found to be associated with development of neurological impairment. There has been increasing trend of using MR spectroscopy as a diagnosis tool for neurological disorders. We established statistical methodology to analyze data obtained from the MR spectroscopy in the context of the HIV associated neurological disorder. First, we have developed novel methodology to study the association of marker of neurological disorder with MR spectrum from brain and how this association evolves with time. The entire problem fits into the framework of scalar-on-function regression model with individual spectrum being the functional predictor. We have extended one of the existing cross-sectional scalar-on-function regression techniques to longitudinal set-up. Advantage of proposed method includes: 1) ability to model flexible time-varying association between response and functional predictor and (2) ability to incorporate prior information. Second part of research attempts to study the influence of the clinical and demographic factors on the progression of brain metabolites over time. In order to understand the influence of these factors in fully non-parametric way, we proposed LongCART algorithm to construct regression tree with longitudinal data. Such a regression tree helps to identify smaller subpopulations (characterized by baseline factors) with differential longitudinal profile and hence helps us to identify influence of baseline factors. Advantage of LongCART algorithm includes: (1) it maintains of type-I error in determining best split, (2) substantially reduces computation time and (2) applicable even observations are taken at subject-specific time-points. Finally, we carried out an in-depth analysis of longitudinal changes in the brain metabolite concentrations in three brain regions, namely, white matter, gray matter and basal ganglia in chronically infected HIV patients enrolled in HIV Neuroimaging Consortium study. We studied the influence of important baseline factors (clinical and demographic) on these longitudinal profiles of brain metabolites using LongCART algorithm in order to identify subgroup of patients at higher risk of neurological impairment. / Partial research support was provided by the National Institutes of Health grants U01-MH083545, R01-CA126205 and U01-CA086368

Indiana University-Purdue University Indianapolis (IUPUI) / The objective of this research is to examine the development of the California alcohol outlets over time and the relationship between neighborhood characteristics and densities of the alcohol outlets. Two types of advanced analyses were done after the usual preliminary description of data. Firstly, fixed and random effects linear regression were used for the county panel data across time (1945-2010) with a dummy variable added to capture the change in law regarding limitations on alcohol outlets density. Secondly, a Bayesian spatio-temporal Poisson regression of the census tract panel data was conducted to capture recent availability of population characteristics affecting outlet density. The spatial Conditional Autoregressive model was embedded in the Poisson regression to detect spatial dependency of unexplained variance of alcohol outlet density. The results show that the alcohol outlets density reduced under the limitation law over time. However, it was no more effective in reducing the growth of alcohol outlets after the limitation was modified to be more restrictive. Poorer, higher vacancy rate and lower percentage of Black neighborhoods tend to have higher alcohol outlet density (numbers of alcohol outlets to population ratio) for both on-sale general and off-sale general. Other characteristics like percentage of Hispanics, percentage of Asians, percentage of younger population and median income of adjacency neighbors were associated with densities of on-sale general and off sale general alcohol outlets. Some regions like the San Francisco Bay area and the Greater Los Angeles area have more alcohol outlets than the predictions of neighborhood characteristics included in the model.