Matrix-Variate Statistical Distributions and Fractional Calculus

MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthday

Application of MARS for the Construction of Nonparametric Models

2000 Mathematics Subject Classification: 62G08, 62P30.

Statistical Inference for Processes Depending on Environments and Application in Regenerative Processes

We build the Conditional Least Squares Estimator of 0 based on the observation of a single trajectory of {Zk,Ck}k, and give conditions ensuring its strong consistency. The particular case of general linear models according to 0=( 0, 0) and among them, regenerative processes, are studied more particularly. In this frame, we may also prove the consistency of the estimator of 0 although it belongs to an asymptotic negligible part of the model, and the asymptotic law of the estimator may also be calculated.

Statistical Analysis of Data on Linker Histones/DNA Interactions

2000 Mathematics Subject Classification: 62P10, 92C40

Multiple Dipole Source Models for Scalp-Recorded Event-Related Potentials: Example from Complex Visual Processing in the Human Brain

2000 Mathematics Subject Classification: 62P10, 92C20

Az ajánlati könyv statisztikai tulajdonságai (Statistical properties of the limit order book)

A pénzügyi modellek jelentős része feltételezi a piacok hatékony működését. Ennek következtében számos tudományos kutatás központi témája volt a piacok hatékonyságának tesztelése és ennek igazolása, esetleg cáfolata. Ezen próbálkozások azonban mind a mai napig eredménytelenül zárultak. A tesztelések nyomán a kutatások a termékek áralakulásából indultak ki, és a hozamokat ezen keresztül elemezték. Az elmúlt években azonban a fókusz átterelődött az árak alakulásáról egy elemibb tényezőre, az ajánlati könyvre. Ugyanis végső soron az ajánlatvezérelt piacokon az árakat az ajánlati könyvbe benyújtott megbízások alakulása fogja meghatározni. Mivel a tőzsdék jelentős része ajánlatvezérelt piacként működik, ezért érdemesnek tartották a kutatók, hogy inkább az ajánlati könyv alakulásának statisztikai jellemzőit elemezzék, hátha az eredményre vezet, és sikerül közelebb jutni a hatékony piacok elméletének igazolásához vagy cáfolatához. Jelen tanulmány célja az, hogy az eddig megjelent tudományos kutatások alapján ismertesse az ajánlati könyv alapvető statisztikai tulajdonságait, és rávilágítson arra: mindez valójában hozzájárult-e a hatékony piacok elméletének igazolásához? ______ Most of the fi nancial models assume that markets are effi cient. As a result, numerous scientifi c researchers were focused on testing the effi cient market hypothesis, and tried to prove, or deny it. However, all these attempts are still unsuccessful. During these researches, the analyses of the effi cient market hypothesis were based on the price evolution of a certain asset, and through this the returns were examined. In the recent years the research interest has changed, and instead of analyzing the returns, a more primary factor got into focus, namely the limit order book. The reason is that on order driven markets the prices and the order sizes in the limit order book infl uence the price evolution on the market. Since a notable number of stock markets operate as an order driven market, the researchers thought that it worth analyzing the statistical properties of the limit order book, because maybe it will get us closer to the proof of the effi cient market hypothesis. The purpose of this study is to summarize the statistical properties of the limit order book, based on the scientifi c works published so far. The study would like to highlight whether these studies contributed to the proof or disproof of the effi cient market hypothesis.

Növelhető-e a csőd-előrejelző modellek előre jelző képessége az új klasszifikációs módszerek nélkül? (Can the predictive capacity of bankruptcy forecasting models be increased without new classification methods?)

A Bázel–2. tőkeegyezmény bevezetését követően a bankok és hitelintézetek Magyarországon is megkezdték saját belső minősítő rendszereik felépítését, melyek karbantartása és fejlesztése folyamatos feladat. A szerző arra a kérdésre keres választ, hogy lehetséges-e a csőd-előrejelző modellek előre jelző képességét növelni a hagyományos matematikai-statisztikai módszerek alkalmazásával oly módon, hogy a modellekbe a pénzügyi mutatószámok időbeli változásának mértékét is beépítjük. Az empirikus kutatási eredmények arra engednek következtetni, hogy a hazai vállalkozások pénzügyi mutatószámainak időbeli alakulása fontos információt hordoz a vállalkozás jövőbeli fizetőképességéről, mivel azok felhasználása jelentősen növeli a csődmodellek előre jelző képességét. A szerző azt is megvizsgálja, hogy javítja-e a megfigyelések szélsőségesen magas vagy alacsony értékeinek modellezés előtti korrekciója a modellek klasszifikációs teljesítményét. ______ Banks and lenders in Hungary also began, after the introduction of the Basel 2 capital agreement, to build up their internal rating systems, whose maintenance and development are a continuing task. The author explores whether it is possible to increase the predictive capacity of business-failure forecasting models by traditional mathematical-cum-statistical means in such a way that they incorporate the measure of change in the financial indicators over time. Empirical findings suggest that the temporal development of the financial indicators of firms in Hungary carries important information about future ability to pay, since the predictive capacity of bankruptcy forecasting models is greatly increased by using such indicators. The author also examines whether the classification performance of the models can be improved by correcting for extremely high or low values before modelling.

Evaluation of the internal structural validity of the Diagnostic and Statistical Manual of Mental Disorders (Fourth Edition) anxiety disorders in children and adolescents

The purpose of the present dissertation was to evaluate the internal validity of symptoms of four common anxiety disorders included in the Diagnostic and Statistical Manual of Mental Disorders fourth edition (text revision) (DSM-IV-TR; American Psychiatric Association, 2000), namely, separation anxiety disorder (SAD), social phobia (SOP), specific phobia (SP), and generalized anxiety disorder (GAD), in a sample of 625 youth (ages 6 to 17 years) referred to an anxiety disorders clinic and 479 parents. Confirmatory factor analyses (CFAs) were conducted on the dichotomous items of the SAD, SOP, SP, and GAD sections of the youth and parent versions of the Anxiety Disorders Interview Schedule for DSM-IV (ADIS-IV: C/P; Silverman & Albano, 1996) to test and compare a number of factor models including a factor model based on the DSM. Contrary to predictions, findings from CFAs showed that a correlated model with five factors of SAD, SOP, SP, GAD worry, and GAD somatic distress, provided the best fit of the youth data as well as the parent data. Multiple group CFAs supported the metric invariance of the correlated five factor model across boys and girls. Thus, the present study’s finding supports the internal validity of DSM-IV SAD, SOP, and SP, but raises doubt regarding the internal validity of GAD.^

The effects of student -centered and traditional models of teaching on reading skills

A pre-test, post-test, quasi-experimental design was used to examine the effects of student-centered and traditional models of reading instruction on outcomes of literal comprehension and critical thinking skills. The sample for this study consisted of 101 adult students enrolled in a high-level developmental reading course at a large, urban community college in the Southeastern United States. The experimental group consisted of 48 students, and the control group consisted of 53 students. Students in the experimental group were limited in the time spent reading a course text of basic skills, with instructors using supplemental materials such as poems, news articles, and novels. Discussions, the reading-writing connection, and student choice in material selection were also part of the student-centered curriculum. Students in the control group relied heavily on a course text and vocabulary text for reading material, with great focus placed on basic skills. Activities consisted primarily of multiple-choice questioning and quizzes. The instrument used to collect pre-test data was Descriptive Tests of Language Skills in Reading Comprehension; post-test data were taken from the Florida College Basic Skills Exit Test. A MANCOVA was used as the statistical method to determine if either model of instruction led to significantly higher gains in literal comprehension skills or critical thinking skills. A paired samples t-test was also used to compare pre-test and post-test means. The results of the MANCOVA indicated no significant difference between instructional models on scores of literal comprehension and critical thinking. Neither was there any significant difference in scores between subgroups of age (under 25 and 25 and older) and language background (native English speaker and second-language learner). The results of the t-test indicated, however, that students taught under both instructional models made significant gains in on both literal comprehension and critical thinking skills from pre-test to post-test.

Bone morphology of the femur and tibia captured by statistical shape modelling predicts rapid bone loss in acute spinal cord injury patients

We would like to thank the study participants and the clinical and research staff at the Queen Elizabeth National Spinal Injury Unit, as without them this study would not have been possible. We are grateful for the funding received from Glasgow Research Partnership in Engineering for the employment of SC during data collection for this study. We would like to thank the Royal Society of Edinburgh's Scottish Crucible scheme for providing the opportunity for this collaboration to occur. We are also indebted to Maria Dumitrascuta for her time and effort in producing inter-repeatability results for the shape models.

Bone morphology of the femur and tibia captured by statistical shape modelling predicts rapid bone loss in acute spinal cord injury patients

We would like to thank the study participants and the clinical and research staff at the Queen Elizabeth National Spinal Injury Unit, as without them this study would not have been possible. We are grateful for the funding received from Glasgow Research Partnership in Engineering for the employment of SC during data collection for this study. We would like to thank the Royal Society of Edinburgh's Scottish Crucible scheme for providing the opportunity for this collaboration to occur. We are also indebted to Maria Dumitrascuta for her time and effort in producing inter-repeatability results for the shape models.

Multilevel structural equation models for longitudinal data where predictors are measured more frequently than outcomes : an application to the effects of stress on the cognitive function of nurses

Funded by Chief Scientist Office, Scotland. Grant Number: CZH/4/394 Economic and Social Research Council grant as part of the National Centre for Research Methods. Grant Number: RES-576-25-0032

Using Helix-coil Models to Study Protein Unfolded States

An abstract of a thesis devoted to using helix-coil models to study unfolded states.\\

Research on polypeptide unfolded states has received much more attention in the last decade or so than it has in the past. Unfolded states are thought to be implicated in various

misfolding diseases and likely play crucial roles in protein folding equilibria and folding rates. Structural characterization of unfolded states has proven to be

much more difficult than the now well established practice of determining the structures of folded proteins. This is largely because many core assumptions underlying

folded structure determination methods are invalid for unfolded states. This has led to a dearth of knowledge concerning the nature of unfolded state conformational

distributions. While many aspects of unfolded state structure are not well known, there does exist a significant body of work stretching back half a century that

has been focused on structural characterization of marginally stable polypeptide systems. This body of work represents an extensive collection of experimental

data and biophysical models associated with describing helix-coil equilibria in polypeptide systems. Much of the work on unfolded states in the last decade has not been devoted

specifically to the improvement of our understanding of helix-coil equilibria, which arguably is the most well characterized of the various conformational equilibria

that likely contribute to unfolded state conformational distributions. This thesis seeks to provide a deeper investigation of helix-coil equilibria using modern

statistical data analysis and biophysical modeling techniques. The studies contained within seek to provide deeper insights and new perspectives on what we presumably

know very well about protein unfolded states. \\

Chapter 1 gives an overview of recent and historical work on studying protein unfolded states. The study of helix-coil equilibria is placed in the context

of the general field of unfolded state research and the basics of helix-coil models are introduced.\\

Chapter 2 introduces the newest incarnation of a sophisticated helix-coil model. State of the art modern statistical techniques are employed to estimate the energies

of various physical interactions that serve to influence helix-coil equilibria. A new Bayesian model selection approach is utilized to test many long-standing

hypotheses concerning the physical nature of the helix-coil transition. Some assumptions made in previous models are shown to be invalid and the new model

exhibits greatly improved predictive performance relative to its predecessor. \\

Chapter 3 introduces a new statistical model that can be used to interpret amide exchange measurements. As amide exchange can serve as a probe for residue-specific

properties of helix-coil ensembles, the new model provides a novel and robust method to use these types of measurements to characterize helix-coil ensembles experimentally

and test the position-specific predictions of helix-coil models. The statistical model is shown to perform exceedingly better than the most commonly used

method for interpreting amide exchange data. The estimates of the model obtained from amide exchange measurements on an example helical peptide

also show a remarkable consistency with the predictions of the helix-coil model. \\

Chapter 4 involves a study of helix-coil ensembles through the enumeration of helix-coil configurations. Aside from providing new insights into helix-coil ensembles,

this chapter also introduces a new method by which helix-coil models can be extended to calculate new types of observables. Future work on this approach could potentially

allow helix-coil models to move into use domains that were previously inaccessible and reserved for other types of unfolded state models that were introduced in chapter 1.

Latent Space and Social Psychological Models of Diffusion

The problem of social diffusion has animated sociological thinking on topics ranging from the spread of an idea, an innovation or a disease, to the foundations of collective behavior and political polarization. While network diffusion has been a productive metaphor, the reality of diffusion processes is often muddier. Ideas and innovations diffuse differently from diseases, but, with a few exceptions, the diffusion of ideas and innovations has been modeled under the same assumptions as the diffusion of disease. In this dissertation, I develop two new diffusion models for "socially meaningful" contagions that address two of the most significant problems with current diffusion models: (1) that contagions can only spread along observed ties, and (2) that contagions do not change as they spread between people. I augment insights from these statistical and simulation models with an analysis of an empirical case of diffusion - the use of enterprise collaboration software in a large technology company. I focus the empirical study on when people abandon innovations, a crucial, and understudied aspect of the diffusion of innovations. Using timestamped posts, I analyze when people abandon software to a high degree of detail.

To address the first problem, I suggest a latent space diffusion model. Rather than treating ties as stable conduits for information, the latent space diffusion model treats ties as random draws from an underlying social space, and simulates diffusion over the social space. Theoretically, the social space model integrates both actor ties and attributes simultaneously in a single social plane, while incorporating schemas into diffusion processes gives an explicit form to the reciprocal influences that cognition and social environment have on each other. Practically, the latent space diffusion model produces statistically consistent diffusion estimates where using the network alone does not, and the diffusion with schemas model shows that introducing some cognitive processing into diffusion processes changes the rate and ultimate distribution of the spreading information. To address the second problem, I suggest a diffusion model with schemas. Rather than treating information as though it is spread without changes, the schema diffusion model allows people to modify information they receive to fit an underlying mental model of the information before they pass the information to others. Combining the latent space models with a schema notion for actors improves our models for social diffusion both theoretically and practically.

The empirical case study focuses on how the changing value of an innovation, introduced by the innovations' network externalities, influences when people abandon the innovation. In it, I find that people are least likely to abandon an innovation when other people in their neighborhood currently use the software as well. The effect is particularly pronounced for supervisors' current use and number of supervisory team members who currently use the software. This case study not only points to an important process in the diffusion of innovation, but also suggests a new approach -- computerized collaboration systems -- to collecting and analyzing data on organizational processes.

Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.