Source: Dissertation Abstracts International, Volume: 35-02, Section: B, page: 1120. / Thesis (Ph.D.)--The Florida State University, 1973.

Source: Dissertation Abstracts International, Volume: 35-10, Section: B, page: 5190. / Thesis (Ph.D.)--The Florida State University, 1974.

Source: Dissertation Abstracts International, Volume: 35-08, Section: B, page: 4267. / Thesis (Ph.D.)--The Florida State University, 1974.

The research contained in this thesis extends multivariate marked point process modeling methods for neuroscience, generalizes goodness-of-fit techniques for the class of marked point processes, and introduces the use of a general history-dependent point process model to the domain of sleep apnea. Our first project involves further development of a modeling tool for spiking data from neural populations using the theory of marked point processes. This marked point process model uses features of spike waveforms as marks in order to estimate a state variable of interest. We examine the informational content of geometric features as well as principal components of the waveforms at hippocampal place cell activity by comparing decoding accuracies of a rat's position along a track. We determined that there was additional information available beyond that contained in traditional geometric features used for decoding in practice. The expanded use of this marked point process model in neuroscience necessitates corresponding goodness-of-fit protocols for the marked case. In our second project, we develop a generalized time-rescaling method for marked point processes that produces uniformly distributed spikes under a proper model. Once rescaled, the ground process then behaves as a Poisson process and can be analyzed using traditional point process goodness-of-fit methods. We demonstrate the method's ability to detect quality and manner of fit through both simulation and real neural data analysis. In the final project, we introduce history-dependent point process modeling as a superior method for characterizing severe sleep apnea over the current clinical standard known as the apnea-hypopnea index (AHI). We analyze model fits using combinations of both clinical covariates and event observations themselves through functions of history. Ultimately, apnea onset times were consistently estimated with significantly higher accuracy when history was incorporated alongside sleep stage. We present this method to the clinical audience as a means to gain detailed information on patterns of apnea and to provide more customized diagnoses and treatment prescriptions. These separate yet complementary projects extend existing point process modeling methods and further demonstrate their value in the neurosciences, sleep sciences, and beyond.

Consider the semimartingale regression model $X(t)$ = $X(0)$ + $\int\sbsp{0}{t}$ $Y(s)\alpha(s,Z(s))$ $ds + M(t)$, where $Y, Z$ are observable covariate processes, $\alpha$ is a (deterministic) function of both time and the covariate process $Z$, and $M$ is a square integrable martingale. Under the assumption that i.i.d. copies of $X, Y, Z$ are observed continuously over a finite time interval, inference for the function $\alpha(t,z)$ is investigated. Applications of this model include hazard function estimation for survival analysis and inference for the drift function of a diffusion process. / An estimator $\ A$ for the time integrated $\alpha(t,z)$ and a kernel estimator of $\alpha(t,z)$ itself are introduced. For $X$ a counting process, $\ A$ reduces to the Nelson-Aalen estimator when $Z$ is not present in the model. Various forms of consistency are proved, rates of convergence and asymptotic distributions of the estimators are derived. Asymptotic confidence bands for the time integrated $\alpha(t,z)$ and a Kolmogorov-Smirnov-type test of equality of $\alpha$ at different levels of the covariate are given. / For the case $Y$ $\equiv$ 1 we introduce an estimator $\{\cal A}$ of the time and space integrated $\alpha(t,z)$. The asymptotic distribution of the estimator $\{\cal A}$ is derived under the assumption that the covariate process $Z$ is $\cal F\sb0$-adapted, where ($\cal F\sb{t}$) is the filtration with respect to which $M$ is a martingale. In the counting process case this amounts to assuming that $X$ is a doubly stochastic Poisson process. Weak convergence of the appropriately normalized time and state indexed process $\{\cal A}$ to a Gaussian random field is shown. As an application of this result, confidence bands for the covariate state integrated hazard function of a doubly stochastic Poisson process whose intensity does not explicitly depend on time are derived. / Source: Dissertation Abstracts International, Volume: 49-03, Section: B, page: 0816. / Major Professor: Ian W. McKeague. / Thesis (Ph.D.)--The Florida State University, 1987.

We consider the finite horizon problem of tracking a Brownian Motion, with possibly non zero drift, by a process of bounded variation, in such a way as to minimize total expected cost of "action" and "deviation from a target state." The cost of "action" is given by two functions (of time), which represent price per unit of increase and decrease in the state process; the cost of "deviation" is incurred continuously at a rate given by a function convex in the state variable and a terminal cost function. We obtain the optimal cost function for this problem, as well an $\varepsilon$-optimal strategy, through the solution of a system of variational inequalities, which has a stochastic representation as the value function for an appropriate two-person game. / Source: Dissertation Abstracts International, Volume: 49-06, Section: B, page: 2256. / Major Professor: Michael Taksar. / Thesis (Ph.D.)--The Florida State University, 1988.

Longitudinal studies are widely used in various fields, such as public health, clinic trials and financial data analysis. A major challenge for longitudinal studies is repeated measurements from each subject, which cause time dependent correlation within subjects. Generalized Estimating Equations can deal with correlated outcomes for longitudinal data through marginal effect. My model will base on Generalized Estimating Equations with semi-parametric approach, providing a flexible structure for regression models: coefficients for parametric covariates will be estimated and nuisance covariates will be fitted in kernel smoothers for non-parametric part. Profile kernel estimator and the seemingly unrelated kernel estimator (SUR) will be used to deliver consistent and efficient semi-parametric estimators comparing to parametric models. We provide simulation results for estimating semi-parametric models with one or multiple non-parametric terms. In application part, we would like to focus on financial market: a credit card loan data will be used with the payment information for each customer across 6 months, investigating whether gender, income, age or other factors will influence payment status significantly. Furthermore, we propose model comparisons to evaluate whether our model should be fitted based on different levels of factors, such as male and female or based on different types of estimating methods, such as parametric estimation or semi-parametric estimation. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2017. / November 15, 2017. / Includes bibliographical references. / Xufeng Niu, Professor Directing Dissertation; Yingmei Cheng, University Representative; Fred Huffer, Committee Member; Minjing Tao, Committee Member.

As we routinely encounter high-throughput datasets in complex biological and environment research, developing novel models and methods for variable selection has received widespread attention. In this dissertation, we addressed a few key challenges in Bayesian modeling and variable selection for high-dimensional data with complex spatial structures. a) Most Bayesian variable selection methods are restricted to mixture priors having separate components for characterizing the signal and the noise. However, such priors encounter computational issues in high dimensions. This has motivated continuous shrinkage priors, resembling the two-component priors facilitating computation and interpretability. While such priors are widely used for estimating high-dimensional sparse vectors, selecting a subset of variables remains a daunting task. b) Spatial/spatial-temporal data sets with complex structures are nowadays commonly encountered in various scientific research fields ranging from atmospheric sciences, forestry, environmental science, biological science, and social science. Selecting important spatial variables that have significant influences on occurrences of events is undoubtedly necessary and essential for providing insights to researchers. Self-excitation, which is a feature that occurrence of an event increases the likelihood of more occurrences of the same type of events nearby in time and space, can be found in many natural/social events. Research on modeling data with self-excitation feature has increasingly drawn interests recently. However, existing literature on self-exciting models with inclusion of high-dimensional spatial covariates is still underdeveloped. c) Gaussian Process is among the most powerful model frames for spatial data. Its major bottleneck is the computational complexity which stems from inversion of dense matrices associated with a Gaussian process covariance. Hierarchical divide-conquer Gaussian Process models have been investigated for ultra large data sets. However, computation associated with scaling the distributing computing algorithm to handle a large number of sub-groups poses a serious bottleneck. In chapter 2 of this dissertation, we propose a general approach for variable selection with shrinkage priors. The presence of very few tuning parameters makes our method attractive in comparison to ad hoc thresholding approaches. The applicability of the approach is not limited to continuous shrinkage priors, but can be used along with any shrinkage prior. Theoretical properties for near-collinear design matrices are investigated and the method is shown to have good performance in a wide range of synthetic data examples and in a real data example on selecting genes affecting survival due to lymphoma. In Chapter 3 of this dissertation, we propose a new self-exciting model that allows the inclusion of spatial covariates. We develop algorithms which are effective in obtaining accurate estimation and variable selection results in a variety of synthetic data examples. Our proposed model is applied on Chicago crime data where the influence of various spatial features is investigated. In Chapter 4, we focus on a hierarchical Gaussian Process regression model for ultra-high dimensional spatial datasets. By evaluating the latent Gaussian process on a regular grid, we propose an efficient computational algorithm through circulant embedding. The latent Gaussian process borrows information across multiple sub-groups, thereby obtaining a more accurate prediction. The hierarchical model and our proposed algorithm are studied through simulation examples. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2017. / October 23, 2017. / Includes bibliographical references. / Debdeep Pati, Professor Co-Directing Dissertation; Fred Huffer, Professor Co-Directing Dissertation; Alec Kercheval, University Representative; Debajyoti Sinha, Committee Member; Jonathan Bradley, Committee Member.

This dissertation presents some topics in spatial statistics and their application in biostatistics and environmental statistics. The field of spatial statistics is an energetic area in statistics. In Chapter 2 and Chapter 3, the goal is to build subregion models under the assumption that the responses or the parameters are spatially correlated. For regression models, considering spatially varying coecients is a reasonable way to build subregion models. There are two different techniques for exploring spatially varying coecients. One is geographically weighted regression (Brunsdon et al. 1998). The other is a spatially varying coecients model which assumes a stationary Gaussian process for the regression coecients (Gelfand et al. 2003). Based on the ideas of these two techniques, we introduce techniques for exploring subregion models in survival analysis which is an important area of biostatistics. In Chapter 2, we introduce modied versions of the Kaplan-Meier and Nelson-Aalen estimators which incorporate geographical weighting. We use ideas from counting process theory to obtain these modied estimators, to derive variance estimates, and to develop associated hypothesis tests. In Chapter 3, we introduce a Bayesian parametric accelerated failure time model with spatially varying coefficients. These two techniques can explore subregion models in survival analysis using both nonparametric and parametric approaches. In Chapter 4, we introduce Bayesian parametric covariance regression analysis for a response vector. The proposed method denes a regression model between the covariance matrix of a p-dimensional response vector and auxiliary variables. We propose a constrained Metropolis-Hastings algorithm to get the estimates. Simulation results are presented to show performance of both regression and covariance matrix estimates. Furthermore, we have a more realistic simulation experiment in which our Bayesian approach has better performance than the MLE. Finally, we illustrate the usefulness of our model by applying it to the Google Flu data. In Chapter 5, we give a brief summary of future work. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2017. / November 9, 2017. / Biostatistics, Environment Statistics, Spatial Statistics / Includes bibliographical references. / Fred Huffer, Professor Directing Dissertation; Insu Paek, University Representative; Debajyoti Sinha, Committee Member; Elizabeth Slate, Committee Member; Jonathan Bradley, Committee Member.

Tämän tutkielman yhtenä tavoitteena on kartoittaa suomalaisten kiinnostusta tiedettä, tutkimusta ja teknologiaa kohtaan. Tutkielman toinen ja ehkä tärkein tavoite on kuitenkin selvittää yleisimpien joukkoviestimien tärkeyttä suomalaisille tiedettä sekä tutkimusta koskevan tiedon välittäjinä. Tutkielmassa käytetty aineisto on peräisin vuoden 2016 Tiedebarometrista. Kaikkiaan 7000:sta yksinkertaisella satunnaisotannalla väestötietojärjestelmästä poimitusta henkilöstä, joille kysely lähetettiin, vastasi 1056 henkilöä. Aineisto kerättiin strukturoidulla kyselylomakkeella, joka kullekkin vastaajalle lähetettiin kirjeitse. Keruu tapahtui aikavälillä 31.5.2016–8.8.2016. Tilastollisen analyysin menetelmien osalta tässä tutkielmassa on käytetty ehdollisia prosenttijakaumia ja ristiintaulukointia. Tutkielman vastemuuttujia on mitattu kysymyksillä ”Kuinka kiinnostunut olette/aktiivisesti seuraatte tiedotusvälineistä seuraavia aihepiirejä koskevia uutisia, ohjelmia ja kirjoituksia? Tiede, tutkimus, teknologia”, sekä ”Kuinka tärkeitä seuraavat tietolähteet ovat Teille tiedettä ja tutkimusta koskevan tiedon välittäjinä? Internet, tietoverkot ja sosiaalinen media/televisio ja radio/sanomalehdet”, joista jälkimmäinen on eritelty kolmeen eri kysymykseen. Vastemuuttujia oli siis yhteensä neljä. Taustamuuttujana tutkimuksessa toimii ikä, sekä ensimmäisen kysymyksen kohdalla lisäksi ammatillisen koulutuksen taso. Tutkimuksessa havaittiin, että selkeä enemmistö kaikista vastaajista oli kiinnostuneita tieteestä, tutkimuksesta ja teknologiasta. Iän suhteen kiinnostuneiden suhteellinen osuus oli suurin nuorimmassa ikäluokassa ja laski ikäluokan vanhetessa. Ammatillisen koulutuksen suhteen kaikkein suurin osuus kiinnostuneita oli yliopisto- tai korkeakoulututkinnon suorittaneissa. Muissa koulutusluokissa kiinnostuneiden osuus vaihteli jonkin verran, mutta ei erityisen voimakkaasti. Kaikkien vastaajien keskuudessa internetin, tietoverkot ja sosiaalisen median itselleen tärkeiksi tietolähteeksi tiedettä ja tutkimusta koskevan tiedon välittäjinä luokitteli 70 % vastaajista, television ja radion taas 80% kaikista vastaajista, sekä sanomalehdet 71 % kaikista vastaajista. Internetiä, tietoverkkoja ja sosiaalista mediaa tärkeänä pitävien osuus oli korkein nuorimassa ikäluokassa ja laski ikäluokan vanhetessa. Televisiota ja radioa tärkeinä pitävien osuus taas oli suurin vanhimmassa ikäluokassa ja laski ikäluokan nuortuessa. Sanomalehtiä tärkeänä pitävien osuus oli jälleen kaikkein korkein vanhimmassa ikäluokassa ja laski ikäluokan nuortuessa.