Univariate hierarchical Bayes models are being vigorously researched for use in disease mapping, engineering, geology, and ecology. This dissertation shows how the models can also be used to build modelbased risk maps for areabased roadway traffic crashes. Countylevel vehicle crash records and roadway data from Texas are used to illustrate the method. A potential extension that uses univariate hierarchical models to develop networkbased risk maps is also discussed. Several Bayesian multivariate spatial models for estimating the traffic crash rates from different types of crashes simultaneously are then developed. The specific class of spatial models considered is conditional autoregressive (CAR) model. The univariate CAR model is generalized for several multivariate cases. A general theorem for each case is provided to ensure that the posterior distribution is proper under improper and flat prior. The performance of various multivariate spatial models is compared using a Bayesian information criterion. The Markov chain Monte Carlo (MCMC) computational techniques are used for the model parameter estimation and statistical inference. These models are illustrated and compared again with the Texas crash data. There are many directions in which this study can be extended. This dissertation concludes with a short summary of this research and recommends several promising extensions.

Better understanding and prediction of tree growth is important because of the many ecosystem services provided by forests and the uncertainty surrounding how forests will respond to anthropogenic climate change. With the ultimate goal of improving models of forest dynamics, here we construct a statistical model that combines complementary data sources, tree-ring and forest inventory data. A Bayesian hierarchical model was used to gain inference on the effects of many factors on tree growth-individual tree size, climate, biophysical conditions, stand-level competitive environment, tree-level canopy status, and forest management treatments-using both diameter at breast height (dbh) and tree-ring data. The model consists of two multiple regression models, one each for the two data sources, linked via a constant of proportionality between coefficients that are found in parallel in the two regressions. This model was applied to a data set of similar to 130 increment cores and similar to 500 repeat measurements of dbh at a single site in the Jemez Mountains of north-central New Mexico, USA. The tree-ring data serve as the only source of information on how annual growth responds to climate variation, whereas both data types inform non-climatic effects on growth. Inferences from the model included positive effects on growth of seasonal precipitation, wetness index, and height ratio, and negative effects of dbh, seasonal temperature, southerly aspect and radiation, and plot basal area. Climatic effects inferred by the model were confirmed by a den-droclimatic analysis. Combining the two data sources substantially reduced uncertainty about non-climate fixed effects on radial increments. This demonstrates that forest inventory data measured on many trees, combined with tree-ring data developed for a small number of trees, can be used to quantify and parse multiple influences on absolute tree growth. We highlight the kinds of research questions that can be addressed by combining the high-resolution information on climate effects contained in tree rings with the rich tree-and stand-level information found in forest inventories, including projection of tree growth under future climate scenarios, carbon accounting, and investigation of management actions aimed at increasing forest resilience.

京都大学 / 新制・課程博士 / 博士(人間健康科学) / 甲第24539号 / 人健博第110号 / 新制||人健||8(附属図書館) / 京都大学大学院医学研究科人間健康科学系専攻 / (主査)教授 木下 彩栄, 教授 中尾 恵, 教授 中山 健夫 / 学位規則第4条第1項該当 / Doctor of Human Health Sciences / Kyoto University / DFAM

No description available.

Data from the 1995 National Health Interview Survey (NHIS) indicate that, due to chronic conditions, the onset of activity limitation typically occurs between age 40-70 years (i.e., the proportion of young adults with activity limitation is small and roughly constant with age and then it starts to change, roughly increasing). We use a Bayesian hierarchical model to detect the change point of a positive activity limitation status (ALS) across twelve domains based on race, gender, and education. We have two types of data: weighted and unweighted. We obtain weighted binomial counts using a regression analysis with the sample weights. Given the proportion of individuals in the population with positive ALS, we assume that the number of individuals with positive ALS at each age group has a binomial probability mass function. The proportions across age are different, and have the same beta distribution up to the change point (unknown), and the proportions after the change point have a different beta distribution. We consider two different analyses. The first considers each domain individually in its own model and the second considers the twelve domains simultaneously in a single model to“borrow strength" as in small area estimation. It is reasonable to assume that each domain has its own onset.In the first analysis, we use the Gibbs sampler to fit the model, and a computation of the marginal likelihoods, using an output analysis from the Gibbs sampler, provides the posterior distribution of the change point. We note that a reversible jump sampler fails in this analysis because it tends to get stuck either age 40 or age 70. In the second analysis, we use the Gibbs sampler to fit only the joint posterior distribution of the twelve change points. This is a difficult problem because the joint density requires the numerical computation of a triple integral at each iteration. The other parameters of the process are obtained using data augmentation by a Metropolis sampler and a Rao-Blackwellization. We found that overall the age of onset is about 50 to 60 years.

No description available.

Modeling of compositional data is emerging as an active area in statistics. It is assumed that compositional data represent the convex linear mixing of definite numbers of independent sources usually referred to as end members. A generic problem in practice is to appropriately separate the end members and quantify their fractions from compositional data subject to nonnegative and unit-sum constraints. A number of methods essentially related to polytope expansion have been proposed. However, these deterministic methods have some potential problems. In this study, a hierarchical Bayesian model was formulated, and the algorithms were coded in MATLABÒ. A test run using both a synthetic and real-word dataset yields scientifically sound and mathematically optimal outputs broadly consistent with other non-Bayesian methods. Also, the sensitivity of this model to the choice of different priors and structure of the covariance matrix of error were discussed.

Les Phases I sont un domaine des essais cliniques dans lequel les statisticiens ont encore beaucoup à apporter. Depuis trente ans, ce secteur bénéficie d'un intérêt croissant et de nombreuses méthodes ont été proposées pour gérer l'allocation séquentielle des doses aux patients intégrés à l'étude. Durant cette Phase, il s'agit d'évaluer la toxicité, et s'adressant à des patients gravement atteints, il s'agit de maximiser les effets curatifs du traitement dont les retours toxiques sont une conséquence. Parmi une gamme de doses, on cherche à déterminer celle dont la probabilité de toxicité est la plus proche d'un seuil souhaité et fixé par les praticiens cliniques. Cette dose est appelée la MTD (maximum tolerated dose). La situation canonique dans laquelle sont introduites la plupart des méthodes consiste en une gamme de doses finie et ordonnée par probabilité de toxicité croissante. Dans cette thèse, on introduit une modélisation très générale du problème, la SPM (semi-parametric methods), qui recouvre une large classe de méthodes. Cela permet d'aborder des questions transversales aux Phases I. Quels sont les différents comportements asymptotiques souhaitables? La MTD peut-elle être localisée? Comment et dans quelles circonstances? Différentes paramétrisations de la SPM sont proposées et testées par simulations. Les performances obtenues sont comparables, voir supérieures à celles des méthodes les plus éprouvées. Les résultats théoriques sont étendus au cas spécifique de l'ordre partiel. La modélisation de la SPM repose sur un traitement hiérarchique inférentiel de modèles satisfaisant des contraintes linéaires de paramètres inconnus. Les aspects théoriques de cette structure sont décrits dans le cas de lois à supports discrets. Dans cette circonstance, de vastes ensembles de lois peuvent aisément être considérés, cela permettant d'éviter les cas de mauvaises spécifications. / Phase I clinical trials is an area in which statisticians have much to contribute. For over 30 years, this field has benefited from increasing interest on the part of statisticians and clinicians alike and several methods have been proposed to manage the sequential inclusion of patients to a study. The main purpose is to evaluate the occurrence of dose limiting toxicities for a selected group of patients with, typically, life threatening disease. The goal is to maximize the potential for therapeutic success in a situation where toxic side effects are inevitable and increase with increasing dose. From a range of given doses, we aim to determine the dose with a rate of toxicity as close as possible to some threshold chosen by the investigators. This dose is called the MTD (maximum tolerated dose). The standard situation is where we have a finite range of doses ordered with respect to the probability of toxicity at each dose. In this thesis we introduce a very general approach to modeling the problem - SPM (semi-parametric methods) - and these include a large class of methods. The viewpoint of SPM allows us to see things in, arguably, more relevant terms and to provide answers to questions such as asymptotic behavior. What kind of behavior should we be aiming for? For instance, can we consistently estimate the MTD? How, and under which conditions? Different parametrizations of SPM are considered and studied theoretically and via simulations. The obtained performances are comparable, and often better, to those of currently established methods. We extend the findings to the case of partial ordering in which more than one drug is under study and we do not necessarily know how all drug pairs are ordered. The SPM model structure leans on a hierarchical set-up whereby certain parameters are linearly constrained. The theoretical aspects of this structure are outlined for the case of distributions with discrete support. In this setting the great majority of laws can be easily considered and this enables us to avoid over restrictive specifications than can results in poor behavior.

No description available.

現今市場競爭愈來愈激烈，迫使廠商紛紛至海外尋求產品消費市場，在跨國銷售的背景之下，需要有更多可以確定國家選擇、預測銷售及估計需求的方法。而其中可以滿足這些需求的方法之中，就是研究產品跨國擴散型態，藉以瞭解後進國家與領先國家中新產品如何擴散且會如何互相影響 (Douglas and Craig, 1992)。 在眾多的跨國產品中，本研究選擇好萊塢電影做為實證分析的對象。 經由集群分析，本研究發現（一）台灣高首週票房且口碑佳的電影，會遇到假日人潮、有很高的美國總票房、以及很高的美國首週票房；（二）美國影片在美國及台灣映演的每週票房趨勢有差異存在；（三）片商沒有做好影片在台灣映演的檔期歸劃；（四）三群電影中，在影片類型沒有明顯地區別。 經由十二個新產品銷售預測模型的建立：對數線性迴歸模式（LN-Regression Model）（不考慮新產品領先國擴散經驗）（以OLS估計）、卜瓦松迴歸模式(Poisson Regression Model) （不考慮新產品領先國擴散經驗）（以MLE估計）、負二項分配迴歸模式(Negative Binomial Distribution Regression Model) （不考慮新產品領先國擴散經驗）（以MLE估計）、Exponential Decay模式（以OLS估計）＋迴歸方程式體系（不考慮新產品領先國擴散經驗）（以SUR估計）、Exponential Decay模式（以OLS估計）＋迴歸方程式體系（考慮新產品領先國擴散經驗）（以SUR估計）、Exponential Decay模式＋層級貝氏迴歸模式（考慮新產品領先國擴散經驗）、Bass連續型擴散模式（以NLS估計）＋迴歸方程式體系（不考慮新產品領先國擴散經驗（以SUR估計）、Bass連續型擴散模式（以NLS估計）＋迴歸方程式體系（考慮新產品領先國擴散經驗（以SUR估計）、Bass離散型擴散模式（以OLS估計）＋迴歸方程式體系（不考慮新產品領先國擴散經驗）（以SUR估計）、Bass離散型擴散模式（以OLS估計）＋迴歸方程式體系（考慮新產品領先國擴散經驗）（以SUR估計）、層級貝氏BASS離散型擴散模式＋迴歸方程式體系（不考慮新產品領先國擴散經驗）（以SUR估計）、層級貝氏BASS離散型擴散模式＋迴歸方程式體系（考慮新產品領先國擴散經驗）（以SUR估計）。本研究發現：（一）在考慮影響後進國的新產品擴散速度時，領先國的擴散經驗為絕對必要的考慮因子；（二）必須使用Bass連續型擴散模式做為建構新產品銷售預測模型的基礎；（三）必須使用Bass連續型擴散模式的NLS估計法估計Bass模型的創新係數p、模仿係數q及市場潛量m。