Latent Stick-Breaking Processes.

We develop a model for stochastic processes with random marginal distributions. Our model relies on a stick-breaking construction for the marginal distribution of the process, and introduces dependence across locations by using a latent Gaussian copula model as the mechanism for selecting the atoms. The resulting latent stick-breaking process (LaSBP) induces a random partition of the index space, with points closer in space having a higher probability of being in the same cluster. We develop an efficient and straightforward Markov chain Monte Carlo (MCMC) algorithm for computation and discuss applications in financial econometrics and ecology. This article has supplementary material online.

Analysis of traumatic injuries presenting to a referral hospital emergency department in Moshi, Tanzania.

BACKGROUND: Injuries represent a significant and growing public health concern in the developing world, yet their impact on patients and the emergency health-care system in the countries of East Africa has received limited attention. This study evaluates the magnitude and scope of injury related disorders in the population presenting to a referral hospital emergency department in northern Tanzania. METHODS: A retrospective chart review of patients presenting to the emergency department at Kilimanjaro Christian Medical Centre was performed. A standardized data collection form was used for data abstraction from the emergency department logbook and the complete medical record for all injured patients. Patient demographics, mechanism of injury, location, type and outcomes were recorded. RESULTS: Ten thousand six hundred twenty-two patients presented to the emergency department for evaluation and treatment during the 7-month study period. One thousand two hundred twenty-four patients (11.5%) had injuries. Males and individuals aged 15 to 44 years were most frequently injured, representing 73.4% and 57.8%, respectively. Road traffic injuries were the most common mechanism of injury, representing 43.9% of injuries. Head injuries (36.5%) and extremity injuries (59.5%) were the most common location of injury. The majority of injured patients, 59.3%, were admitted from the emergency department to the hospital wards, and 5.6%, required admission to an intensive care unit. Death occurred in 5.4% of injured patients. CONCLUSIONS: These data give a detailed and more robust picture of the patient demographics, mechanisms of injury, types of injury and patient outcomes from similar resource-limited settings.

Bayesian Gaussian Copula Factor Models for Mixed Data.

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.

A Dynamic Directional Model for Effective Brain Connectivity using Electrocorticographic (ECoG) Time Series.

We introduce a dynamic directional model (DDM) for studying brain effective connectivity based on intracranial electrocorticographic (ECoG) time series. The DDM consists of two parts: a set of differential equations describing neuronal activity of brain components (state equations), and observation equations linking the underlying neuronal states to observed data. When applied to functional MRI or EEG data, DDMs usually have complex formulations and thus can accommodate only a few regions, due to limitations in spatial resolution and/or temporal resolution of these imaging modalities. In contrast, we formulate our model in the context of ECoG data. The combined high temporal and spatial resolution of ECoG data result in a much simpler DDM, allowing investigation of complex connections between many regions. To identify functionally segregated sub-networks, a form of biologically economical brain networks, we propose the Potts model for the DDM parameters. The neuronal states of brain components are represented by cubic spline bases and the parameters are estimated by minimizing a log-likelihood criterion that combines the state and observation equations. The Potts model is converted to the Potts penalty in the penalized regression approach to achieve sparsity in parameter estimation, for which a fast iterative algorithm is developed. The methods are applied to an auditory ECoG dataset.

Functional Variants in Notch Pathway Genes NCOR2, NCSTN, and MAML2 Predict Survival of Patients with Cutaneous Melanoma.

BACKGROUND: The Notch signaling pathway is constitutively activated in human cutaneous melanoma to promote growth and aggressive metastatic potential of primary melanoma cells. Therefore, genetic variants in Notch pathway genes may affect the prognosis of cutaneous melanoma patients. METHODS: We identified 6,256 SNPs in 48 Notch genes in 858 cutaneous melanoma patients included in a previously published cutaneous melanoma genome-wide association study dataset. Multivariate and stepwise Cox proportional hazards regression and false-positive report probability corrections were performed to evaluate associations between putative functional SNPs and cutaneous melanoma disease-specific survival. Receiver operating characteristic curve was constructed, and area under the curve was used to assess the classification performance of the model. RESULTS: Four putative functional SNPs of Notch pathway genes had independent and joint predictive roles in survival of cutaneous melanoma patients. The most significant variant was NCOR2 rs2342924 T>C (adjusted HR, 2.71; 95% confidence interval, 1.73-4.23; Ptrend = 9.62 × 10(-7)), followed by NCSTN rs1124379 G>A, NCOR2 rs10846684 G>A, and MAML2 rs7953425 G>A (Ptrend = 0.005, 0.005, and 0.013, respectively). The receiver operating characteristic analysis revealed that area under the curve was significantly increased after adding the combined unfavorable genotype score to the model containing the known clinicopathologic factors. CONCLUSIONS: Our results suggest that SNPs in Notch pathway genes may be predictors of cutaneous melanoma disease-specific survival. IMPACT: Our discovery offers a translational potential for using genetic variants in Notch pathway genes as a genotype score of biomarkers for developing an improved prognostic assessment and personalized management of cutaneous melanoma patients.

Ensino médio: un olhar sobre o currículo de matemática na perspectiva de representaçôes semióticas

Essa comunicação apresenta uma pesquisa em desenvolvimento que busca investigar o currículo de Matemática das escolas estaduais de Ensino Médio do Estado do Rio Grande do Sul, sob a ótica das representações semióticas como possibilidade teórica, didática e metodológica para o desenvolvimento dos conhecimentos e procedimentos matemáticos que fazem parte desse nível de escolaridade. No presente momento, a investigação de cunho qualitativo está centrada na análise do currículo de Ensino Médio e nos projetos pedagógicos das escolas pertencentes à área de abrangência da pesquisa. Também fazem parte do estudo as avaliações nacionais propostas para os egressos do Ensino Médio. Resultados preliminares apontam a necessidade de se trabalhar com “outras representações”, principalmente quando os documentos analisados consideram a resolução de problemas como princípio para a organização das atividades escolares, o que, entende-se, indica uma abertura para o trabalho com semiótica na matemática escolar do Ensino Médio.

Some models for discretized series of events

A discretized series of events is a binary time series that indicates whether or not events of a point process in the line occur in successive intervals. Such data are common in environmental applications. We describe a class of models for them, based on an unobserved continuous-time discrete-state Markov process, which determines the rate of a doubly stochastic Poisson process, from which the binary time series is constructed by discretization. We discuss likelihood inference for these processes and their second-order properties and extend them to multiple series. An application involves modeling the times of exposures to air pollution at a number of receptors in Western Europe.

Delivering processing instruction in classroom and virtual contexts

Processing Instruction (PI) is an approach to grammar instruction for second language learning. It derives its name from the fact that the instruction (both the explicit explanation as well as the practices) attempt to influence, alter, and/or improve the way learners process input. PI contrasts with traditional grammar instruction in many ways, most principally in its focus on input whereas traditional grammar instruction focuses on learners' output. The greatest contribution of PI to both theory and practice is the concept of "structured input", a form of comprehensible input that has been manipulated to maximize learners' benefit of exposure to input. This volume focuses on a new issue for PI, the role of technology in language learning. It examines empirically the differential effects of delivering PI in classrooms with an instructor and students interacting (with each other and with the instructor) versus on computers to students working individually. It also contributes to the growing body of research on the effects of PI on different languages as well as different linguistic items: preterite/imperfect aspectual contrast and negative informal commands in Spanish, the subjunctive of doubt and opinion in Italian, and the subjunctive of doubt in French. Further research contributions are made by comparing PI with other types of instruction, specifically, with meaning-oriented output instruction.

Statistical Techniques In Stereology

Stereology typically concerns estimation of properties of a geometric structure from plane section information. This paperprovides a brief review of some statistical aspects of this rapidly developing field, with some reference to applications in the earth sciences. After an introductory discussion of the scope of stereology, section 2 briefly mentions results applicable when no assumptions can be made about the stochastic nature of the sampled matrix, statistical considerations then arising solelyfrom the ‘randomness’ of the plane section. The next two sections postulate embedded particles of specific shapes, the particular case of spheres being discussed in some detail. References are made to results for ‘thin slices’ and other prob-ing mechanisms. Randomly located convex particles, of otherwise arbitrary shape, are discussed in section 5 and the review concludes with a specific application of stereological ideas to some data on neolithic mining.