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The value of intravascular ultrasound (IVUS) in the diagnosis and treatment of the venous system is not well established. Introducing a novel approach to utilizing IVUS to evaluate cerebral venous sinus (CVS) stenosis and select stent. Idiopathic intracranial hypertension (IIH) patients with CVS stenosis who underwent IVUS-guided stenting were included in the data analysis from January 2014 to February 2022. The degree of maximum stenosis was determined based on the cross-sectional area (CSA) measured by IVUS, and a stent selection method was applied in the study. Follow-up evaluations were conducted at 6 months to 1 year after endovascular treatment to assess symptom improvement. Additionally, repeated digital subtraction angiography (DSA) or Magnetic resonance venography (MRV) / CT venography（CTV） was performed to evaluate the stent patency at 6 months to 1 year post-procedure. The study included 61 patients. IVUS indicated a lower degree of stenosis compared to conventional DSA measurements when evaluating the degree of stenotic segments preprocedure (74.84 ± 10.12% vs. 78.48 ± 8.72%, p  = 0.035). Post-procedural CSA of the most severe stenotic segments showed significant improvement (36.44 ± 8.07 mm 2 vs. 7.42 ± 3.28 mm 2 , p  < 0.001). The stent achieved complete expansion (mean stent expansion index, 0.93 ± 0.20) with no significant change in the structure of the reference segment. The trans-stenotic mean pressure gradients (MPGs) across 61 patients significantly decreased from 11.00 ± 6.23 mmHg to 2.09 ± 2.34 mmHg. 47 out of 61 patients received imaging follow-up; among them, 44 (93.6%) demonstrated stent patency in the follow-up imaging. IVUS has great potential to evaluate the degree and extent of CVS stenosis, assist stent selection, and optimize stent position during the interventional procedure in conjunction with DSA.

We consider Bayesian analysis for testing the general linear hypotheses in linear models with spherically symmetric errors. These error distributions not only include some of the classical linear models as special cases, but also reduce the influence of outliers and result in a robust statistical inference. Meanwhile, the design matrix is not necessarily of full rank. By appropriately modifying mixtures of g -priors for the regression coefficients under some general linear constraints, we derive closed-form Bayes factors in terms of the ratio between two Gaussian hypergeometric functions. The proposed Bayes factors rely on the data only through the modified coefficient of determinations of the two models and are shown to be independent of the error distributions, so long as they are spherically symmetric. Moreover, we establish the results of the model selection consistency with the proposed Bayes factors in the model settings with a full-rank design matrix when the number of parameters increases with the sample size. We carry out simulation studies to assess the finite sample performance of the proposed methodology. The presented results extend some existing Bayesian testing procedures in the literature.

Gaussian copula models allow a more direct modeling of the marginal distributions and associa- tion structure of the data, but the modeling of geostatistical count data using copulas is more recent and less studied than that of the Generalized Linear Mixed Models (GLMMs) proposed by Diggle et al. (1998). In this dissertation, we consider Gaussian copula models for geostatistical count data. We first describe a class of random field models for geostatistical count data based on Gaussian copulas and study the properties of these random fields. We contrast the correlation structure of one of these Gaussian copula models with that of a Poisson-Gamma 2 model (De Oliveira, 2013) and show that the former is more flexible than the latter in terms of range of feasible correlation, sensitivity to the mean function and modeling of isotropy. To fit the model, we investigated the computational efficiency of two existing simulated likeli- hood methods, and proposed a new method based on Markov chain Monte Carlo. We first formu- lated the Gaussian copula models hierarchically when the nugget effect is present. Such formu- lation allows us to adapt a new inferential approach, the data cloning method (Lele et al., 2010), to the Gaussian copula models from its use in the GLMMs. Efficient group updating strategies and Langevin-Hastings algorithms are proposed. We also compared the length and the coverage probabilities of the profile-likelihood confidence intervals and the Wald-type confidence intervals after appropriate reparameterization. Finally, two spatial plug-in prediction methods are discussed. An R package gcKrig was developed to implement all the functions and algorithms discussed in this dissertation using advanced computing techniques, such as Rcpp, RcppArmadillo and parallel computing.

The Matern family of covariance functions is currently the most commonly used for the analysis of geostatistical data due to its ability to describe different smoothness behaviors. Yet, in many applications the smoothness parameter is set at an arbitrary value. This practice is due partly to computational challenges faced when attempting to estimate all covariance parameters and partly to unqualified claims in the literature stating that geostatistical data have little or no information about the smoothness parameter. This work critically investigates this claim and shows it is not true in general. Specifically, it is shown that the information the data have about the correlation parameters varies substantially depending on the true model and sampling design and, in particular, the information about the smoothness parameter can be large, in some cases larger than the information about the range parameter. In light of these findings, we suggest to reassess the aforementioned practice and instead establish inferences from data-based estimates of both range and smoothness parameters, especially for strongly dependent non-smooth processes observed on irregular sampling designs. A data set of daily rainfall totals is used to motivate the discussion and gauge this common practice.

Reference priors are theoretically attractive for the analysis of geostatistical data since they enable automatic Bayesian analysis and have desirable Bayesian and frequentist properties. But their use is hindered by computational hurdles that make their application in practice challenging. In this work, we derive a new class of default priors that approximate reference priors for the parameters of some Gaussian random fields. It is based on an approximation to the integrated likelihood of the covariance parameters derived from the spectral approximation of stationary random fields. This prior depends on the structure of the mean function and the spectral density of the model evaluated at a set of spectral points associated with an auxiliary regular grid. In addition to preserving the desirable Bayesian and frequentist properties, these approximate reference priors are more stable, and their computations are much less onerous than those of exact reference priors. Unlike exact reference priors, the marginal approximate reference prior of correlation parameter is always proper, regardless of the mean function or the smoothness of the correlation function. This property has important consequences for covariance model selection. An illustration comparing default Bayesian analyses is provided with a data set of lead pollution in Galicia, Spain.

The power prior and its variations have been proven to be a useful class of informative priors in Bayesian inference due to their flexibility in incorporating the historical information by raising the likelihood of the historical data to a fractional power {\\delta}. The derivation of the marginal likelihood based on the original power prior,and its variation, the normalized power prior, introduces a scaling factor C({\\delta}) in the form of a prior predictive distribution with powered likelihood. In this paper, we show that the scaling factor might be infinite for some positive {\\delta} with conventionally used initial priors, which would change the admissible set of the power parameter. This result seems to have been almost completely ignored in the literature. We then illustrate that such a phenomenon may jeopardize the posterior inference under the power priors when the initial prior of the model parameters is improper. The main findings of this paper suggest that special attention should be paid when the suggested level of borrowing is close to 0, while the actual optimum might be below the suggested value. We use a normal linear model as an example for illustrative purposes.

The elicitation of power priors, based on the availability of historical data, is realized by raising the likelihood function of the historical data to a fractional power {\\delta}, which quantifies the degree of discounting of the historical information in making inference with the current data. When {\\delta} is not pre-specified and is treated as random, it can be estimated from the data using Bayesian updating paradigm. However, in the original form of the joint power prior Bayesian approach, certain positive constants before the likelihood of the historical data could be multiplied when different settings of sufficient statistics are employed. This would change the power priors with different constants, and hence the likelihood principle is violated. In this article, we investigate a normalized power prior approach which obeys the likelihood principle and is a modified form of the joint power prior. The optimality properties of the normalized power prior in the sense of minimizing the weighted Kullback-Leibler divergence is investigated. By examining the posteriors of several commonly used distributions, we show that the discrepancy between the historical and the current data can be well quantified by the power parameter under the normalized power prior setting. Efficient algorithms to compute the scale factor is also proposed. In addition, we illustrate the use of the normalized power prior Bayesian analysis with three data examples, and provide an implementation with an R package NPP.

One-on-one tutoring is an effective instructional method for enhancing learning, yet its efficacy hinges on tutor competencies. Novice math tutors often prioritize content-specific guidance, neglecting aspects such as social-emotional learning. Social-emotional learning promotes equity and inclusion and nurturing relationships with students, which is crucial for holistic student development. Assessing the competencies of tutors accurately and efficiently can drive the development of tailored tutor training programs. However, evaluating novice tutor ability during real-time tutoring remains challenging as it typically requires experts-in-the-loop. To address this challenge, this preliminary study aims to harness Generative Pre-trained Transformers (GPT), such as GPT-3.5 and GPT-4 models, to automatically assess tutors' ability of using social-emotional tutoring strategies. Moreover, this study also reports on the financial dimensions and considerations of employing these models in real-time and at scale for automated assessment. The current study examined four prompting strategies: two basic Zero-shot prompt strategies, Tree of Thought prompt, and Retrieval-Augmented Generator (RAG) based prompt. The results indicate that the RAG prompt demonstrated more accurate performance (assessed by the level of hallucination and correctness in the generated assessment texts) and lower financial costs than the other strategies evaluated. These findings inform the development of personalized tutor training interventions to enhance the the educational effectiveness of tutored learning.

A 3D icing simulation code is developed in the open-source CFD toolbox OpenFOAM. A hybrid Cartesian/body-fitted meshing method is used to generate high-quality meshes around complex ice shapes. Steady-state 3D Reynolds-averaged Navier-Stokes (RANS) equations are solved to provide the ensemble-averaged flow around the airfoil. Considering the multi-scale nature of droplet size distribution, and more importantly, to represent the less uniform nature of the Super-cooled Large Droplets (SLD), two droplet tracking methods are realized: the Eulerian method is used to track the small-size droplets (below 50 μm) for the sake of efficiency; the Lagrangian method with random sampling is used to track the large droplets (above 50 μm); the heat transfer of the surface overflow is solved on a virtual surface mesh; the ice accumulation is estimated via the Myers model; finally, the final ice shape is predicted by time marching. Limited by the availability of experimental data, validations are performed on 3D simulations of 2D geometries using the Eulerian and Lagrangian methods, respectively. The code proves to be feasible and accurate enough in predicting ice shapes. Finally, an icing simulation result of the M6 wing is presented to illustrate the full 3D capability.

Single cell approaches have increased our knowledge about the cell type composition of the non-human primate (NHP), but a detailed characterization of area-specific regulatory features remains outstanding. We generated single-cell transcriptomic and chromatin accessibility (single-cell ATAC) data of 358,237 cells from prefrontal cortex (PFC), primary motor cortex (M1) and primary visual cortex (V1) of adult female cynomolgus monkey brain, and integrated this dataset with Stereo-seq (spatial enhanced resolution omics-sequencing) of the corresponding cortical areas to assign topographic information to molecular states. We identified area-specific chromatin accessible sites and their targeted genes, including the cell type-specific transcriptional regulatory network associated with excitatory neurons heterogeneity. We reveal calcium ion transport and axon guidance genes related to specialized functions of PFC and M1, identified the similarities and differences between adult macaque and human oligodendrocyte trajectories, and mapped the genetic variants and gene perturbations of human diseases to NHP cortical cells. This resource establishes a transcriptomic and chromatin accessibility combinatory regulatory landscape at a single-cell and spatially resolved resolution in NHP cortex. Cell type epigenetic and topographic information of primate brain is lacking. Here, authors identified transcriptional regulatory network, gradient expression pattern and disease vulnerability at cell type level in PFC, M1 and V1 of monkey brain by snRNAseq, snATAC-seq and Stereo-seq.