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Articles 451 - 480 of 1562
Full-Text Articles in Statistics and Probability
Mechanical Behavior Of Composite Structures Of Wearing Course And Underlying Layer For Asphalt Pavements, Yang Xiaohua, Yuan Zhanwen, Wen Yongbing, Zhou Chao, Wu Hao
Mechanical Behavior Of Composite Structures Of Wearing Course And Underlying Layer For Asphalt Pavements, Yang Xiaohua, Yuan Zhanwen, Wen Yongbing, Zhou Chao, Wu Hao
Journal of China & Foreign Highway
The interlayer bonding state of pavement structures changes due to the influence of various factors under service conditions，and this change exhibits a significant influence on the mechanical behavior of pavement structures.Through the composite structure test and numerical analysis，the mechanical behavior of the composite structure of different wearing courses and underlying layers under different stresses and bonding states was studied.The test used three commonly used wearing course （surface layer ） materials of asphalt pavements，namely AC- 13，OGFC- 13，and SMA- 13 for comparative analysis.The test results show that different composite structures exhibit different interlayer bonding properties and fatigue characteristics due to the difference …
Shear Strength Test Of Hefei Expansive Soil Under Low Stress Conditions With Controlled Suction, Hou Chaoqun, Zhang Rongjian, Li Yongxin
Shear Strength Test Of Hefei Expansive Soil Under Low Stress Conditions With Controlled Suction, Hou Chaoqun, Zhang Rongjian, Li Yongxin
Journal of China & Foreign Highway
Topsoil slide and instability of expansive soil slopes may occur under variable saturation conditions.In order to study the strength characteristics of unsaturated expansive soil under low stress conditions，several different matrix suction and stress conditions were set by unsaturated triaxial apparatus.The triaxial shear test of Hefei expansive soil was carried out，and the test data were analyzed.The test results show that when the net confining stress on the expansive soil continues to weaken，the stress-strain curve transitions from strain hardening to strain softening.The strength of unsaturated expansive soil increases with increasing matrix suction.The shear strength of shallow expansive soil shows a significant reduction …
Influence Of Aerodynamic Shape Change On Wind Resistance Performance Of Large Span Truss Bridge, Jing Dade, Su Yi
Influence Of Aerodynamic Shape Change On Wind Resistance Performance Of Large Span Truss Bridge, Jing Dade, Su Yi
Journal of China & Foreign Highway
The development of the transportation an d tourism industry has led to bridges fulfilling additional roles，such as tourism，alongside their transportation functions，resulting in significant changes in structural aerodynamic shape and ventilation rate.This paper analyzed a double-tower single-span steel truss suspension bridge with a main span of 1 088 m，re-evaluated its wind resistance performance through the full-bridge aeroelastic model wind tunnel test，and evaluated the pedestrian comfort problem while studying the wind-resistant stability of the structure.The results indicate that the structural dynamic characteristics of the bridge remain almost unchanged before and after altering the aerodynamic shape of the bridge for its scenic spot …
Influence Of Section Selection On Mechanical Performance Of Corrugated Steel Box Culvert, Zhang Shun, Liu Baodong, Gao Meng, Wu Fei, Wang Zhihong
Influence Of Section Selection On Mechanical Performance Of Corrugated Steel Box Culvert, Zhang Shun, Liu Baodong, Gao Meng, Wu Fei, Wang Zhihong
Journal of China & Foreign Highway
Corrugated steel box culverts exhibit a higher section utilization rate compared with circular，arched，and pipe-arch corrugated steel structures，making them more suitable for for scenarios with restricted embankment height.While numerous studies focus on strengthening strategies for corrugated steel box culverts，research on selecting cross-sectional forms is scarce.This study utilized the finite element analysis software Abaqus to develop finite element models of corrugated steel box culverts with sidewall inclination angles of 0°，5°，10°，15° and 20° respectively.The impact of these inclination angles on the structural stress and deformation outcomes was analyzed.The results indicate that increasing the sidewall inclination angles can effectively reduce vertical deformation and maximum …
Study On Anchorage Reliability For Strand Shoe And Pull Rod Of Air‑Spinning Suspension Bridge, Huang Anming, Yang Bo, Chen Long, Xie Jun, Chen Xin
Study On Anchorage Reliability For Strand Shoe And Pull Rod Of Air‑Spinning Suspension Bridge, Huang Anming, Yang Bo, Chen Long, Xie Jun, Chen Xin
Journal of China & Foreign Highway
Each strand wire of the main cable in the suspension bridge constructed by the AS method is sleeved and anchored on the strand shoes on both banks.The strand shoe transmits the strand force to the anchoring system through the pull rod.The bearing capacity of the strand shoe after the interaction between the strand shoe and the wires of the main cable，the stress state of the wires after small curvature bending，and the influence of installation accuracy of the pull rod on the anchoring reliability all need to be qualitatively and quantitatively studied and verified by the experiment.In this paper，the main cable …
Research On Gravity Anchorage Foundation Of Dadu River Bridge In Luding, Zhou Ti Ng, Tao Qiyu, Li Zejun
Research On Gravity Anchorage Foundation Of Dadu River Bridge In Luding, Zhou Ti Ng, Tao Qiyu, Li Zejun
Journal of China & Foreign Highway
Moraine soils formed during th e Qua ternary glacial period are widely distributed in the west of China，exhibiting good mechanical properties and deep overburden.This paper studied the Dadu River bridge in Luding and investigated the influence of various foundation forms on anchorage stability in the case of considering moraine soils as the soil supporting layer of gravity anchorage foundation through theoretical analysis and numerical simulation.The findings suggest that a slant expanded foundation with a notched sill demonstrates good force-bearing capability and is cost-effective.These results can provide a reference for similar construction projects in the west of China.
Test On Water Mist Wrapped Dust Reduction Technology For Tunnels, Wang Yijun, Wang Fei, Jia Yuedi, Pan Weihua, He Xingchun, Yao Wenhui
Test On Water Mist Wrapped Dust Reduction Technology For Tunnels, Wang Yijun, Wang Fei, Jia Yuedi, Pan Weihua, He Xingchun, Yao Wenhui
Journal of China & Foreign Highway
In order to eliminate the dust produced by tunnel blasting more quickly and effectively，two kinds of mist spray and dust reduction schemes were put forward，which were the “air duct water mist wrapped type ” and the “vehicle-mounted water mist wrapped type ”.The field test was carried out on Jiaoding Tunnel in Yunnan.The results show that for the dust reduction technology scheme of “air duct water mist wrapped type ”，the dust concentration of the No.1 characteristic position at the tunnel face decreases to 3.87 mg/m3 after 10 minutes of dust reduction，which meets the specification requirements.For the dust reduction technology of “vehicle-mounted …
Numerical Simulation On Bearing Characteristics Of Tunnel‑Type Anchorage Of A Grand Bridge Over Qingjiang River, Yin Hongmei, Shi Qian, Zhang Yihu
Numerical Simulation On Bearing Characteristics Of Tunnel‑Type Anchorage Of A Grand Bridge Over Qingjiang River, Yin Hongmei, Shi Qian, Zhang Yihu
Journal of China & Foreign Highway
This paper took the tunnel-type anchorage on the left bank of a grand bridge over the Qingjiang River as an example and established a three-dimensional geological generalization model based on the engineering geological analysis.In addition，the paper used different software to realize the approximate grid discrete division of complex rock mass and tunnel-type anchorage structure.FLAC3D software was used to simulate different working conditions，and the deformation characteristics and bearing capacity of the tunnel-type anchorage were obtained.It is found that the potential failure mode of the tunnel-type anchorage is that the anchor and the rock mass cut by the structural plane on the …
Study On Length Of Deceleration Lane Of Left Off‑Ramp For Urban Underground Interchanges Based On Traffic Conflicts, Wang Hailiang, Cheng Chong, Guan Hong, Ding Naikan
Study On Length Of Deceleration Lane Of Left Off‑Ramp For Urban Underground Interchanges Based On Traffic Conflicts, Wang Hailiang, Cheng Chong, Guan Hong, Ding Naikan
Journal of China & Foreign Highway
To set a reasonable range of the length of the deceleration lane in the diverge area of the left off-ramp for urban underground interchanges，the effects of the length of the deceleration lane，as well as interactions between traffic volumes and design speeds of mainline and ramp on traffic conflict in the diverge area，were exami ned.By taking the underground interchange of the Wuhan East-South Lakes Tunnel Project as an example，the VISSIM micro traffic simulation test was carried out，and the conflict rate （RCR） and exposed time to collision （TTET） were extracted.The results show that ① when the length of the deceleration lane increases，the …
Study On Safety Risk Assessment System For Waste Dump Of Mountainous Expressways, Ye Xian, Yin Hao, Zhao Xin, Wang Guanqun, Gao Yu
Study On Safety Risk Assessment System For Waste Dump Of Mountainous Expressways, Ye Xian, Yin Hao, Zhao Xin, Wang Guanqun, Gao Yu
Journal of China & Foreign Highway
The safety of waste dump projects of mountainous expressways is related to environmental protection，water and soil conservation，highway building protection，and downstream environment-sensitive point protection，so it is necessary to put forward safety assessment methods.Based on the data analysis of 1 369 waste dumps in Yunnan Province，the safety risk factors of the waste dump engineering were proposed and summarized as five primary indicators，including site selection and design factors，construction factors，regional geological factors，external influencing factors，and data integrity factors，and 18 secondary indicators were further put forward.The group decision-making analytic hierarchy process （AHP ） model was established，and the weight of secondary indexes was determined by 64 technical …
Analysis On Design Concept Of Subgrade And Pavement Of Colombia High‑Grade Highway, Liu Tao, Hu Guanhua, Yuan Yi
Analysis On Design Concept Of Subgrade And Pavement Of Colombia High‑Grade Highway, Liu Tao, Hu Guanhua, Yuan Yi
Journal of China & Foreign Highway
Colombian highway design predominantly adheres to American Standards，emphasizing design concepts reflective of the United States while encompassing Colombia's engineering design habits，concepts，and characteristics.This paper introduced the main design schemes of the Colombia MAR 2 Highway Project in northern Colombia，including protection engineering，drainage engineering，subgrade filling，spoil ground，and pavement.It conducted a comparative analysis between Colombian and Chinese design concepts，highlighting similarities and disparities，and put forward the thinking of mutual learning.
Study On Flexural Behavior Of Wet Joints Of Prefabricated Steel‑Uhpc Composite Bridge Deck, Liao Wancheng, Zhao Hua, An Jiahe
Study On Flexural Behavior Of Wet Joints Of Prefabricated Steel‑Uhpc Composite Bridge Deck, Liao Wancheng, Zhao Hua, An Jiahe
Journal of China & Foreign Highway
Prefabricated steel-UHPC composite bridge deck is a new deck structure system that places the longitudinal rib at the upper layer and forms PBL shear connectors.This structure can be prefabricated in the factory and assembled on-site.The adjacent steel beams are integrated by welding，and the cast in-situ UHPC wet joints connect the adjacent UHPC bridge decks.However，these wet joints represent the structure's vulnerable segments but with little research.To this end，a full-scale model test has been conducted to study the flexural behavior of the wet joints in a steel-UHPC composite bridge deck in a practical project.The Abaqus finite element model was established and verified …
Research On Shape Optimization Of Four‑Center Circular Highway Tunnel Based On Parametric Modeling Idea, Zhu Lei, Guo Meng, Guo Jinyong, Shen Caihua, Zhang Hanyi
Research On Shape Optimization Of Four‑Center Circular Highway Tunnel Based On Parametric Modeling Idea, Zhu Lei, Guo Meng, Guo Jinyong, Shen Caihua, Zhang Hanyi
Journal of China & Foreign Highway
The rational cross-sectional form of the four-center circular highway tunnel contributes to enhancing the stress state of the lining structure，reducing cracks in the composite lining，and enhancing the durability of the tunnel structure.Utilizing the Ansys APDL programming platform and guided by the design principle of continuous-curvature，a parametric modeling equation for the geometrical dimensions of local tunnel shape in arch foot area was established.The calculation method and numerical simulation models for the equivalent mechanical parameters of the anchor reinforcement area were also developed.The study revealed the impact of the local tunnel shape parameter design in the arch foot area on the internal …
Assessment Of Method Effects Of Keying And Wording In Instruments: A Mixed-Methods Explanatory Sequential Study, Lin Ma
Electronic Theses and Dissertations
This dissertation presents an innovative approach to examining the keying method, wording method, and construct validity on psychometric instruments. By employing a mixed methods explanatory sequential design, the effects of keying and wording in two psychometric assessments were examined and validated. Those two self-report psychometric assessments were the Effortful Control assessment (Ellis & Rothbart, 2001) and the Grit assessment (Duckworth & Quinn, 2009). Moreover, the quantitative phase utilized structural equation modeling to analyze 2,104 students’ responses and assess the construct of keying and wording. Various hypothetical models were investigated and evaluated. The reliability of each construct in each method was …
Identifying Rural Health Clinics Within The Transformed Medicaid Statistical Information System (T-Msis) Analytic Files, Katherine Ahrens Mph, Phd, Zachariah Croll, Yvonne Jonk Phd, John Gale Ms, Heidi O'Connor Ms
Identifying Rural Health Clinics Within The Transformed Medicaid Statistical Information System (T-Msis) Analytic Files, Katherine Ahrens Mph, Phd, Zachariah Croll, Yvonne Jonk Phd, John Gale Ms, Heidi O'Connor Ms
Rural Health Clinics
Researchers at the Maine Rural Health Research Center describe a methodology for identifying Rural Health Clinic encounters within the Medicaid claims data using Transformed Medicaid Statistical Information System (T-MSIS) Analytic Files.
Background: There is limited information on the extent to which Rural Health Clinics (RHC) provide pediatric and pregnancy-related services to individuals enrolled in state Medicaid/CHIP programs. In part this is because methods to identify RHC encounters within Medicaid claims data are outdated.
Methods: We used a 100% sample of the 2018 Medicaid Demographic and Eligibility and Other Services Transformed Medicaid Statistical Information System (T-MSIS) Analytic Files for 20 states …
Session 6: The Size-Biased Lognormal Mixture With The Entropy Regularized Algorithm, Tatjana Miljkovic, Taehan Bae
Session 6: The Size-Biased Lognormal Mixture With The Entropy Regularized Algorithm, Tatjana Miljkovic, Taehan Bae
SDSU Data Science Symposium
A size-biased left-truncated Lognormal (SB-ltLN) mixture is proposed as a robust alternative to the Erlang mixture for modeling left-truncated insurance losses with a heavy tail. The weak denseness property of the weighted Lognormal mixture is studied along with the tail behavior. Explicit analytical solutions are derived for moments and Tail Value at Risk based on the proposed model. An extension of the regularized expectation–maximization (REM) algorithm with Shannon's entropy weights (ewREM) is introduced for parameter estimation and variability assessment. The left-truncated internal fraud data set from the Operational Riskdata eXchange is used to illustrate applications of the proposed model. Finally, …
Session 6: Model-Based Clustering Analysis On The Spatial-Temporal And Intensity Patterns Of Tornadoes, Yana Melnykov, Yingying Zhang, Rong Zheng
Session 6: Model-Based Clustering Analysis On The Spatial-Temporal And Intensity Patterns Of Tornadoes, Yana Melnykov, Yingying Zhang, Rong Zheng
SDSU Data Science Symposium
Tornadoes are one of the nature’s most violent windstorms that can occur all over the world except Antarctica. Previous scientific efforts were spent on studying this nature hazard from facets such as: genesis, dynamics, detection, forecasting, warning, measuring, and assessing. While we want to model the tornado datasets by using modern sophisticated statistical and computational techniques. The goal of the paper is developing novel finite mixture models and performing clustering analysis on the spatial-temporal and intensity patterns of the tornadoes. To analyze the tornado dataset, we firstly try a Gaussian distribution with the mean vector and variance-covariance matrix represented as …
Sparse Bayesian Variable Selection In High‐Dimensional Logistic Regression Models With Correlated Priors, Zhuanzhuan Ma, Zifei Han, Souparno Ghosh, Liucang Wu, Min Wang
Sparse Bayesian Variable Selection In High‐Dimensional Logistic Regression Models With Correlated Priors, Zhuanzhuan Ma, Zifei Han, Souparno Ghosh, Liucang Wu, Min Wang
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we propose a sparse Bayesian procedure with global and local(GL) shrinkage priors for the problems of variable selection and classification in high-dimensional logistic regression models. In particular, we consider two types of GL shrinkage priors for the regression coefficients, the horseshoe (HS)prior and the normal-gamma (NG) prior, and then specify a correlated prior for the binary vector to distinguish models with the same size. The GL priors are then combined with mixture representations of logistic distribution to construct a hierarchical Bayes model that allows efficient implementation of a Markov chain Monte Carlo (MCMC) to generate samples from …
A Computerized Mastitis Classification Aid Using A Dairy Herd-Based Records: Multi-Layer Perceptron (Mlp) Neural Network With Backpropagation Approach, Ahmed M. Gad Prof, Dina Faris De, Sherif Ramadan Prof, Ghada Afifi Dr, Eman Manaa Prof, Mahmoud El-Tarabany Prof
A Computerized Mastitis Classification Aid Using A Dairy Herd-Based Records: Multi-Layer Perceptron (Mlp) Neural Network With Backpropagation Approach, Ahmed M. Gad Prof, Dina Faris De, Sherif Ramadan Prof, Ghada Afifi Dr, Eman Manaa Prof, Mahmoud El-Tarabany Prof
Business Administration
The main objective of this study is to develop an efficient machine learning-based model for the early prediction of clinical mastitis in Holstein Friesian dairy cattle where automatic milking system (AMS) data is used. The model aims to offer a costless opportunity for mastitis control and reduce its negative impact on livestock production. Different forward multilayer perceptron (MLP) neural networks with backpropagation (BP) learning algorithms using various numbers of hidden neurons and epochs have been introduced. The results of the established models are evaluated based on different metrics such as the accuracy, the F1 core, the precision, the recall, and …
Advancing Deep Learning With Graph-Based Structural Insights: From Graph Classification To Semantic Segmentation, Xin Ma
Computer Science and Engineering Dissertations - Archive
Deep learning has profoundly transformed machine learning by offering sophisticated data representations, yet effectively incorporating structural information remains a challenge. Structural data, whether explicit or implicit, has the potential to significantly enhance the performance of deep learning tasks. This research investigates the benefits of structural information across three crucial tasks: classification, clustering, and segmentation. For explicit structural data, where inputs are directly represented as graphs, we investigate graph-level classification in brain connectivity networks. We introduce the Multi-resolution Edge Network (MENET), a novel framework designed to identify disease-specific connectomic benchmarks with high discriminatory power across diagnostic categories. MENET leverages graph-level representations …
Predicting Superconducting Critical Temperature Using Regression Analysis, Roland Fiagbe
Predicting Superconducting Critical Temperature Using Regression Analysis, Roland Fiagbe
Data Science and Data Mining
This project estimates a regression model to predict the superconducting critical temperature based on variables extracted from the superconductor’s chemical formula. The regression model along with the stepwise variable selection gives a reasonable and good predictive model with a lower prediction error (MSE). Variables extracted based on atomic radius, valence, atomic mass and thermal conductivity appeared to have the most contribution to the predictive model.
Defensive Impact Wins: Developing A New Method To Rate Individual Defense In Nba Games, Dylan J. Stiles
Defensive Impact Wins: Developing A New Method To Rate Individual Defense In Nba Games, Dylan J. Stiles
Honors Theses and Capstones
With the analytics revolution in sports in the past 20 years, it seems that everything that can be quantified is. In basketball though, trying to break the game down into a set of numbers comes with a unique problem. While we've come up with a good set of advanced numbers to measure offensive efficiency, defense is fundamentally harder to quantify. The game is played five on five, but it has often been popular or convenient to model defense as a set of five one on one games. As defenses became more complex into the 2010s, this methodology became more insignificant. …
Machine Learning Approaches For Cyberbullying Detection, Roland Fiagbe
Machine Learning Approaches For Cyberbullying Detection, Roland Fiagbe
Data Science and Data Mining
Cyberbullying refers to the act of bullying using electronic means and the internet. In recent years, this act has been identifed to be a major problem among young people and even adults. It can negatively impact one’s emotions and lead to adverse outcomes like depression, anxiety, harassment, and suicide, among others. This has led to the need to employ machine learning techniques to automatically detect cyberbullying and prevent them on various social media platforms. In this study, we want to analyze the combination of some Natural Language Processing (NLP) algorithms (such as Bag-of-Words and TFIDF) with some popular machine learning …
The Performance Of Marginal Modeling Methods For Rare Events With Application To Opioid Overdose Mortality And Morbidity, Shawn Nigam
Theses and Dissertations--Epidemiology and Biostatistics
Opioid misuse is a nationwide epidemic, with Kentucky having one of the highest opioid overdose-related fatality rates across all US states. These rates have increased significantly over the past decade, with particularly large increases during the COVID-19 pandemic. This dissertation aims to study the behavior of these increases and the methods for the marginal modeling of count outcomes related to opioid overdose.
Opioid overdose-related fatality rates in Kentucky increased significantly during the COVID-19 pandemic. In this chapter, we characterize the changes in opioid overdose fatality rates in Kentucky and identify associations between potential factors and fatality rates. County-level opioid overdose …
Variable Selection For High-Dimensional Data With Interaction Effects: Methods, Applications, And Inferences, Leiyue Li
Theses and Dissertations--Statistics
For high-dimensional data where the number of variables greatly exceeds the number of observations, selecting important variables while maintaining the required heredity conditions can be challenging. This dissertation is structured into three interconnected parts. In the first part, we propose a variable selection method by implementing a well-known optimization technique, the Genetic Algorithm. An R package was developed to simplify the implementation and usage of the proposed method. We then propose another variable selection method by extending the study from the Genetic Algorithm to a different but related optimization technique, Simulated Annealing. We consider three different hierarchical structures in both …
From Non-Parametric Methods To Self-Supervised Learning: Applications In Edge Detection And Image Denoising, Jiacheng Xu
From Non-Parametric Methods To Self-Supervised Learning: Applications In Edge Detection And Image Denoising, Jiacheng Xu
Theses and Dissertations--Statistics
This dissertation explores advanced methodologies for edge detection and image denoising through the application of both traditional non-parametric methods and modern self-supervised deep learning techniques. Beginning with non-parametric approaches, we refine surface fitting and jump detection criteria to enhance the detection of discontinuous regression surfaces in grayscale images. These foundational techniques are extended to color images, with analyses across RGB and CIELAB color spaces to improve edge detection accuracy. We then introduce a self-supervised neural network model that integrates Masked Modeling into the Bi-Directional Cascade Network (BDCN) framework. This approach shows the potential of reducing the dependency on annotated data …
Imputation Strategies For Different Categories Of Missing Data, Karthik Chalumuri
Imputation Strategies For Different Categories Of Missing Data, Karthik Chalumuri
Honors Theses and Capstones
Addressing missing data in research is crucial for ensuring the reliability and validity of study findings, yet it remains a significant challenge. This study investigates the impact of missing data on research outcomes and explores the underutilization of existing tools for managing missingness, potentially leading to gaps in critical information with tangible implications for decision-making processes (Dziura et al.).
Focusing on the different categories of missing data—Missing Completely At Random (MCAR), Missing At Random (MAR), and Missing Not At Random (MNAR)—this research examines various imputation strategies tailored to each category. Specifically, we compare the efficacy of several model-based imputation methods, …
Pitching The Use Of Squared And Interaction Terms In Regression Via Baseball Heat Maps, Lucas Chepelsky
Pitching The Use Of Squared And Interaction Terms In Regression Via Baseball Heat Maps, Lucas Chepelsky
Williams Honors College, Honors Research Projects
This project will examine the impact of using second-order terms in regression. For illustration, we use an example of regression where a baseball player's three by three heat map, including the height and distance from inside to outside of the pitch, are variables used to predict batting average. We find that second-order terms are crucial in discovering nonlinear relationships and interaction effects in regression models, and maintain that the common practice of using first-order additive models is insufficient.
Ensemble Classification: An Analysis Of The Random Forest Model, Jarod Korn
Ensemble Classification: An Analysis Of The Random Forest Model, Jarod Korn
Williams Honors College, Honors Research Projects
The random forest model proposed by Dr. Leo Breiman in 2001 is an ensemble machine learning method for classification prediction and regression. In the following paper, we will conduct an analysis on the random forest model with a focus on how the model works, how it is applied in software, and how it performs on a set of data. To fully understand the model, we will introduce the concept of decision trees, give a summary of the CART model, explain in detail how the random forest model operates, discuss how the model is implemented in software, demonstrate the model by …
Bayesian Estimation Of Hierarchical Linear Models From Incomplete Data: Cluster-Level Non-Linear Effects And Small Sample Sizes, Dongho Shin
Theses and Dissertations
We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other nonlinear effects given small sample sizes, however, maximum likelihood estimation is suboptimal, and existing Gibbs samplers are based on a Bayesian joint distribution compatible with the HLM, but impute missing values of C by a Metropolis algorithm via a proposal density having a constant variance while the target …