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Full-Text Articles in Physical Sciences and Mathematics
Model-Based Imputation Of Below Detection Limit Missing Data And Group Selection In Bayesian Group Index Regression, Matthew Carli
Model-Based Imputation Of Below Detection Limit Missing Data And Group Selection In Bayesian Group Index Regression, Matthew Carli
Theses and Dissertations
Investigations into the association between chemical exposure and health outcomes are increasingly focused on the role of chemical mixtures, as opposed to individual chemicals. The analysis of chemical mixture data required the development of novel statistical methods, one of these being Bayesian group index regression. A statistical challenge common to all chemical mixture analyses is the ubiquitous presence of below detection limit (BDL) data. We propose an extension of Bayesian group index regression that treats both regression effects and missing BDL observations as parameters in a model estimated through a Markov Chain Monte Carlo algorithm that we refer to as …
Parametric, Nonparametric, And Semiparametric Linear Regression In Classical And Bayesian Statistical Quality Control, Chelsea L. Jones
Parametric, Nonparametric, And Semiparametric Linear Regression In Classical And Bayesian Statistical Quality Control, Chelsea L. Jones
Theses and Dissertations
Statistical process control (SPC) is used in many fields to understand and monitor desired processes, such as manufacturing, public health, and network traffic. SPC is categorized into two phases; in Phase I historical data is used to inform parameter estimates for a statistical model and Phase II implements this statistical model to monitor a live ongoing process. Within both phases, profile monitoring is a method to understand the functional relationship between response and explanatory variables by estimating and tracking its parameters. In profile monitoring, control charts are often used as graphical tools to visually observe process behaviors. We construct a …
Applications Of Dynamic Linear Models To Random Allocation Models, Albert H. Lee Iii
Applications Of Dynamic Linear Models To Random Allocation Models, Albert H. Lee Iii
Theses and Dissertations
Although advances in modern computational algorithms have provided researchers the ability to work problems which were once too computationally complex to solve, problems with high computation or large parameter spaces still remain. Problems such as those involving Time Series can be such problems. Chapter 1 looks at the the use of Exponentially Weighted Moving Averages developed by \citep{holt2004forecasting, winters1960forecasting} which were thought to provide sufficient solutions to these Time Series. A discussion is provided which illustrates the shortcomings of the EWMA and how its infinite number of possible starting values provides the modeler with an endless number of possible solutions …
Site- And Location-Adjusted Approaches To Adaptive Allocation Clinical Trial Designs, Brian S. Di Pace
Site- And Location-Adjusted Approaches To Adaptive Allocation Clinical Trial Designs, Brian S. Di Pace
Theses and Dissertations
Response-Adaptive (RA) designs are used to adaptively allocate patients in clinical trials. These methods have been generalized to include Covariate-Adjusted Response-Adaptive (CARA) designs, which adjust treatment assignments for a set of covariates while maintaining features of the RA designs. Challenges may arise in multi-center trials if differential treatment responses and/or effects among sites exist. We propose Site-Adjusted Response-Adaptive (SARA) approaches to account for inter-center variability in treatment response and/or effectiveness, including either a fixed site effect or both random site and treatment-by-site interaction effects to calculate conditional probabilities. These success probabilities are used to update assignment probabilities for allocating patients …
Dynamic Bayesian Approaches To The Statistical Calibration Problem, Derick Lorenzo Rivers
Dynamic Bayesian Approaches To The Statistical Calibration Problem, Derick Lorenzo Rivers
Theses and Dissertations
The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the "classical" approach and the "inverse" regression approach. Both of these models are static models and are used to estimate "exact" measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe the measurement. The Bayesian time series analysis method of Dynamic Linear Models (DLM) can be used …