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Modified-Half-Normal Distribution And Different Methods To Estimate Average Treatment Effect., Jingchao Sun
Modified-Half-Normal Distribution And Different Methods To Estimate Average Treatment Effect., Jingchao Sun
Electronic Theses and Dissertations
This dissertation consists of three projects related to Modified-Half-Normal distribution and causal inference. In my first project, a new distribution called Modified-Half-Normal distribution was introduced. I explored a few of its distributional properties, the procedures for generating random samples based on Bayesian approaches, and the parameter estimation based on the method of moments. The second project deals with the problem of selection bias of average treatment effect (ATE) if we use the observational data. I combined the propensity score based inverse probability of treatment weighting (IPTW) method and the directed acyclic graph (DAG) to solve this problem. The third project …
Novel Inference Methods For Generalized Linear Models Using Shrinkage Priors And Data Augmentation., Arinjita Bhattacharyya
Novel Inference Methods For Generalized Linear Models Using Shrinkage Priors And Data Augmentation., Arinjita Bhattacharyya
Electronic Theses and Dissertations
Generalized linear models have broad applications in biostatistics and sociology. In a regression setup, the main target is to find a relevant set of predictors out of a large collection of covariates. Sparsity is the assumption that only a few of these covariates in a regression setup have a meaningful correlation with an outcome variate of interest. Sparsity is incorporated by regularizing the irrelevant slopes towards zero without changing the relevant predictors and keeping the resulting inferences intact. Frequentist variable selection and sparsity are addressed by popular techniques like Lasso, Elastic Net. Bayesian penalized regression can tackle the curse of …