A General Method to Couple Prior Distributions

Liu, Yiding (2021) A General Method to Couple Prior Distributions. Master's Thesis, University of Pittsburgh. (Unpublished)

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Abstract

There is a lot of statistic models based on marginal distribution and joint distribution relationships. Such statistical models are widely used in medicine, biology, finance, etc. Many modern medical datasets contain observations from multiple time points and treatment conditions. Adaptive shrinkage, a general method to estimate marginal prior distributions, has been developed to analyze such data for a single time point or condition, few method has been developed to analyze joint distribution for different time points or different conditions. The reason is mainly because the difficulty of constructing multi-dimensional prior distributions with dependent variables. A few Bayes' methods can be applied to these type data. Although, it is non-trivial and difficult to estimate joint distribution directly, we can easily estimate marginal prior distributions separately. In this thesis, I develop a simple, general and straightforward method to couple prior distributions for multi-dimensional genetic effects. The main goal is to research the relationship between the sign of effect of a phenotype at different time points. I couple prior distributions to model joint distribution and estimate parameters at multiple time points. Copula Estimation described from Copula Theory and Its Applications provides a parametric copula inference method for my estimation. I construct a model and develop a method to couple prior distributions to estimate my parameters at multiple time points by deriving useful expressions, applying R language for data simulations, and using maximum likelihood estimation. I simulate data from both the real copula model and multivariate normal distribution. The true model performs better in estimating the parameters. This copula model successfully bridge the gap between joint distribution and dependent marginal distributions. There is still more room to improve my copula model.

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Details

Item Type:	University of Pittsburgh ETD
Status:	Unpublished
Creators/Authors:	Creators Email Pitt Username ORCID Liu, Yiding YIL219@pitt.edu YIL219 0000-0003-4052-1372
ETD Committee:	Title Member Email Address Pitt Username ORCID Committee Chair McKennan, Chris chm195@pitt.edu chm195 Committee Member Ren, Zhao zren@pitt.edu zren Committee Member Iyengar, Satish ssi@pitt.edu ssi
Date:	3 May 2021
Date Type:	Publication
Defense Date:	6 April 2021
Approval Date:	3 May 2021
Submission Date:	6 April 2021
Access Restriction:	No restriction; Release the ETD for access worldwide immediately.
Number of Pages:	38
Institution:	University of Pittsburgh
Schools and Programs:	Dietrich School of Arts and Sciences > Statistics
Degree:	MS - Master of Science
Thesis Type:	Master's Thesis
Refereed:	Yes
Uncontrolled Keywords:	Copula, Couple prior distributions, Dependent variables, Bayes' methods, Maximum Likelihood Estimation, marginal distribution
Related URLs:	Copula Theory and Its Applications ON MODELING INSURANCE CLAIMS USING COPULAS DNA Methylation: Methods and Analyses Copula-Based Models for Multivariate Discrete Response Data An Introduction to Copulas Introductory statistics with R The Truncated Normal Distribution false discovery rates: a new deal Longitudinal data reveal strong genetic and weak non-genetic components of ethnicity-dependent blood DNA methylation levels
Date Deposited:	03 May 2021 15:47
Last Modified:	03 May 2021 15:47
URI:	http://d-scholarship.pitt.edu/id/eprint/40480

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