SIAM Undergraduate Research Online
Volume 8
In This Volume
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Numerical Methods for Estimating Correlation Coefficient of Trivariate Gaussians
Published electronically December 10, 2015DOI: 10.1137/15S013831
Authors
Weronika J. Swiechowicz (Illinois Institute of Technology), Yuanfang Xiang (Illinois Institute of Technology)
Project Advisors
Sonja Petrovic (Illinois Institute of Technology)
Abstract
Given observed data, the fundamental task of statistical inference is to understand the underlying data-generating mechanism. This task usually entails several steps, including determining a good family of probability distributions that could have given rise to the observed data, and identifying the specific distribution from that family that best fits the data. The second step is usually called parameter estimation, where the parameters are what determines the specific distribution. In many instances, however, estimating parameters of a statistical model poses a significant challenge for statistical inference. Currently, there are many standard optimization methods used for estimating parameters, including numerical approximations such as the Newton-Raphson method. However, they may fail to find a correct set of maximum values of the function and draw incorrect conclusions, since their performance depends on both the geometry of the function and location of the starting point for the approximation. An alternative approach, used in the field of algebraic statistics, involves numerical approximations of the roots of the critical equations by the method of numerical algebraic geometry. This method is used to find all critical points of a function, before choosing the maximum value(s). In this paper, we focus on estimating correlation coefficients for multivariate normal random vectors when the mean is known. The bivariate case was solved in 2000 by Small, Wang and Yang, who emphasize the problem of multiple critical points of the likelihood function. The goal of this paper is to consider the first generalization of their work to the trivariate case, and offer a computational study using both numerical approaches to find the global maximum value of the likelihood function.
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A Reliability Analysis of Personnel Protection Systems at the Spallation Neutron Source
Published electronically December 3, 2015 -
Insights into the Computation for pi
Published electronically November 10, 2015 -
Transitions in a Metastable Neuronal Network
Published electronically November 3, 2015 -
Analysis and Simulation of a Mathematical Model of Ebola Virus Dynamics in vivo
Published electronically August 26, 2015 -
Swarm Shape and its Dynamics in a Predator-swarm Model
Published electronically July 14, 2015 -
STEM Sells: What is higher education really worth?
Published electronically July 7, 2015 -
Quantifying Option Implications
Published electronically July 1, 2015 -
Effective Ranges of a Modeled Open Limestone Channel
Published electronically June 29, 2015 -
Concurrent Solutions to Linear Systems using Hybrid CPU/GPU Nodes
Published electronically June 9, 2015 -
Numerical Computation of Wave Breaking Times
Published electronically April 22, 2015 -
Improving the Error-correcting Code used in 3-G Communication
Published electronically April 14, 2015 -
Realistic Modeling and Simulation of Influenza Transmission Over an Urban Community
Published electronically March 25, 2015 -
The Spreading of an Insoluble Surfactant on a Thin Non-Newtonian Fluid
Published electronically March 18, 2015 -
A New Look at the St. Petersburg Paradox
Published electronically February 3, 2015 -
Numerically Computing Zeros of the Evans Function
Published electronically February 2, 2015 -
Separating Mixed Signals in a Noisy Environment Using Global Optimization
Published electronically February 2, 2015 -
Determining the Top All-time College Coaches through Markov Chain-based Rank Aggregation
Published electronically January 30, 2015 -
Estimation of Unmodeled Gravitational Wave Transients with Spline Regression and Particle Swarm Optimization
Published electronically January 26, 2015
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