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Full-Text Articles in Mathematics
Em Estimation For Zero- And K-Inflated Poisson Regression Model, Monika Arora, N. Rao Chaganty
Em Estimation For Zero- And K-Inflated Poisson Regression Model, Monika Arora, N. Rao Chaganty
Mathematics & Statistics Faculty Publications
Count data with excessive zeros are ubiquitous in healthcare, medical, and scientific studies. There are numerous articles that show how to fit Poisson and other models which account for the excessive zeros. However, in many situations, besides zero, the frequency of another count k tends to be higher in the data. The zero- and k-inflated Poisson distribution model (ZkIP) is appropriate in such situations The ZkIP distribution essentially is a mixture distribution of Poisson and degenerate distributions at points zero and k. In this article, we study the fundamental properties of this mixture distribution. Using stochastic representation, we …
Empirical Bayesian Approach To Testing Multiple Hypotheses With Separate Priors For Left And Right Alternatives, Naveen K. Bansal, Mehdi Maadooliat, Steven J. Schrodi
Empirical Bayesian Approach To Testing Multiple Hypotheses With Separate Priors For Left And Right Alternatives, Naveen K. Bansal, Mehdi Maadooliat, Steven J. Schrodi
Mathematics, Statistics and Computer Science Faculty Research and Publications
We consider a multiple hypotheses problem with directional alternatives in a decision theoretic framework. We obtain an empirical Bayes rule subject to a constraint on mixed directional false discovery rate (mdFDR≤α) under the semiparametric setting where the distribution of the test statistic is parametric, but the prior distribution is nonparametric. We proposed separate priors for the left tail and right tail alternatives as it may be required for many applications. The proposed Bayes rule is compared through simulation against rules proposed by Benjamini and Yekutieli and Efron. We illustrate the proposed methodology for two sets of …
On The Mixtures Of Weibull And Pareto (Iv) Distribution: An Alternative To Pareto Distribution, I. Ghosh, Gholamhossein G. Hamedani, Naveen K. Bansal, Mehdi Maadooliat
On The Mixtures Of Weibull And Pareto (Iv) Distribution: An Alternative To Pareto Distribution, I. Ghosh, Gholamhossein G. Hamedani, Naveen K. Bansal, Mehdi Maadooliat
Mathematics, Statistics and Computer Science Faculty Research and Publications
Finite mixture models have provided a reasonable tool to model various types of observed phenomena, specially those which are random in nature. In this article, a finite mixture of Weibull and Pareto (IV) distribution is considered and studied. Some structural properties of the resulting model are discussed including estimation of the model parameters via expectation maximization (EM) algorithm. A real-life data application exhibits the fact that in certain situations, this mixture model might be a better alternative than the rival popular models.
Empirical Bayes And Hierarchical Bayes Estimation Of Skew Normal Populations, Naveen K. Bansal, Mehdi Maadooliat, Xiaowei Wang
Empirical Bayes And Hierarchical Bayes Estimation Of Skew Normal Populations, Naveen K. Bansal, Mehdi Maadooliat, Xiaowei Wang
Naveen Bansal
We develop empirical and hierarchical Bayesian methodologies for the skew normal populations through the EM algorithm and the Gibbs sampler. A general concept of skewness to the normal distribution is considered throughout. Motivations are given for considering the skew normal population in applications, and an example is presented to demonstrate why the skew normal distribution is more applicable than the normal distribution for certain applications.
Ricean Over Gaussian Modelling In Magnitude Fmri Analysis—Added Complexity With Negligible Practical Benefits, Daniel W. Adrian, Ranjan Maitra, Daniel B. Rowe
Ricean Over Gaussian Modelling In Magnitude Fmri Analysis—Added Complexity With Negligible Practical Benefits, Daniel W. Adrian, Ranjan Maitra, Daniel B. Rowe
Mathematics, Statistics and Computer Science Faculty Research and Publications
It is well known that Gaussian modelling of functional magnetic resonance imaging (fMRI) magnitude time-course data, which are truly Rice distributed, constitutes an approximation, especially at low signal-to-noise ratios (SNRs). Based on this fact, previous work has argued that Rice-based activation tests show superior performance over their Gaussian-based counterparts at low SNRs and should be preferred in spite of the attendant additional computational and estimation burden. Here, we revisit these past studies and, after identifying and removing their underlying limiting assumptions and approximations, provide a more comprehensive comparison. Our experimental evaluations using Receiver Operating Characteristic (ROC) curve methodology show that …
Empirical Bayes And Hierarchical Bayes Estimation Of Skew Normal Populations, Naveen K. Bansal, Mehdi Maadooliat, Xiaowei Wang
Empirical Bayes And Hierarchical Bayes Estimation Of Skew Normal Populations, Naveen K. Bansal, Mehdi Maadooliat, Xiaowei Wang
Mathematics, Statistics and Computer Science Faculty Research and Publications
We develop empirical and hierarchical Bayesian methodologies for the skew normal populations through the EM algorithm and the Gibbs sampler. A general concept of skewness to the normal distribution is considered throughout. Motivations are given for considering the skew normal population in applications, and an example is presented to demonstrate why the skew normal distribution is more applicable than the normal distribution for certain applications.
Self-Consistency: A Fundamental Concept In Statistics, Thaddeus Tarpey, Bernard Flury
Self-Consistency: A Fundamental Concept In Statistics, Thaddeus Tarpey, Bernard Flury
Mathematics and Statistics Faculty Publications
The term ''self-consistency'' was introduced in 1989 by Hastie and Stuetzle to describe the property that each point on a smooth curve or surface is the mean of all points that project orthogonally onto it. We generalize this concept to self-consistent random vectors: a random vector Y is self-consistent for X if E[X|Y] = Y almost surely. This allows us to construct a unified theoretical basis for principal components, principal curves and surfaces, principal points, principal variables, principal modes of variation and other statistical methods. We provide some general results on self-consistent random variables, give …