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Articles 1 - 5 of 5
Full-Text Articles in Statistics and Probability
Counting And Coloring Sudoku Graphs, Kyle Oddson
Counting And Coloring Sudoku Graphs, Kyle Oddson
Mathematics and Statistics Dissertations, Theses, and Final Project Papers
A sudoku puzzle is most commonly a 9 × 9 grid of 3 × 3 boxes wherein the puzzle player writes the numbers 1 - 9 with no repetition in any row, column, or box. We generalize the notion of the n2 × n2 sudoku grid for all n ϵ Z ≥2 and codify the empty sudoku board as a graph. In the main section of this paper we prove that sudoku boards and sudoku graphs exist for all such n we prove the equivalence of [3]'s construction using unions and products of graphs to the definition of …
Bayesian And Related Methods: Techniques Based On Bayes' Theorem, Mehmet Vurkaç
Bayesian And Related Methods: Techniques Based On Bayes' Theorem, Mehmet Vurkaç
Systems Science Friday Noon Seminar Series
Bayes' theorem is a simple algebraic consequence of conditional probability. Yet, its consequences are critical to philosophy, society, and technology. Starting from its simple derivation, we will show how its interpretation in terms of base rates (priors) and class-conditional likelihoods illuminates everyday problems in medicine and law, and provides signal processing, communications, machine learning, model selection, and other applications of statistics with powerful classification and estimation tools. Next, we will briefly examine some of the ways in which this theorem can be adopted to include multiple attributes, contexts, hypotheses, and levels of risk. Methods derived from or related to Bayes’ …
On The Skewness Of Order Statistics With Applications, Subhash C. Kochar, Maochao Xu
On The Skewness Of Order Statistics With Applications, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
Order statistics from heterogenous samples have been extensively studied in the literature. However, most of the work focused on the effect of heterogeneity on the magnitude and dispersion of order statistics. In this paper, we study the skewness of order statistics from heterogeneous samples in the sense of star order. The main results extended the results in Kochar and Xu (2009, 2011). Examples and applications in statistical inference are highlighted.
Fundamental Conditions For The Evolution Of Altruism: Towards A Unification Of Theories, Jeffrey Alan Fletcher
Fundamental Conditions For The Evolution Of Altruism: Towards A Unification Of Theories, Jeffrey Alan Fletcher
Dissertations and Theses
In evolutionary theory the existence of self-sacrificing cooperative traits poses a problem that has engendered decades of debate. The principal theories of the evolution of altruism are inclusive fitness, reciprocal altruism, and multilevel selection. To provide a framework for the unification o f these apparently disparate theories, this dissertation identifies two fundamental conditions required for the evolution of altruism: 1) non-zero-sum fitness benefits for cooperation and 2) positive assortment among altruistic behaviors. I demonstrate the underlying similarities in these three theories in the following two ways. First, I show that the game-theoretic model of the prisoner’s dilemm a (PD) is …
Estimation Of Cumulative Incidence Functions In Competing Risks Studies Under An Order Restriction, Hammou El Barmi, Subhash C. Kochar, Hari Mukerjee, Francisco J. Samaniego
Estimation Of Cumulative Incidence Functions In Competing Risks Studies Under An Order Restriction, Hammou El Barmi, Subhash C. Kochar, Hari Mukerjee, Francisco J. Samaniego
Mathematics and Statistics Faculty Publications and Presentations
In the competing risks problem an important role is played by the cumulative incidence function (CIF), whose value at time t is the probability of failure by time t for a particular type of failure in the presence of other risks. Its estimation and asymptotic distribution theory have been studied by many. In some cases there are reasons to believe that the CIFs due to two types of failure are order restricted. Several procedures have appeared in the literature for testing for such orders. In this paper we initiate the study of estimation of two CIFs subject to a type …