The Polya’s Urn model is notable within statistics because it generalizes the binomial, hypergeometric, and beta-Bernoulli (beta-binomial) distributions through a single formula. In addition, Polya’s Urn is a multivariate distribution whose variables are exchangeable but not independent. This paper introduces basic probability and Bayesian concepts in order to prove these properties.

the Normal Distribution's familiar "bell curve". The latter term can be interpreted as a description of squared of distance (x  between some value of x who's probability is being assessed (along the x axis), and  the center of the probability density distribution, "standardized" by the distribution's known variance 2. It should be noted that f(x) only depends on this single scalar range var...

1 General case 1.1 Cumulative distribution function 1.2 A counterexample 1.3 Normally distributed and independent 2 Bivariate case 3 Affine transformation 4 Geometric interpretation 5 Correlations and independence 6 Higher moments 7 Conditional distributions 8 Fisher information matrix 9 Kullback-Leibler divergence 10 Estimation of parameters 11 Entropy 12 Multivariate normality tests 13 Drawin...

A widely held viewpoint in the field of predictive biomarkers for disease holds that no single marker can provide high enough discrimination and that a panel of markers, combined in some type of algorithm, will be needed. Motivated by a recent study where 27 additional markers for ovarian cancer, many of which had good predictive value alone, failed to substantially increase the predictive abil...

With the development of high-throughput sequencing and genotyping technologies, the number of markers collected in genetic association studies is growing rapidly, increasing the importance of methods for correcting for multiple hypothesis testing. The permutation test is widely considered the gold standard for accurate multiple testing correction, but it is often computationally impractical for...