جستجوی مقالات مرتبط با کلیدواژه « exchangeability » در نشریات گروه « آمار »

Bayesian nonparametric inference is increasingly demanding in statistical modeling due to incorporating flexible prior processes in complex data analysis. This paper represents the Polya urn scheme for the generalized Dirichlet process (GDP). It utilizes the partition analysis to construct the joint distribution of a random sample from the GDP as a mixture prior distribution of countable components. Using permutation theory, we present the components' weights in a computationally accessible manner to make the resulting joint prior equation applicable. The advantages of our findings include tractable algebraic operations that lead to closed-form equations. The paper recommends the Polya urn Gibbs sampler algorithm, derive full conditional posterior distributions, and as an illustration, implement the algorithm for fitting some popular statistical models in nonparametric Bayesian settings.

In this paper, assuming that (X, Y1, Y2)T has a trivariate normal distribution, we derive the exact joint distribution of (X, Y(1), Y(2))^T, where Y(1) and Y(2) are order statistics arising from (Y1, Y2)T. We show that this joint distribution is a mixture of truncated trivariate normal distributions and then use this mixture representation to derive the best (nonlinear) predictiors of X in terms of (Y(1), Y(2))^T. We also predict Y(1) in terms of (X, Y(2))^T, and Y(2) in terms of (X, Y(1))^T. Finally illustrate the usefulness of these results by using real-life data.