A Characterization of the Dirichlet Distribution through Global and Local Parameter Independence
نویسندگان
چکیده
We provide a new characterization of the Dirichlet distribution. Let ij , 1 i k; 1 j n, be positive random variables that sum to unity. Deene i = P n j=1 ij , I = f i g k?1 i=1 , jji = ij = P j ij , and Jji = f jji g n?1 j=1. We prove that if f I ; Jj1 ; : : :; Jjk g are mutually independent and f J ; Ij1 ; : : :; Ijn g are mutually independent (where J and Ijj are deened analogously), and assuming strictly positive pdfs, then the pdf of ij is Dirichlet. This characterization implies that under assumptions made by several previous authors for selecting a Bayesian-network structure out of a set of candidate structures, a Dirichlet prior on the parameters is inevitable.
منابع مشابه
On Parameter Priors for Discrete DAG Models
We investigate parameter priors for discrete DAG models. It was shown in previous works that a Dirichlet prior on the parameters of a discrete DAG model is inevitable assuming global and local parameter independence for all possible complete DAG structures. A similar result for Gaussian DAG models hinted that the assumption of local independence may be redundant. Herein, we prove that the local...
متن کاملA Three-Coefficient Model with Global Optimization for Heavy End Characterization of Gas Condensate PVT Data
Characterization of heavy end, as plus fraction, is among the most crucial steps in predicting phase behavior of a hydrocarbon fluid system. Proper selection of single carbon number (SCN) distribution function is essential for heavy end characterization. The SCN distribution function is subject to fluid nature. The exponential distribution function has been and is widely applied to gas condensa...
متن کاملLearning Conditional Gaussian Networks
This paper considers conditional Gaussian networks. The parameters in the network are learned by using conjugate Bayesian analysis. As conjugate local priors, we apply the Dirichlet distribution for discrete variables and the Gaussian-inverse gamma distribution for continuous variables, given a configuration of the discrete parents. We assume parameter independence and complete data. Further, t...
متن کاملThe effects of the violation of local independence assumption on the person measures under the Rasch model
Local independence of test items is an assumption in all Item Response Theory (IRT) models. That is, the items in a test should not be related to each other. Sharing a common passage, which is prevalent in reading comprehension tests, cloze tests and C-Tests, can be a potential source of local item dependence (LID). It is argued in the literature that LID results in biased parameter estimation ...
متن کاملA Differential Evolution and Spatial Distribution based Local Search for Training Fuzzy Wavelet Neural Network
Abstract Many parameter-tuning algorithms have been proposed for training Fuzzy Wavelet Neural Networks (FWNNs). Absence of appropriate structure, convergence to local optima and low speed in learning algorithms are deficiencies of FWNNs in previous studies. In this paper, a Memetic Algorithm (MA) is introduced to train FWNN for addressing aforementioned learning lacks. Differential Evolution...
متن کامل