Q-Markov Random Probability Measures and Their Posterior Distributions
نویسنده
چکیده
In this paper, we use the Markov property introduced in Balan and Ivanoff (2002) for set-indexed processes and we prove that a Markov prior distribution leads to a Markov posterior distribution. In particular, by proving that a neutral to the right prior distribution leads to a neutral to the right posterior distribution, we extend a fundamental result of Doksum (1974) to arbitrary sample spaces.
منابع مشابه
Markov Jump Random C.D.F.’s and Their Posterior Distributions
In this article we introduce the class of Markov jump random c.d.f.’s as a sub-class of the Q-Markov prior distributions studied in (Balan, 2004) and we prove that this sub-class is closed in the Bayesian sense.
متن کاملMarkov Processes Involving q-Stirling Numbers
In this paper we consider the Markov process deened by for transition probabilities n;` = q ` and n;` = q n?1. We give closed forms for the distributions and the moments of the underlying random variables. Thereby we observe that the distributions can be easily described in terms of q{Stirling numbers of the second kind. Their occurrence in a purely time dependent Markov process allows a natura...
متن کاملIMAGE SEGMENTATION USING GAUSSIAN MIXTURE MODEL
Stochastic models such as mixture models, graphical models, Markov random fields and hidden Markov models have key role in probabilistic data analysis. In this paper, we have learned Gaussian mixture model to the pixels of an image. The parameters of the model have estimated by EM-algorithm. In addition pixel labeling corresponded to each pixel of true image is made by Bayes rule. In fact, ...
متن کاملImage Segmentation using Gaussian Mixture Model
Abstract: Stochastic models such as mixture models, graphical models, Markov random fields and hidden Markov models have key role in probabilistic data analysis. In this paper, we used Gaussian mixture model to the pixels of an image. The parameters of the model were estimated by EM-algorithm. In addition pixel labeling corresponded to each pixel of true image was made by Bayes rule. In fact,...
متن کاملq-distributions and Markov processes
We consider a sequence of integer{valued random variables Xn; n 1; representing a special Markov process with transition probability the transition probability is given by n;` = q n+`+ and n;` = 1 ? q n+`+ , we can nd closed forms for the distribution and the moments of the corresponding random variables, showing that they involve functions such as the q{binomial coeecients and the q{Stirling n...
متن کامل