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Yayın Application of stochastic differential equations models for solving ship roll motion(Maltepe Üniversitesi, 2009) Nabati, P.; Farnoosh, R.Stochastic differential equation (SDE) models play a relevant role in many application areas including environmental modeling, biological and engineering modeling. This paper is intended to provide a second order SDE model excited by random sea waves for ship roll motion.The mathematical (SDE) model for the responses of a ship to the random sea waves will be presented and then this model will be solved analytically and numerically. Numerical examples are performed by using the Euler-Maruyama method in order to show the accuracy of the present work.Yayın Bayesian test for homogeneity hypothesis(Maltepe Üniversitesi, 2009) Farnoosh, R.; Hajrajabi, A.Population which consist of several subpopulation with different properties is called heterogeneous. Hence homogeneity means not mixing population distribution. Modified likelihood ratio test and EM test which are based penalized likelihood function are usually used for testing homogeneity under the mixture models. In this paper we will show that efficiency of these tests is influenced by the shape of the chosen penalty function, Hence none of these tests is generally optimal. Parameters of poisson mixture models and parameter of determinative shape of the penalty function are estimated by a bayesian approch and homogeneity test is implemented by using the criteria of the optimal model choice.