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Publication Metadata only A new family of random graphs for testing spatial segregation(Wiley, 2007) Priebe, Carey E.; Marchette, David J.; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AThe authors discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. The authors address specifically the problem of testing. complete spatial randomness against spatial patterns of segregation or association between two or more classes of points on the plane. To this end, they use a particular type of parameterized random digraph called a proximity catch digraph (PCD) which is based on relative positions of the data points from various classes. The statistic employed is the relative density of the PCD, which is a U-statistic when scaled properly. The authors derive the limiting distribution of the relative, density, using the standard asymptotic theory of U-statistics. They evaluate the finite-sample performance of their test statistic by Monte Carlo simulations and assess its asymptotic performance via Pitman's asymptotic efficiency, thereby yielding the optimal parameters for testing. They further stress that their methodology remains valid for data in higher dimensions.Publication Metadata only A note on the geometric ergodicity of a nonlinear AR-ARCH model(Elsevier Science Bv, 2010) Saikkonen, Pentti; Department of Economics; Meitz, Mika; Faculty Member; Department of Economics; College of Administrative Sciences and Economics; N/AThis note studies the geometric ergodicity of nonlinear autoregressive models with conditionally heteroskedastic errors. A nonlinear autoregression of order p (AR(p)) with the conditional variance specified as the conventional linear autoregressive conditional heteroskedasticity model of order q (ARCH(q)) is considered. Conditions under which the Markov chain representation of this nonlinear AR-ARCH model is geometrically ergodic and has moments of known order are provided. The obtained results complement those of Liebscher [Liebscher, E., 2005. Towards a unified approach for proving geometric ergodicity and mixing properties of nonlinear autoregressive processes, journal of Time Series Analysis, 26,669-689] by showing how his approach based on the concept of the joint spectral radius of a set of matrices can be extended to establish geometric ergodicity in nonlinear autoregressions with conventional ARCH(q) errors.Publication Metadata only Admission and termination control of a two class loss system(Taylor & Francis Inc, 2011) Ulukuş, Mehmet Yasin; Güllü, Refik; Department of Industrial Engineering; Örmeci, Lerzan; Faculty Member; Department of Industrial Engineering; College of Engineering; 32863We consider dynamic admission and termination control policies in a Markovian loss system with two classes, each with a fixed reward, a termination cost, an arrival and service rate. The system may admit or reject an arriving job or admit it by terminating a job in the system to maximize its total expected discounted reward. We prove that (1) when there is an idle server, it is never optimal to terminate a job, (2) there exists an optimal threshold policy for both admission and termination decisions. Furthermore, we identify the conditions which ensure that a class is "preferred" or "strongly preferred."Publication Metadata only Admission policies for a two class loss system with general interarrival times(Taylor & Francis Inc, 2006) van der Wal, J.; Department of Industrial Engineering; Örmeci, Lerzan; Faculty Member; Department of Industrial Engineering; College of Engineering; 32863This paper considers the problem of dynamic admission control in a loss queueing system with two classes of jobs. The jobs require an exponential amount of service time with different means and bring different revenues, whereas the arrivals occur according to a general distribution. We establish the existence of optimal acceptance thresholds for both job classes and show that under certain conditions there exists a preferred class. We also provide an example to demonstrate that for a Markov modulated Poisson arrival process there may be states in which both classes are rejected.Publication Metadata only Balanced and strongly balanced 4-kite designs(Utilitas Mathematica Publishing, 2013) Gionfriddo, Mario; Milazzo, Lorenzo; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252A G-design is called balanced if the degree of each vertex x is a constant. A G-design is called strongly balanced if for every i = 1, 2, ⋯, h, there exists a constant Ci such that dAi(x)= Ci for every vertex x, where AiS are the orbits of the automorphism group of G on its vertex-set and dAi(x) of a vertex is the number of blocks of containing x as an element of Ai. We say that a G-design is simply balanced if it is balanced, but not strongly balanced. In this paper we determine the spectrum of simply balanced and strongly balanced 4-kite designs.Publication Metadata only Bayesian analysis of multiple-inflation Poisson models and its application to infection data(Brazilian Statistical Association, 2018) Ryu, Duchwan; Bilgili, Devrim; Ebrahimi, Nader; Ergönül, Önder; Faculty Member; School of Medicine; Koç University Hospital; 110398In this article we propose a multiple-inflation Poisson regression to model count response data containing excessive frequencies at more than one non-negative integer values. To handle multiple excessive count responses, we generalize the zero-inflated Poisson regression by replacing its binary regression with the multinomial regression, while Su et al. [Statist. Sinica 23 (2013) 1071-1090] proposed a multiple-inflation Poisson model for consecutive count responses with excessive frequencies. We give several properties of our proposed model, and do statistical inference under the fully Bayesian framework. We perform simulation studies and also analyze the data related to the number of infections collected in five major hospitals in Turkey, using our methodology.Publication Metadata only Cell-specific and post-hoc spatial clustering tests based on nearest neighbor contingency tables(Korean Statistical Soc, 2017) Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/ASpatial clustering patterns in a multi-class setting such as segregation and association between classes have important implications in various fields, e.g., in ecology, and can be tested using nearest neighbor contingency tables (NNCTs). a NNCT is constructed based on the types of the nearest neighbor (NN) pairs and their frequencies. We survey the cell-specific (or pairwise) and overall segregation tests based on NNCTs in literature and introduce new ones and determine their asymptotic distributions. We demonstrate that cell-specific tests enjoy asymptotic normality, while overall tests have chi-square distributions asymptotically. Some of the overall tests are confounded by the unstable generalized inverse of the rank-deficient covariance matrix. To overcome this problem, we propose rank-based corrections for the overall tests to stabilize their behavior. We also perform an extensive' Monte Carlo simulation study to compare the finite sample performance of the tests in terms of empirical size and power based on the asymptotic and Monte Carlo critical values and determine the tests that have the best size and power performance and are robust to differences in relative abundances (of the classes). in addition to the cell-specific tests, we discuss one(-class)-versus-rest type of tests as post-hoc,tests after a significant overall test. We also introduce the concepts of total, strong, and partial segregatioN/Association to differentiate different levels of these patterns. We compare the new tests with the existing NNCT-tests in literature with simulations and illustrate the tests on an ecological data set. (C) 2016 the Korean Statistical Society. Published by Elsevier B.V. all rights reserved.Publication Open Access Distribution of maximum loss of fractional Brownian motion with drift(Elsevier, 2013) Vardar-Acar, Ceren; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131In this paper, we find bounds on the distribution of the maximum loss of fractional Brownian motion with H >= 1/2 and derive estimates on its tail probability. Asymptotically, the tail of the distribution of maximum loss over [0, t] behaves like the tail of the marginal distribution at time t.Publication Metadata only MTTF and availability of semi-Markov missions with non-identical generally distributed component lifetimes(Taylor & Francis) Cekyay, Bora; Department of Industrial Engineering; Özekici, Süleyman; Faculty Member; Department of Industrial Engineering; College of Engineering; 32631We analyze mean time to failure and availability of systems that perform semi-Markov missions. The mission process is the minimal semi-Markov process associated with a Markov renewal process. Therefore, the successive phases of the mission follow a Markov chain, and the phase durations are generally distributed. The lifetimes of the non-identical components in the system are assumed to be generally distributed and are modeled using intrinsic aging concepts. Moreover, the lifetime parameters of the components and the configuration of the system change depending on the phases of the mission. We characterize the mean time to failure through solving a Poisson equation, and we analyze the system availability assuming that repair duration has a general distribution which is dependent on the phase of the mission during which the failure has occurred and on the deterioration level of the system.Publication Metadata only On regular embedding of H-designs into G-designs(Utilitas Mathematica, 2013) Quattrocchi, Gaetano; Department of Mathematics; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Smith, Benjamin R.; Yazıcı, Emine Şule; Faculty Member; Researcher; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; College of Sciences; 105252; N/A; 27432The graph H is embedded in the graph G, if H is a subgraph of G. An H-design is a decomposition of a complete graph into edge disjoint copies of the graph H, called blocks. An H-i-design with k blocks, say H-1, H-2, ...H-k is embedded in a G-design if for every H-i, there exists a distinct block, say G(i), in the G-design that embeds H-i. If G(i) are all isomorphic for 1 <= i <= k then the embedding is called regular. This paper solves the problem of the regular embedding of H-designs into G-designs when G has at most four vertices and four edges.