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Now showing 1 - 5 of 5
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    PublicationOpen Access
    Density of a random interval catch digraph family and its use for testing uniformity
    (National Statistical Institute (NSI), 2016) Department of Mathematics; Ceyhan, Elvan; Undergraduate Student; Faculty Member; Department of Mathematics; College of Sciences
    We consider (arc) density of a parameterized interval catch digraph (ICD) family with random vertices residing on the real line. The ICDs are random digraphs where randomness lies in the vertices and are defined with two parameters, a centrality parameter and an expansion parameter, hence they will be referred as central similarity ICDs (CS-ICDs). We show that arc density of CS-ICDs is a U-statistic for vertices being from a wide family of distributions with support on the real line, and provide the asymptotic (normal) distribution for the (interiors of) entire ranges of centrality and expansion parameters for one dimensional uniform data. We also determine the optimal parameter values at which the rate of convergence (to normality) is fastest. We use arc density of CS-ICDs for testing uniformity of one dimensional data, and compare its performance with arc density of another ICD family and two other tests in literature (namely, Kolmogorov-Smirnov test and Neyman’s smooth test of uniformity) in terms of empirical size and power. We show that tests based on ICDs have better power performance for certain alternatives (that are symmetric around the middle of the support of the data).
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    PublicationOpen 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; 105131
    In 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.
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    PublicationOpen Access
    Optimal obstacle placement with disambiguations
    (Institute of Mathematical Statistics (IMS), 2012) Aksakalli, Vural; Department of Mathematics; Ceyhan, Elvan; Undergraduate Student; Faculty Member; Department of Mathematics; College of Sciences
    We introduce the optimal obstacle placement with disambiguations problem wherein the goal is to place true obstacles in an environment cluttered with false obstacles so as to maximize the total traversal length of a navigating agent (NAVA). Prior to the traversal, the NAVA is given location information and probabilistic estimates of each disk-shaped hindrance (hereinafter referred to as disk) being a true obstacle. The NAVA can disambiguate a disk's status only when situated on its boundary. There exists an obstacle placing agent (OPA) that locates obstacles prior to the NAVA's traversal. The goal of the OPA is to place true obstacles in between the clutter in such a way that the NAVA's traversal length is maximized in a game-theoretic sense. We assume the OPA knows the clutter spatial distribution type, but not the exact locations of clutter disks. We analyze the traversal length using repeated measures analysis of variance for various obstacle number, obstacle placing scheme and clutter spatial distribution type combinations in order to identify the optimal combination. Our results indicate that as the clutter becomes more regular (clustered), the NAVA's traversal length gets longer (shorter). On the other hand, the traversal length tends to follow a concave-down trend as the number of obstacles increases. We also provide a case study on a real-world maritime minefield data set.
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    PublicationRestricted
    Statistical learning with proximity catch digraphs
    (Koç University, 2017) Manukyan, Artür; Çağlar, Mine; 0000-0001-9452-5251; Koç University Graduate School of Sciences and Engineering; Computational Sciences and Engineering; 105131
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    PublicationOpen Access
    Tail probability of avoiding Poisson traps for branching Brownian motion
    (Elsevier, 2013) Department of Mathematics; Öz, Mehmet; Çağlar, Mine; PhD. Student; Faculty Member; Department of Mathematics; College of Sciences; N/A; 105131
    We consider a branching Brownian motion Z with exponential branching times and general offspring distribution evolving in R-d, where Poisson traps are present. A Poisson trap configuration with radius a is defined to be the random subset K of R-d given by K = boolean OR(x)l(,is an element of supp)(M) (B) over bar (x(i), a), where M is a Poisson random measure on B(R-d) with constant trap intensity. Survival up to time t is defined to be the event {T > t) with T = inf{s >= 0 : Z(s)(K) > 0} being the first trapping time. Following the work of Englander (2000), Englander and den Hollander (2003), where strictly dyadic branching is considered, we consider here a general offspring distribution for Z and settle the problem of survival asymptotics for the system.