1,720,981 research outputs found
Central limit theorems for multicolor urns with dominated colors
Full text linkAn urn contains balls of d≥2 colors. At each time n≥1, a ball is drawn and then replaced together with a random number of balls of the same color. Let A n = diag (An,1,…,An,d) be the n-th reinforce matrix. Assuming that EAn,j=EAn,1 for all n and j, a few central limit theorems (CLTs) are available for such urns. In real problems, however, it is more reasonable to assume that EA n,j = EA n,1 whenever n ≥ 1 and 1 ≤ j ≤ d0 , liminfn EAn,1 > limsupn EAn,j whenever j > d0 for some integer 1≤d0≤d. Under this condition, the usual weak limit theorems may fail, but it is still possible to prove the CLTs for some slightly different random quantities. These random quantities are obtained by neglecting dominated colors, i.e., colors from d0+1 to d, and they allow the same inference on the urn structure. The sequence (An : n ≥ 1) is independent but need not be identically distributed. Some statistical applications are given as well
An almost sure conditional convergence result and an application to a generalized Polya urn
Full text linkWe prove an almost sure conditional convergence result toward a Gaussian kernel and we apply it to a two-colors randomly reinforced urn
Convergence results for multivariate martingales
No full textWe present a new version of the Central Limit Theorem for multivariate martingales
A Network Model characterized by a Latent Attribute Structure with Competition
Full text linkThe quest for a model that is able to explain, describe, analyze and simulate real-world complex networks is of uttermost practical, as well as theoretical, interest. In fact, networks can be a natural way to represent many phenomena; often, they arise from a complex interweaving of some features of the nodes. For example, in a co-authorship network, a link stems more easily between authors with similar interests; similarly, in a genetic regulatory network, links are affected by the different biological functions of the regulators.
In this paper we introduce and study a novel network model that is based on a latent attribute structure: this model, inspired by a generalization of the Indian Buffet process, is simple and contains a small number of parameters, with a clear and intuitive role. Each node is characterized by a number of features and the probability of the existence of an edge between two nodes depends on the features they share; the number of possible features is not fixed a priori and can grow indefinitely. Moreover, a random fitness parameter is introduced for each node in order to determine its ability to transmit its own features to other nodes; this behavior is added on top of a process of Indian-Buffet type. Because of the fitness property, a node’s connectivity does not depend on its age alone, so that also
“young but fit” nodes are able to compete and succeed in propagating their features and acquiring links. We also show how, considering the resulting bipartite node-attribute network, it is possible to gain some insight about which nodes were originally the most “fit”.
Our model for this bipartite network depends on few parameters, that are characterized by their straightforward interpretation and by the availability of proper estimators. Even if the parameters are easy to interpret and tune, the model is general enough to represent
complex phenomena—e.g., homophily, heterophily, or any interplay between features. We provide some theoretical as well as experimental results regarding the power-law behavior of the model and the proposed tools for the estimation of the parameters. We also show, through a number of experiments, how the proposed model naturally captures most local and global properties (e.g., degree distributions, connectivity and distance distributions)
real networks exhibit
Networks of reinforced stochastic processes: Asymptotics for the empirical means
Full text linkThis work deals with systems of interacting reinforced stochastic processes, where each process X^j = (X_{n,j})_n is located at a vertex j of a finite weighted direct graph, and it can be interpreted as the sequence of “actions” adopted by an agent j of the network. The interaction
among the evolving dynamics of these processes depends on the weighted adjacency matrix W associated to the underlying graph: indeed, the probability that an agent j chooses a certain action depends on its personal “inclination” Z_{n,j} and on the inclinations Z_{n,h} , with h not equal to j, of the other agents according to the elements of W.
Asymptotic results for the stochastic processes of the personal inclinations Z^j = (Z_{n,j})_n have
been subject of studies in recent papers (e.g. [2, 21]); while the asymptotic behavior of the stochastic
processes of the actions (X_{n,j})_n has never been studied yet. In this paper, we fill this gap by characterizing the asymptotic behavior of the empirical means N_{n,j} = \sum_{k=1}^n X_{k,j} /n, proving their almost sure synchronization and some central limit theorems in the sense of stable convergence. Moreover, we discuss some statistical applications of these convergence results concerning confidence intervals for the random limit toward which all the processes of the system converge and tools to
make inference on the matrix W
Rate of convergence of predictive distributions for dependent data
Full text linkThis paper deals with empirical processes of the type
[C_{n}(B)=\sqrt{n}\{\mu_{n}(B)-P(X_{n+1}\in B\mid X_{1},\ldots,X_{n})\},\]
where (Xn) is a sequence of random variables and μn=(1/n)∑i=1nδXi the empirical measure. Conditions for supB|Cn(B)| to converge stably (in particular, in distribution) are given, where B ranges over a suitable class of measurable sets. These conditions apply when (Xn) is exchangeable or, more generally, conditionally identically distributed (in the sense of Berti et al. [Ann. Probab. 32 (2004) 2029–2052]). By such conditions, in some relevant situations, one obtains that or even that converges a.s. Results of this type are useful in Bayesian statistics
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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