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  Subjects -> STATISTICS (Total: 130 journals)
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Sankhya A
Journal Prestige (SJR): 0.106
Number of Followers: 3  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0976-836X - ISSN (Online) 0976-8378
Published by Springer-Verlag Homepage  [2469 journals]
  • An Overview of Discrete Distributions in Modelling COVID-19 Data Sets

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      Abstract: Abstract The mathematical modeling of the coronavirus disease-19 (COVID-19) pandemic has been attempted by a large number of researchers from the very beginning of cases worldwide. The purpose of this research work is to find and classify the modelling of COVID-19 data by determining the optimal statistical modelling to evaluate the regular count of new COVID-19 fatalities, thus requiring discrete distributions. Some discrete models are checked and reviewed, such as Binomial, Poisson, Hypergeometric, discrete negative binomial, beta-binomial, Skellam, beta negative binomial, Burr, discrete Lindley, discrete alpha power inverse Lomax, discrete generalized exponential, discrete Marshall-Olkin Generalized exponential, discrete Gompertz-G-exponential, discrete Weibull, discrete inverse Weibull, exponentiated discrete Weibull, discrete Rayleigh, and new discrete Lindley. The probability mass function and the hazard rate function are addressed. Discrete models are discussed based on the maximum likelihood estimates for the parameters. A numerical analysis uses the regular count of new casualties in the countries of Angola,Ethiopia, French Guiana, El Salvador, Estonia, and Greece. The empirical findings are interpreted in-depth.
      PubDate: 2022-09-09
       
  • An Integral Representation for Inverse Moments

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      Abstract: Abstract Inverse moments of discrete random variables are traditionally expressed by summations. But summations are often difficult to simplify. In this note, we derive an integral representation for inverse moments involving the probability generating function, making simplifications a lot easier. Two examples are provided to illustrate the result.
      PubDate: 2022-09-08
       
  • A Class of Multivariate Power Skew Symmetric Distributions: Properties and
           Inference for the Power-Parameter

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      Abstract: Abstract Let SPd be the class of all multivariate sign and permutation invariant densities and SPD be the corresponding class of distribution functions. The class of all distributions corresponding to a positive power of the members of SPD is called the Power Skew Symmetric class of distributions and it is denoted by PSS. We consider the problem of inference associated with the nonnegative power, in the PSS class, with a member of SPD as a nuisance parameter. As the structural forms of the members of PSS are not known, one can’t directly use the sufficiency, invariance, or likelihood function. Hence by using certain properties of the SPD and the PSS classes, we identify maximal statistics whose distributions depend only on the power but not on the members of SPD. We then use the concept of minimal dimensionality for retaining the information about the parameter of interest. We use the minimax criterion, which leads to a statistic having Binomial distribution depending only on the parameter of interest. Hence inferences about the parameter of interest can be carried out using the standard methods for the binomial model. A simulation study indicates that the proposed estimator of the power parameter is asymptotically normal and is insensitive to the nuisance parameter. The proposed method is implemented for the analysis of a data set.
      PubDate: 2022-08-22
       
  • Bayesian P-Splines Applied to Semiparametric Models with Errors Following
           a Scale Mixture of Normals

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      Abstract: Abstract This work is about semiparametric models assuming that the error follows a scale mixture of gaussian distributions and such that the functional relation between the response and explanatory variables is unknown. This class of distributions is particularly interesting since it includes heavy tailed distributions such as the Student’s t, symmetric stable distributions and double exponential. They are specially useful for modelling data with high incidence of extreme values. Exploring the nature of these distributions and using the concept of P-splines we obtain the complete posterior conditional distributions of all the parameters involved in the model and apply the Gibbs sampler. In this way, we show how to combine P-splines and mixture of normals under a Bayesian perspective in order to estimate such curves. We conduct some simulations in order to illustrate the proposed methodology and also analyze the case of partially linear models.
      PubDate: 2022-08-11
       
  • Complete and Complete f -Moment Convergence for Arrays of Rowwise END
           Random Variables and Some Applications

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      Abstract: Abstract In this paper, complete convergence and complete f -moment convergence for arrays of rowwise Extended Negatively Dependent (END, in short) random variables are investigated, and some sufficient conditions for the convergence are provided. The results obtained improved the corresponding ones for random variables with independence structure and some dependence structures.
      PubDate: 2022-07-12
      DOI: 10.1007/s13171-022-00289-0
       
  • On some Bivariate Semi Parametric Families of Distributions with a
           Singular Component

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      Abstract: Abstract The main idea of this paper is to present families of bivariate distributions that depend in their formation on adding a shape parameter to the powers of the hazard and reversed hazard functions in different manners, which would provide additional flexibility in applications. Different baseline distributions were used namely, exponential, inverse exponential, uniform, inverse uniform, inverse Rayleigh, Gompertz and Pareto. Many of the mathematical properties of these families are discussed in detail. Moreover, it is observed that the new bivariate distributions also can make appropriate modeling of three real data sets.
      PubDate: 2022-06-30
      DOI: 10.1007/s13171-022-00288-1
       
  • A Robust Bayesian Analysis of Variable Selection under Prior Ignorance

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      Abstract: Abstract We propose a cautious Bayesian variable selection routine by investigating the sensitivity of a hierarchical model, where the regression coefficients are specified by spike and slab priors. We exploit the use of latent variables to understand the importance of the co-variates. These latent variables also allow us to obtain the size of the model space which is an important aspect of high dimensional problems. In our approach, instead of fixing a single prior, we adopt a specific type of robust Bayesian analysis, where we consider a set of priors within the same parametric family to specify the selection probabilities of these latent variables. We achieve that by considering a set of expected prior selection probabilities, which allows us to perform a sensitivity analysis to understand the effect of prior elicitation on the variable selection. The sensitivity analysis provides us sets of posteriors for the regression coefficients as well as the selection indicators and we show that the posterior odds of the model selection probabilities are monotone with respect to the prior expectations of the selection probabilities. We also analyse synthetic and real life datasets to illustrate our cautious variable selection method and compare it with other well known methods.
      PubDate: 2022-06-16
      DOI: 10.1007/s13171-022-00287-2
       
  • The Bethe Hessian and Information Theoretic Approaches for Online
           Change-Point Detection in Network Data

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      Abstract: Abstract Sequences of networks are currently a common form of network data sets. Identification of structural change-points in a network data sequence is a natural problem. The problem of change-point detection can be classified into two main types - offline change-point detection and online or sequential change-point detection. In this paper, we propose three different algorithms for online change-point detection based on certain cusum statistics for network data with community structures. For two of the proposed algorithms, we use information theoretic measures to construct the statistic for the estimation of a change-point. In the third algorithm, we use eigenvalues of the Bethe Hessian matrix to construct the statistic for the estimation of a change-point. We show the consistency property of the estimated change-point theoretically under networks generated from the multi-layer stochastic block model and the multi-layer degree-corrected block model. We also conduct an extensive simulation study to demonstrate the key properties of the algorithms as well as their efficacy.
      PubDate: 2022-06-01
      DOI: 10.1007/s13171-021-00248-1
       
  • Improvements on SCORE, Especially for Weak Signals

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      Abstract: Abstract A network may have weak signals and severe degree heterogeneity, and may be very sparse in one occurrence but very dense in another. SCORE (Ann. Statist. 43, 57–89, 2015) is a recent approach to network community detection. It accommodates severe degree heterogeneity and is adaptive to different levels of sparsity, but its performance for networks with weak signals is unclear. In this paper, we show that in a broad class of network settings where we allow for weak signals, severe degree heterogeneity, and a wide range of network sparsity, SCORE achieves prefect clustering and has the so-called “exponential rate” in Hamming clustering errors. The proof uses the most recent advancement on entry-wise bounds for the leading eigenvectors of the network adjacency matrix. The theoretical analysis assures us that SCORE continues to work well in the weak signal settings, but it does not rule out the possibility that SCORE may be further improved to have better performance in real applications, especially for networks with weak signals. As a second contribution of the paper, we propose SCORE+ as an improved version of SCORE. We investigate SCORE+ with 8 network data sets and found that it outperforms several representative approaches. In particular, for the 6 data sets with relatively strong signals, SCORE+ has similar performance as that of SCORE, but for the 2 data sets (Simmons, Caltech) with possibly weak signals, SCORE+ has much lower error rates. SCORE+ proposes several changes to SCORE. We carefully explain the rationale underlying each of these changes, using a mixture of theoretical and numerical study.
      PubDate: 2022-06-01
      DOI: 10.1007/s13171-020-00240-1
       
  • Bayesian Testing for Exogenous Partition Structures in Stochastic Block
           Models

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      Abstract: Abstract Network data often exhibit block structures characterized by clusters of nodes with similar patterns of edge formation. When such relational data are complemented by additional information on exogenous node partitions, these sources of knowledge are typically included in the model to supervise the cluster assignment mechanism or to improve inference on edge probabilities. Although these solutions are routinely implemented, there is a lack of formal approaches to test if a given external node partition is in line with the endogenous clustering structure encoding stochastic equivalence patterns among the nodes in the network. To fill this gap, we develop a formal Bayesian testing procedure which relies on the calculation of the Bayes factor between a stochastic block model with known grouping structure defined by the exogenous node partition and an infinite relational model that allows the endogenous clustering configurations to be unknown, random and fully revealed by the block–connectivity patterns in the network. A simple Markov chain Monte Carlo method for computing the Bayes factor and quantifying uncertainty in the endogenous groups is proposed. This strategy is evaluated in simulations, and in applications studying brain networks of Alzheimer’s patients.
      PubDate: 2022-06-01
      DOI: 10.1007/s13171-020-00231-2
       
  • Scalable Estimation of Epidemic Thresholds via Node Sampling

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      Abstract: Abstract Infectious or contagious diseases can be transmitted from one person to another through social contact networks. In today’s interconnected global society, such contagion processes can cause global public health hazards, as exemplified by the ongoing Covid-19 pandemic. It is therefore of great practical relevance to investigate the network transmission of contagious diseases from the perspective of statistical inference. An important and widely studied boundary condition for contagion processes over networks is the so-called epidemic threshold. The epidemic threshold plays a key role in determining whether a pathogen introduced into a social contact network will cause an epidemic or die out. In this paper, we investigate epidemic thresholds from the perspective of statistical network inference. We identify two major challenges that are caused by high computational and sampling complexity of the epidemic threshold. We develop two statistically accurate and computationally efficient approximation techniques to address these issues under the Chung-Lu modeling framework. The second approximation, which is based on random walk sampling, further enjoys the advantage of requiring data on a vanishingly small fraction of nodes. We establish theoretical guarantees for both methods and demonstrate their empirical superiority.
      PubDate: 2022-06-01
      DOI: 10.1007/s13171-021-00249-0
       
  • Dynamic Networks with Multi-scale Temporal Structure

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      Abstract: Abstract We describe a novel method for modeling non-stationary multivariate time series, with time-varying conditional dependencies represented through dynamic networks. Our proposed approach combines traditional multi-scale modeling and network based neighborhood selection, aiming at capturing temporally local structure in the data while maintaining sparsity of the potential interactions. Our multi-scale framework is based on recursive dyadic partitioning, which recursively partitions the temporal axis into finer intervals and allows us to detect local network structural changes at varying temporal resolutions. The dynamic neighborhood selection is achieved through penalized likelihood estimation, where the penalty seeks to limit the number of neighbors used to model the data. We present theoretical and numerical results describing the performance of our method, which is motivated and illustrated using task-based magnetoencephalography (MEG) data in neuroscience.
      PubDate: 2022-06-01
      DOI: 10.1007/s13171-021-00256-1
       
  • The Hierarchy of Block Models

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      Abstract: Abstract There exist various types of network block models such as the Stochastic Block Model (SBM), the Degree Corrected Block Model (DCBM), and the Popularity Adjusted Block Model (PABM). While this leads to a variety of choices, the block models do not have a nested structure. In addition, there is a substantial jump in the number of parameters from the DCBM to the PABM. The objective of this paper is formulation of a hierarchy of block model which does not rely on arbitrary identifiability conditions. We propose a Nested Block Model (NBM) that treats the SBM, the DCBM and the PABM as its particular cases with specific parameter values, and, in addition, allows a multitude of versions that are more complicated than DCBM but have fewer unknown parameters than the PABM. The latter allows one to carry out clustering and estimation without preliminary testing, to see which block model is really true.
      PubDate: 2022-06-01
      DOI: 10.1007/s13171-021-00247-2
       
  • Null Models and Community Detection in Multi-Layer Networks

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      Abstract: Abstract Multi-layer networks of multiplex type represent relational data on a set of entities (nodes) with multiple types of relations (edges) among them where each type of relation is represented as a network layer. A large group of popular community detection methods in networks are based on optimizing a quality function known as the modularity score, which is a measure of the extent of presence of module or community structure in networks compared to a suitable null model. Here we introduce several multi-layer network modularity and model likelihood quality function measures using different null models of the multi-layer network, motivated by empirical observations in networks from a diverse field of applications. In particular, we define multi-layer variants of the Chung-Lu expected degree model as null models that differ in their modeling of the multi-layer degrees. We propose simple estimators for the models and prove their consistency properties. A hypothesis testing procedure is also proposed for selecting an appropriate null model for data. These null models are used to define modularity measures as well as model likelihood based quality functions. The proposed measures are then optimized to detect the optimal community assignment of nodes (Code available at: https://u.osu.edu/subhadeep/codes/). We compare the effectiveness of the measures in community detection in simulated networks and then apply them to four real multi-layer networks.
      PubDate: 2022-06-01
      DOI: 10.1007/s13171-021-00257-0
       
  • Overlapping Community Detection in Networks via Sparse Spectral
           Decomposition

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      Abstract: Abstract We consider the problem of estimating overlapping community memberships in a network, where each node can belong to multiple communities. More than a few communities per node are difficult to both estimate and interpret, so we focus on sparse node membership vectors. Our algorithm is based on sparse principal subspace estimation with iterative thresholding. The method is computationally efficient, with computational cost equivalent to estimating the leading eigenvectors of the adjacency matrix, and does not require an additional clustering step, unlike spectral clustering methods. We show that a fixed point of the algorithm corresponds to correct node memberships under a version of the stochastic block model. The methods are evaluated empirically on simulated and real-world networks, showing good statistical performance and computational efficiency.
      PubDate: 2022-06-01
      DOI: 10.1007/s13171-021-00245-4
       
  • Covariate-Adjusted Inference for Differential Analysis of High-Dimensional
           Networks

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      Abstract: Abstract Differences between biological networks corresponding to disease conditions can help delineate the underlying disease mechanisms. Existing methods for differential network analysis do not account for dependence of networks on covariates. As a result, these approaches may detect spurious differential connections induced by the effect of the covariates on both the disease condition and the network. To address this issue, we propose a general covariate-adjusted test for differential network analysis. Our method assesses differential network connectivity by testing the null hypothesis that the network is the same for individuals who have identical covariates and only differ in disease status. We show empirically in a simulation study that the covariate-adjusted test exhibits improved type-I error control compared with naïve hypothesis testing procedures that do not account for covariates. We additionally show that there are settings in which our proposed methodology provides improved power to detect differential connections. We illustrate our method by applying it to detect differences in breast cancer gene co-expression networks by subtype.
      PubDate: 2022-06-01
      DOI: 10.1007/s13171-021-00252-5
       
  • Estimation Parameters for the Continuous q-Distributions

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      Abstract: Abstract In this paper, we are basically interested in the issue of estimation parameters for continuous q-distributions. The parameters estimation and simulation studies of three classical continuous Lindley, gamma and exponential q-distributions are elaborated. For the parameters estimation problem the moment method is used. The effectiveness of the proposed models are highlighted through simulation studies for different q parameters values and samples sizes of the Lindley, gamma and exponential q-distributions.
      PubDate: 2022-05-11
      DOI: 10.1007/s13171-022-00284-5
       
  • Modeling Transitivity in Local Structure Graph Models

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      Abstract: Abstract Local Structure Graph Models (LSGMs) describe network data by modeling, and thereby controlling, the local structure of networks in a direct and interpretable manner. Specification of such models requires identifying three factors: a saturated, or maximally possible, graph; a neighborhood structure of dependent potential edges; and, lastly, a model form prescribed by full conditional binary distributions with appropriate “centering” steps and dependence parameters. This last aspect particularly distinguishes LSGMs from other model formulations for network data. In this article, we explore the expanded LSGM structure to incorporate dependencies among edges that form potential triangles, thus explicitly representing transitivity in the conditional probabilities that govern edge realization. Two networks previously examined in the literature, the Faux Mesa High friendship network and the 2000 college football network, are analyzed with such models, with a focus on assessing the manner in which terms reflecting two-way and three-way dependencies among potential edges influence the data structures generated by models that incorporate them. One conclusion reached is that explicit modeling of three-way dependencies is not always needed to reflect the observed level of transitivity in an actual graph. Another conclusion is that understanding the manner in which a model represents a given problem is enhanced by examining several aspects of model structure, not just the number of some particular topological structure generated by a fitted model.
      PubDate: 2021-11-27
      DOI: 10.1007/s13171-021-00264-1
       
  • Eigenvalues of Stochastic Blockmodel Graphs and Random Graphs with
           Low-Rank Edge Probability Matrices

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      Abstract: Abstract We derive the limiting distribution for the outlier eigenvalues of the adjacency matrix for random graphs with independent edges whose edge probability matrices have low-rank structure. We show that when the number of vertices tends to infinity, the leading eigenvalues in magnitude are jointly multivariate Gaussian with bounded covariances. As a special case, this implies a limiting normal distribution for the outlier eigenvalues of stochastic blockmodel graphs and their degree-corrected or mixed-membership variants. Our result extends the classical result of Füredi and Komlós on the fluctuation of the largest eigenvalue for Erdős–Rényi graphs.
      PubDate: 2021-11-03
      DOI: 10.1007/s13171-021-00268-x
       
  • Estimation of the Parameters in an Expanding Dynamic Network Model

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      Abstract: Abstract In this paper, we consider an expanding sparse dynamic network model where the time evolution is governed by a Markovian structure. Transition of the network from time t to t + 1 involves three components where a new node joins the existing network, some of the existing edges drop out, and new edges are formed with the incoming node. We consider long term behavior of the network density and establish its limit. We also study asymptotic distributions of the maximum likelihood estimators of key model parameters. We report results from a simulation study to investigate finite sample properties of the estimators.
      PubDate: 2021-09-27
      DOI: 10.1007/s13171-021-00258-z
       
 
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