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There are various parametric models for analyzing pairwise comparison data, including the Bradley–Terry–Luce (BTL) and Thurstone models, but their reliance on strong parametric assumptions is limiting. In this paper, we study a flexible model for pairwise comparisons, under which the probabilities of outcomes are required only to satisfy a natural form of stochastic transitivity. This class includes parametric models, including the BTL and Thurstone models as special cases, but is considerably more general. We provide various examples of models in this broader stochastically transitive class for which classical parametric models provide poor fits. Despite this greater flexibility, we show that the matrix of probabilities can be estimated at the same rate as in standard parametric models up to logarithmic terms. On the other hand, unlike in the BTL and Thurstone models, computing the minimax-optimal estimator in the stochastically transitive model is non-trivial, and we explore various computationally tractable alternatives. We show that a simple singular value thresholding algorithm is statistically consistent but does not achieve the minimax rate. We then propose and study algorithms that achieve the minimax rate over interesting sub-classes of the full stochastically transitive class. We complement our theoretical results with thorough numerical simulations. [ABSTRACT FROM AUTHOR]

The neighborhood counting measure (NCM) is a similarity measure based on the counting of all common neighborhoods in a data space [5]. The minimum risk metric (MRM) [2] is a distance measure based on the minimization of the risk of misclassification. The paper by Argentini and Blanzieri [1] refutes a remark in [5] about the time complexity of MRM, and presents an experimental comparison of MRM and NCM. This paper is a response to the paper by Argentini and Blanzieri [1]. The original remark is clarified by a combination of theoretical analysis of different implementations of MRM and experimental comparison of MRM and NCM using straightforward implementations of the two measures. [ABSTRACT FROM AUTHOR]

This paper considers the statistical performance of the MUSIC method under the condition that two closely spaced sources impinging on an array of sensors are effectively resolved, i.e., the spectrum exhibits two peaks in the neighborhood of the true directions-of-arrival (DOA). The MUSIC algorithm is known to have an infinite resolution power in theory. However, in the presence of modeling errors, sources can not be resolved with certainty, even if the array correlation matrix is perfectly known. The focus of this paper is to predict the bias and variance of the DOA estimates taking into account the possible resolution failure of MUSIC. This performance prediction, based on our recent mathematical investigation, is new to the best of our knowledge. A general mathematical framework to derive closed form expressions of the bias and variance versus the model mismatch, conditioned on a general statistical resolution test is proposed. In order to illustrate our mathematical approach, statistical tests with one and two conditions, respectively, are investigated. The accuracy of the performance prediction is illustrated in a simulation study. It is found that the proposed approach outperforms the "classical" technique, which ignores the possible resolution failure of the MUSIC algorithm. Therefore, our results provide better tools for determining the necessary antenna calibration accuracy to achieve some targeted specifications on the estimator performance. [ABSTRACT FROM AUTHOR]

A random variable with distribution P is observed in Gaussian noise and is estimated by a mismatched minimum meansquare estimator that assumes that the distribution is Q, instead of P. This paper shows that the integral over all signal-to-noise ratios (SNRs) of the excess mean-square estimation error incurred by the mismatched estimator is twice the relative entropy D(P||Q) (in nats). This representation of relative entropy can be generalized to nonreal-valued random variables, and can be particularized to give new general representations of mutual information in terms of conditional means. Inspired by the new representation, we also propose a definition of free relative entropy which fills a gap in, and is consistent with, the literature on free probability. [ABSTRACT FROM AUTHOR]

This paper investigates the probability of a radar being able to resolve two point-targets in an environment in which additive noise is the primary limitation on resolution. The statistical properties of the radar cross-ambiguity function are developed and used to arrive at an expression for the target resolution probability. The analysis is verified through simulations. [ABSTRACT FROM AUTHOR]

In this paper, we show that the cumulative and probability distribution functions (cdf and pdf, respectively) of small-scale wideband signal envelope fading in microcells can be very closely approximated by both the Rice and Nakagami distributions, which are already known to describe the cdfs and pdfs of small-scale narrowband signal envelope fading. Our results are obtained by means of an extensive Monte Carlo-based study of a wideband propagation model by Yan and Kozono, which is itself supported by extensive measurements. Over a comprehensive range of microcell propagation parameters, the average maximum error in the approximation is 1.65% and 1.78% for the Rice and Nakagami cdfs, respectively. The error in the approximation is 3.58% and 3.87% for the 95th percentile and does not exceed 7.61% and 7.80%, respectively, in the worst case. We propose an expression that maps the significant wideband small-scale signal envelope fading parameters to their narrowband counterparts for different standards like Dedicated Short Range Communication, WiMAX, Universal Mobile Telecommunications Service, and the family of the IEEE 802.11 standards. This mapping enables narrowband small-scale signal envelope fading statistical distributions, which are currently used, e.g., in fading simulators, link quality determination algorithms, and outage probability calculators, to be readily adapted to deal with small-scale wide-band signal envelope fading. As an application example of this proposed mapping, we derive the appropriate sample spacing and averaging interval (window size) that ought to be used to estimate the large-scale fading signal in an IEEE 802.11 receiver. [ABSTRACT FROM AUTHOR]

Multiuser diversity has been shown to increase the throughput of mobile ad hoc wireless networks (MANETs) when compared to fixed wireless networks. This paper addresses a multiuser diversity strategy that permits one of multiple one-time relays to deliver a packet to its destination. We show that the e (1) throughput of the original single one-time relay strategy is preserved by our multi-copy technique. The reason behind achieving the same asymptotic throughput is the fact that, as we demonstrate in this paper, interference for communicating among closest neighbors is bounded for different channel path losses, even when n goes to infinity. We show that a significant delay reduction is possible by multi-copy relaying when n is finite. Furthermore, we find that the average delay and delay variance for both the one and multi-copy relay strategies scale like Θ(m) and Θ(n²), respectively. We derive an approximation of the delay for multi-copy forwarding scheme and demonstrate that this approximation is very close to simulation results in MANET systems. [ABSTRACT FROM AUTHOR]

Variability in digital integrated circuits makes timing verification an extremely challenging task. In this paper, a canonical first-order delay model that takes into account both correlated and independent randomness is proposed. A novel linear-time block-based statistical timing algorithm is employed to propagate timing quantities like arrival times and required arrival times through the timing graph in this canonical form. At the end of the statistical timing, the sensitivity of all timing quantities to each of the sources of variation is available. Excessive sensitivities can then be targeted by manual or automatic optimization methods to improve the robustness of the design. This paper also reports the first incremental statistical timer in the literature, which is suitable for use in the inner loop of physical synthesis or other optimization programs. The third novel contribution of this paper is the computation of local and global criticality probabilities. For a very small cost in computer time, the probability of each edge or node of the timing graph being critical is computed. Numerical results are presented on industrial application-specified integrated circuit (ASIC) chips with over two million logic gates, and statistical timing results are compared to exhaustive corner analysis on a chip design whose hardware showed early mode timing violations. [ABSTRACT FROM AUTHOR]

The cutoff rate R0(W) of a discrete memoryless channel (DMC) W is often used as a figure of merit alongside the channel capacity C(W). If a channel W is split into two possibly correlated subchannels W1 , W2, the capacity function always satisfies C(W1) + C(W2) ≤ C(W), while there are examples for which R0 (W1) + R0 (W2) > R0 (W). The fact that cutoff rate can be "created" by channel splitting was noticed by Massey in his study of an optical modulation system. This paper gives a general framework for achieving similar gains in the cutoff rate of arbitrary DMCs by methods of channel combining and splitting. The emphasis is on simple schemes that can be implemented in practice. We give several examples that achieve significant gains in cutoff rate at little extra system complexity. Theoretically, as the complexity grows without bound, the proposed framework is capable of boosting the cutoff rate of a channel to arbitrarily close to its capacity in a sense made precise in the paper. Apart from Massey's work, the methods studied here have elements in common with Forney's concatenated coding idea, a method by Pinsker for cutoff rate improvement, and certain coded-modulation techniques, namely, Ungerboeck's set-partitioning idea and Imai-Hirakawa multilevel coding; these connections are discussed in the paper. [ABSTRACT FROM AUTHOR]

Accelerated life tests are extensively used to provide quickly the information about the life distributions of products. Test units are subjected to elevated stresses which yield shorter lives. For some products whose life is defined by usage, e.g., mileage and cycles, test units are also run at higher usage rates (UR) to compress the test time. This paper presents a method for testing products at both higher stress levels, and UR. Censoring time is pre-determined and fixed, while censoring usage is a function of UR. A UR effect model is proposed to describe the dependence of usage to failure (UTF) on UR. The relationship between UTF, and stress and UR is established, and used to estimate the UTF distribution at design stresses and usual UR. The mode! parameters are estimated by maximum likelihood method. The best compromise test plans, which choose the UR, stress levels, and sample sizes, are devised by minimizing the asymptotic variance of the estimator of a life percentile at design stresses and usual UR. The efficiency, and sensitivity of the test plans are evaluated. The results show that the test plans are efficient, and robust. [ABSTRACT FROM AUTHOR]

This paper studies the performance of a cell-averaging constant false alarm rate (CA-CFAR) receiver that operates in a nonhomogeneous clutter environment with impulsive, heavy-tailed statistics. The clutter distribution is modeled by a positive alpha-stable distribution, which is described by the characteristic exponent ?, where 0 < α <1. Analytical expressions for the false alarm and detection probabilities are derived for arbitrary values of α assuming a nonhomogeneous clutter background. The analytical results are validated with computer simulation. [ABSTRACT FROM PUBLISHER]

One-dimensional (1-D) adaptive noise canceler (ANC) has been used for false alarm reduction in low-frequency SAR change detection. The paper presents possibilities to process 2-D data by a 1-D ANC. Beside concatenating the rows of 2-D data in a matrix form to convert it to 1-D data in a vector form, two conversion approaches are considered—concatenating the columns of 2-D data and local concatenation, i.e., the conversion to 1-D is performed locally on each block of the 2-D data. A ground object can occupy more than one row and/or more than one column of 2-D data. In addition, the properties in cross range and range of an image are not the same. Thus, different conversion approaches may lead to different performance of an 1-D ANC and hence different change detection results. Among the considered approaches, the local concatenating approach is shown to provide slightly better performance in terms of probability of detection and false alarm rate. [ABSTRACT FROM AUTHOR]

This paper is aimed at obtaining the statistics as a probabilistic model pertaining to the geometric, topological and photometric structure of natural images. The image structure is represented by its segmentation graph derived from the low-level hierarchical multiscale image segmentation. We first estimate the statistics of a number of segmentation graph properties from a large number of images. Our estimates confirm some findings reported in the past work, as well as provide some new ones. We then obtain a Markov random field based model of the segmentation graph which subsumes the observed statistics. To demonstrate the value of the model and the statistics, we show how its use as a prior impacts three applications: image classification, semantic image segmentation and object detection. [ABSTRACT FROM AUTHOR]

The GUM and its supplements one and two have come to be regarded as de facto standards for evaluating measurement uncertainty. The latter documents have stressed the benefits of deriving probability density functions (PDFs) for the output quantities instead of just evaluating the standard and expanded uncertainties associated with their best estimates. Those supplements, however, present a brute force numerical method for obtaining the output PDFs. In this paper, we rely instead on the use of the change-of-variables theorem as a way of obtaining analytical expressions for PDFs in the form of integrals that, at least in principle, can be numerically evaluated. But more importantly, the GUM supplements do not include situations in which the available information is more than enough, in the sense that by separately considering its various components one may arrive at concurrent PDFs for the quantity or quantities of interest. In some situations these PDFs will be largely similar, so that implementing some form of merging method would perhaps be reasonable. But it may also happen that significant discrepancies between those PDFs are apparent, in which case a modification of the measurement model might make all information appear to be consistent. Herein we review two procedures for merging concurrent and not too dissimilar PDFs. We also discuss some elements to be considered if extending the measurement model appears to be a better alternative. [ABSTRACT FROM PUBLISHER]

This paper describes a probabilistic method based on a total risk index (probability times consequences) for assessing the number of spare breakers required for a group of similar high voltage breakers used in switching and transformer stations. The proposed method uses a Markov model for assessing the probability of failures and a bulk power system reliability program for evaluating failure consequences. The method considers a number of factors such as the group size, unit failure rate, unit repair time, transmission station layout, and other power system parameters that may impact the number of spare breakers. A cost/benefit analysis approach is used in determining the required number of spare breakers. The number of spare units is determined when the total cost (sum of spare unit costs, system operating costs and system outage costs due to breaker failures) is minimum. An example is given to illustrate the proposed method of assessment. [ABSTRACT FROM PUBLISHER]

Limiting the number of retransmissions in practical random access systems such as S-ALOHA and IEEE 802.11 systems has been used, since it was often considered as a way of preventing the system from being congested, by dropping packets in retransmission or letting users know network congestion after the maximum of retransmissions. Therefore, it can be expected that the smaller the maximum of retransmissions is allowed, the smaller the backlog size gets with a higher packet dropping probability. This paper explores how such a retransmission limit alters the shape of the stability and throughput regions of S-ALOHA systems. To do this, we first consider an S-ALOHA system, where two users with infinite queue length have different packet arrival rate and retransmission probability, which is called asymmetric user. Then, we obtain those results of the systems with $N$ symmetric users. [ABSTRACT FROM PUBLISHER]

The problem of estimation of density functionals like entropy and mutual information has received much attention in the statistics and information theory communities. A large class of estimators of functionals of the probability density suffer from the curse of dimensionality, wherein the mean squared error decays increasingly slowly as a function of the sample size T as the dimension d of the samples increases. In particular, the rate is often glacially slow of order O(T^-\gamma /d), where \gamma >0 is a rate parameter. Examples of such estimators include kernel density estimators, k-nearest neighbor (k\-NN) density estimators, k\-NN entropy estimators, intrinsic dimension estimators, and other examples. In this paper, we propose a weighted affine combination of an ensemble of such estimators, where optimal weights can be chosen such that the weighted estimator converges at a much faster dimension invariant rate of O(T^-1). Furthermore, we show that these optimal weights can be determined by solving a convex optimization problem which can be performed offline and does not require training data. We illustrate the superior performance of our weighted estimator for two important applications: 1) estimating the Panter–Dite distortion-rate factor; and 2) estimating the Shannon entropy for testing the probability distribution of a random sample. [ABSTRACT FROM AUTHOR]

In wireless multicast systems, cooperative multicast, in which successful users help to relay received packets to unsuccessful users, has been shown to be effective in combating channel fading and improving system performance. However, this mechanism requires the users' voluntary contributions, which cannot be guaranteed since users are selfish and only care about their own performance. Furthermore, users may have heterogeneous costs (which are their private information) to forward packets, and they may lie about their costs if cheating can improve their utilities. To address these problems, in this paper, we model the interaction among users in the wireless multicast system as a multiseller multibuyer payment-based game, where users pay to receive relay service and get paid if they forward packets to others. A simplified case with homogeneous users that have the same cost to forward packets is investigated first. Then, for the case with heterogeneous users, to encourage users to tell their true costs, we use the second-price sealed-bid auction, which is a truth-telling auction, since bidding the true cost is a weakly dominant strategy. To analyze the multiseller multibuyer payment-based game, we observe that under different selected prices, the game can converge to different equilibria, resulting in different user free-riding probabilities and system throughput. We also study the price selection problem and derive the optimal price that maximizes the system throughput. Simulation results show the effectiveness of our proposed mechanism. [ABSTRACT FROM PUBLISHER]

This paper presents a study on the interference caused by secondary users (SUs) due to misdetection and its effects on the capacity-outage performance of the primary user (PU) in a cognitive radio (CR) network assuming Rayleigh and Nakagami fading channels. The effect of beacon transmitter placement on aggregate interference distribution and capacity-outage performance is studied, considering two scenarios of beacon transmitter placement: a beacon transmitter located 1) at a PU transmitter or 2) at a PU receiver. Based on the developed statistical models for the interference distribution, closed-form expressions for the capacity-outage probability of the PU are derived to examine the effects of various system parameters on the performance of the PU in the presence of interference from SUs. It is shown that the beacon transmitter at the PU receiver imposes less interference and, hence, better capacity-outage probability to the PU than the beacon transmitter at the PU transmitter. Furthermore, the model is extended to investigate the cooperative sensing effect on aggregate interference statistical model and capacity-outage performance considering or (i.e., logical or operation) and maximum likelihood cooperative detection techniques. Simulation results are also provided to verify the developed analytical models. [ABSTRACT FROM PUBLISHER]

Correlation among channels is a physical phenomenon that affects the performance of a wireless communication system and that cannot be neglected in a myriad of realistic fading scenarios. Providing computable mathematical means to better characterize the corresponding statistics is certainly of interest to any design engineer. In this context, this paper further extends the statistical correlation investigations of the \alpha–\mu fading model, presenting a new, exact, and easily computable series-type formulation for the multivariate \alpha–\mu joint cumulative distribution function (JCDF). Along with this general result and capitalizing on practical assumptions, an alternative, simpler formulation for the \alpha–\mu multivariate joint density function and its corresponding distribution function are also provided. These formulations are still general and yet compact, assuming arbitrary fading parameters and correlations among the marginal variates. An important feature of the series-type distribution is that any truncation version of it is a valid distribution. As an application example, the truncated series-based outage probability of the selection combining scheme is computed and compared with that obtained by means of numerical methods and simulations. The results show that a small number of terms of the series are sufficient to provide excellent agreement between approximate and exact results. [ABSTRACT FROM PUBLISHER]

This paper introduces a bound-based approach to extract a pre-specified number of statistically-critical paths under process variations. These are the paths with the highest “violation probability,” which indicates the probability that a path would violate a given timing constraint. Our approach requires pre-computation of the violation probability of all the nodes and edges in the circuit timing graph, which can be done using two rounds of block-based statistical static timing analysis. Given these node/edge violation probabilities, we derive tight upper and lower bounds for any arbitrary segment of consecutive nodes and edges, which is the major contribution of this paper. We further utilize these bounds to extract the statistically-critical paths and show constant-time for incremental update of the bounds when extending a segment to a longer one. If our goal is to extract the single most statistically-critical path, we show a bound-based reduction that can prune a large portion of circuit without losing optimality. In our simulations, we verify the correctness and accuracy of our bounds for individual paths, and compare with exact path extraction using Monte-Carlo-based simulation, and an alternative which incorporates path-based statistical static timing analysis. [ABSTRACT FROM AUTHOR]

The objective of this paper is to introduce a neural:network-based algorithm for word clustering as an extension of the neural-network-based Boolean factor analysis algorithm (Frolov et al., 2007). It is shown that this extended algorithm supports even the more complex model of signals that are supposed to be related to textual documents. It is hypothesized that every topic in textual data is characterized by a set of words which coherently appear in documents dedicated to a given topic. The appearance of each word in a document is coded by the activity of a particular neuron. In accordance with the Hebbian learning rule implemented in the network, sets of coherently appearing words (treated as factors) create tightly connected groups of neurons, hence, revealing them as attractors of the network dynamics. The found factors are eliminated from the network memory by the Hebbian unlearning rule facilitating the search of other factors. Topics related to the found sets of words can be identified based on the words' semantics. To make the method complete, a special technique based on a Bayesian procedure has been developed for the following purposes: first, to provide a complete description of factors in terms of component probability, and second, to enhance the accuracy of classification of signals to determine whether it contains the factor. Since it is assumed that every word may possibly contribute to several topics, the proposed method might be related to the method of fuzzy clustering. In this paper, we show that the results of Boolean factor analysis and fuzzy clustering are not contradictory, but complementary. To demonstrate the capabilities of this attempt, the method is applied to two types of textual data on neural networks in two different languages. The obtained topics and corresponding words are at a good level of agreement despite the fact that identical topics in Russian and English conferences contain different sets of keywords. [ABSTRACT FROM AUTHOR]

One of the most important questions for manufacturers and users of electric power equipment is the failure probability and the expected lifetime of the produced and installed equipment. This question cannot be answered easily because there are many different parameters that influence lifetime behavior. If a breakdown occurs, it has to be determined whether the machine can made operational again within the technical and economical framework or if it has to be completely or partially replaced. The technical decision concerning repair or replacement often results in electric diagnostic measurements, in which economic decisions determined by corporate policy play a large role. In this paper, the characteristics of typical insulation systems for hydro generators will be discussed and a failure statistics of each system will be calculated. The resulting lifetimes for these systems will then be evaluated with Weibull distributions. [ABSTRACT FROM AUTHOR]

This paper presents a new spatially adaptive wavelet denoising method. Based on a doubly stochastic process model of wavelet coefficients, the method gives a new threshold, which varies spatially according to the variances of the coefficients, using the minimum description length (MDL) principle. The new threshold is not only easier to analyze since it is in a closed form, but also provides more facility for future compression than several other methods, almost without deteriorating mean square error risk. [ABSTRACT FROM AUTHOR]

A joint probabilistic face detection and tracking algorithm combining likelihood estimation and a prior probability is proposed in this paper. The likelihood estimation scheme is based on the statistical training of sets of automatically generated feature points and a mutual information tracking cue, while the prior probability estimation is based on a Gaussian temporal model. The likelihood estimation process is the core of a multiple face detection scheme used to initialize the tracking process. The resulting system was tested on real image sequences and is robust to significant partial occlusion and illumination changes. [ABSTRACT FROM AUTHOR]

In this paper, a Pareto-archived estimation-of-distribution algorithm (PAEDA) is presented for the multiobjective resource-constrained project scheduling problem with makespan and resource investment criteria. First, by combining the activity list and the resource list, an encoding scheme named activity-resource list is presented. Second, a novel hybrid probability model is designed to predict the most promising activity permutation and resource capacities. Third, a new sampling and updating mechanism for the probability model is developed to track the area with promising solutions. In addition, a Pareto archive is used to store the nondominated solutions that have been explored, and another archive is used to store the solutions for updating the probability model. The evolution process of the PAEDA is visualized showing the most promising area of the search space is tracked. Extensive numerical testing results then demonstrate that the PAEDA outperforms the existing methods. [ABSTRACT FROM PUBLISHER]

It is pointed out that the two beta-type distributions introduced by Tardon et al have been known before in the statistics literature. [ABSTRACT FROM AUTHOR]

Given the knowledge of class probability densities, a priori probabilities, and relative risk levels, Bayes classifier provides the optimal minimum-risk decision rule. Specifically, focusing on the two-class (detection) scenario, under certain symmetry assumptions, matched filters provide optimal results for the detection problem. Noticing that the Bayes classifier is in fact a nonlinear projection of the feature vector to a single-dimensional statistic, in this paper, we develop a smooth nonlinear projection filter constrained to the estimated span of class conditional distributions as does the Bayes classifier. The nonlinear projection filter is designed in a reproducing kernel Hilbert space leading to an analytical solution both for the filter and the optimal threshold. The proposed approach is tested on typical detection problems, such as neural spike detection or automatic target detection in synthetic aperture radar (SAR) imagery. Results are compared with linear and kernel discriminant analysis, as well as classification algorithms such as support vector machine, AdaBoost and LogitBoost. [ABSTRACT FROM AUTHOR]

This paper follows the recent work of Helleseth, Kholosha, Johansen, and Ness to study the cross correlation between an m-sequence of period 2m - 1 and the d-decimation of an m-sequence of a shorter period 2n - 1 for an even number m = 2n. Assuming that d satisfies d(2l + 1) = 2i mod 2n - 1) for some l > 0 and i ≥ 0, it is proved that the cross correlation takes on either exactly three or four values depending on whether l and n are coprime or not. The distribution of the cross-correlation values is also completely determined. Our results theoretically confirm the numerical data by Ness and Helleseth. It is conjectured that there are no other decimations that give at most four-valued cross correlation apart from the ones proved here. [ABSTRACT FROM AUTHOR]

In this paper, we measure and analyze the graph features of Semantic Web (SW) schemas with focus on power-Iaw degree distributions. Our main finding is that the majority of SW schemas with a significant number of properties (respectively, classes) approximate a power law for total-degree (respectively, the number of subsumed classes) distribution. Moreover, our analysis revealed some emerging conceptual modeling practices of SW schema developers: 1) each schema has a few focal classes that have been analyzed in detail (that is, they have numerous properties and subclasses), which are further connected with focal classes defined in other schemas, 2) class subsumption hierarchies are mostly unbalanced (that is, some branches are deep and heavy, while others are shallow and light), 3) most properties have as domain/range classes that are located high at the class subsumption hierarchies, and 4) the number of recursive/multiple properties is significant. The knowledge of these features is essential for guiding synthetic SW schema generation, which is an important step toward benchmarking SW repositories and query language implementations. [ABSTRACT FROM AUTHOR]

Dual-tree wavelet decompositions have recently gained much popularity, mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy. When the decomposition of a random process is performed—which occurs in particular when an additive noise is corrupting the signal to be analyzed—it is useful to characterize the statistical properties of the dual-tree wavelet coefficients of this process. As dual-tree decompositions constitute overcomplete frame expansions, correlation structures are introduced among the coefficients, even when a white noise is analyzed. In this paper, we show that it is possible to provide an accurate description of the covariance properties of the dual-tree coefficients of a wide-sense-stationary process. The expressions of the (cross-) covariance sequences of the coefficients are derived in the one- and two-dimensional cases. Asymptotic results are also provided, allowing to predict the behavior of the second-order moments for large lag values or at coarse resolution. In addition, the cross-correlations between the primal and dual wavelets, which play a primary role in our theoretical analysis, are calculated for a number of classical wavelet families. Simulation results are finally provided to validate these results. [ABSTRACT FROM AUTHOR]

This paper introduces a fading model, which explores the nonlinearity of the propagation medium. It derives the corresponding fading distribution—the α-μ distribution-which is in fact a rewritten form of the Stacy (generalized Gamma) distribution. This distribution includes several others such as Gamma (and its discrete versions Erlang and central Chi-squared), Nakagami-m (and its discrete version Chi), exponential, Weibull, one-sided Gaussian, and Rayleigh. Based on the fading model proposed here, higher order statistics are obtained in closed-form formulas. More specifically, level-crossing rate, average fade duration, and joint statistics (joint probability density function, general joint moments, and general correlation coefficient) of correlated α-μ variates are obtained, and they are directly related to the physical fading parameters. [ABSTRACT FROM AUTHOR]

Real-world action recognition applications require the development of systems which are fast, can handle a large variety of actions without a priori knowledge of the type of actions, need a minimal number of parameters, and necessitate as short as possible learning stage, in this paper, we suggest such an approach. We regard dynamic activities as long-term temporal objects, which are characterized by spatio-temporal features at multiple temporal scales. Based on this, we design a simple statistical distance measure between video sequences which captures the similarities in their behavioral content. This measure is nonparametric and can thus handle a wide range of complex dynamic actions having a behavior-based distance measure between sequences, we use it for a variety of tasks, including: video indexing, temporal segmentation, and action-based video clustering. These tasks are performed without prior knowledge of the types of actions, their models, or their temporal extents. [ABSTRACT FROM AUTHOR]

A clock-controlled linear feedback shift register (LFSR) is a simple keystream generator consisting of an LFSR whose clock is controlled by another LFSR so that the output is an irregularly decimated LFSR sequence. Statistical distinguishers for keystream generators are algorithms whose objective is to distinguish the keystream sequence from a purely random sequence. Previously proposed statistical distinguishers for clock-controlled LFSRs are based on detecting binary linear relations in the keystream sequence that hold with a probability sufficiently different from one half. In this paper, a novel approach based on the correlation analysis of clock-controlled LFSRs is introduced. It significantly reduces the required computation time and essentially consists of a probabilistic reconstruction of bits in the regularly clocked LFSR sequence that satisfy the LFSR recurrence or any linear recurrence derived from low-weight multiples of the LFSR characteristic polynomial. The keystream sequence length and the computation time required for a reliable statistical distinction are analyzed both theoretically and experimentally. The new approach shows that there is no need to deal with the majority bits of blocks of LFSR bits as proposed recently. If individual bits or blocks of bits are considered instead, then the underlying probabilities can be computed theoretically instead of heuristically, which in turn allows a simple and general theoretical analysis of the keystream sequence length required. [ABSTRACT FROM AUTHOR]

This paper proposes a novel algorithm to jointly determine the structure and the parameters of a posteriori probability model based on neural networks (NNs). It makes use of well-known ideas of pruning, splitting, and merging neural components and takes advantage of the probabilistic interpretation of these components. The algorithm, so called a posteriori probability model selection (PPMS), is applied to an NN architecture called the generalized softmax perceptron (GSP) whose outputs can be understood as probabilities although results shown can be extended to more general network architectures. Learning rules are derived from the application of the expectation-maximization algorithm to the GSP-PPMS structure. Simulation results show the advantages of the proposed algorithm with respect to other schemes. [ABSTRACT FROM AUTHOR]

Expectation-Maximization (EM) algorithm [10] has been extensively used in density mixture clustering problems, but it is unable to perform model selection automatically. This paper, therefore, proposes to learn the model parameters via maximizing a weighted likelihood. Under a specific weight design, we give out a Rival Penalized Expectation-Maximization (RPEM) algorithm, which makes the components in a density mixture compete each other at each time step. Not only are the associated parameters of the winner updated to adapt to an input, but also all rivals' parameters are penalized with the, strength proportional to the corresponding posterior density probabilities. Compared to the EM algorithm [10], the RPEM is able to fade out the redundant densities from a density mixture during the learning process. Hence, it can automatically select an appropriate number of densities in density mixture clustering. We experimentally demonstrate its outstanding performance on Gaussian mixtures and color image segmentation problem. Moreover, a simplified version of RPEM generalizes our recently proposed RPCCL algorithm [8] so that it is applicable to elliptical clusters as well with any input proportion. Compared to the existing heuristic RPCL [25] and its variants, this generalized RPCCL (G-RPCCL) circumvents the difficult preselection of the so-called delearning rate. Additionally, a special setting of the G-RPCCL not only degenerates to RPCL and its Type A variant, but also gives a guidance to choose an appropriate delearning rate for them. Subsequently, we propose a stochastic version of RPCL and its Type A variant, respectively, in which the difficult selection problem of delearning rate has been novelly circumvented. The experiments show the promising results of this stochastic implementation. [ABSTRACT FROM AUTHOR]

The methods commonly used for degradation analysis deduce the lifetime distribution of a product from the distribution of the random parameters in the degradation path model for the product. This approach requires a functional form of the joint distribution of the random parameters, which poses certain practical difficulties. In this paper, we propose an alternative approach which makes inference directly on the lifetime distribution itself. In the proposed approach, degradation data are first used to derive predictive intervals of individual lifetimes. Then an imputation algorithm is invoked to obtain the estimate of the lifetime distribution. The approach has the following advantages: 1) the adequacy of the assumption on the lifetime distribution can be easily examined, 2) the estimated lifetime distribution has a closed form, and 3) the procedure can be more easily implemented. A simulation study is reported to demonstrate the efficiency of the proposed approach. The approach is applied to two real degradation data sets, and compared with Lu-Meeker's two stage method in the applications. [ABSTRACT FROM AUTHOR]

SAR interferograms are affected by a strong noise component which often prevents correct phase unwrapping and always impairs the phase reconstruction accuracy. To obtain satisfactory performances most filtering techniques exploit prior information by means of ad hoc, empirical strategies. In this paper, we recast phase filtering as a Bayesian estimation problem in which the image prior is modeled as a suitable Markov random field, and the filtered phase field is the configuration with maximum a posteriori probability. Assuming the image to be residue free and generally smooth, a two-component MRF model is adopted, where the first component penalizes residues, while the second one penalizes discontinuities. constrained simulated annealing is then used to find the optimal solution. The experimental analysis shows that, by gradually adjusting the Miff parameters, the algorithm filters out most of the high-frequency noise and, in the limit, eliminates all residues, allowing for a trivial phase unwrapping. Given a limited processing time, the algorithm is still able to eliminate most residues, paving the way for the successful use of any subsequent phase unwrapping technique. [ABSTRACT FROM AUTHOR]

In this paper, we present a multichannel post-filtering approach for minimizing the log-spectral amplitude distortion in nonstationary noise environments. The beamformer is realistically assumed to have a steering error, a blocking matrix that is unable to block all of the desired signal components, and a noise canceller that is adapted to the pseudo-stationary noise but not modified during transient interferences. A mild assumption is made that a desired signal component is stronger at the beamformer output than at any reference noise signal, and a noise component is strongest at one of the reference signals. The ratio between the transient power at the beamformer output and the transient power at the reference noise signals is used to indicate whether such a transient is desired or interfering. Based on a Gaussian statistical model and combined with an appropriate spectral enhancement technique, we derive estimators for the signal presence probability, the noise power spectral density, and the clean signal. The proposed method is tested in various nonstationary noise enviromnehts. Compared with single-channel post-filtering, a significantly reduced level of nonstationary noise is achieved without further distorting the desired signal components. [ABSTRACT FROM AUTHOR]

We study the top- $K$ ranking problem where the goal is to recover the set of top- $K$ ranked items out of a large collection of items based on partially revealed preferences. We consider an adversarial crowdsourced setting where there are two population sets, and pairwise comparison samples drawn from one of the populations follow the standard Bradley-Terry-Luce model (i.e., the chance of item $i$ beating item $j$ is proportional to the relative score of item $i$ to item $j$ ), while in the other population, the corresponding chance is inversely proportional to the relative score. When the relative size of the two populations is known, we characterize the minimax limit on the sample size required (up to a constant) for reliably identifying the top- $K$ items, and demonstrate how it scales with the relative size. Moreover, by leveraging a tensor decomposition method for disambiguating mixture distributions, we extend our result to the more realistic scenario, in which the relative population size is unknown, thus establishing an upper bound on the fundamental limit of the sample size for recovering the top- $K$ set. [ABSTRACT FROM PUBLISHER]

While there is a huge body of research on cooperative spectrum sensing in cognitive radio networks (CRNs), incentives for cooperative behavior or the conditions under which cooperation is more likely have not been explored. We model cooperation among cognitive radios (CRs) as a function of social ties among CRs. In this social CRN , where CRs do not necessarily fulfill every cooperative sensing request, we focus on the cooperator set selection problem, i.e., in which CRs ask for cooperation so that the resulting throughput and sensing accuracy are maximized, subject to detection and false alarm probability constraints. For a single-channel scenario, we devise a multiobjective optimization model and obtain the solution using an evolutionary multiobjective algorithm. Our evaluations show that our solution is near optimal, in terms of throughput under legitimate operation, i.e., no malicious users, whereas it outperforms the expected-throughput-optimal scheme in the case of attackers. A numerical analysis demonstrates the robustness of our proposal with a slight loss in performance when the network is subject to common sensing attacks. In addition, our analysis underlines one significant drawback of existing works: assuming all CRs to be cooperative leads to a substantial overestimation of throughput capacity. Finally, to tackle the increasing complexity under a multichannel setting, we propose a heuristic for multichannel cooperative sensing for the considered social CRN. [ABSTRACT FROM PUBLISHER]

We consider a system consisting of N parallel queues, served by one server. Time is slotted, and the server serves one of the queues in each time slot, according to some scheduling policy. We first characterize the exponent of the buffer overflow probability and the most likely overflow trajectories under the Longest Queue First (LQF) scheduling policy. Under statistically identical arrivals to each queue, we show that the buffer overflow exponents can be simply expressed in terms of the total system occupancy exponent of m parallel queues, for some m\leq N. We next turn our attention to the rate of queue length information needed to operate a scheduling policy, and its relationship to the buffer overflow exponents. It is known that queue length blind policies such as processor sharing and random scheduling perform worse than the queue aware LQF policy, when it comes to buffer overflow probability. However, we show that the overflow exponent of the LQF policy can be preserved with arbitrarily infrequent queue length updates. [ABSTRACT FROM AUTHOR]

We define a statistical angular resolution limit (ARL) on resolving two closely spaced point sources in a 3-D reference frame, using constraints on the probabilities of false alarm and detection for a hypothesis test. The ARL can be used as a performance measure for sensor arrays in localizing remote sources and is applicable to different measurement models and applications (e.g., radar, sonar, or astronomy). By considering the asymptotic performance of the generalized likelihood ratio test (GLRT), we derive the analytical expression of the ARL and show that it is proportional to the square root of the Cramér-Rao bound (CRB) on the angular source separation, or asymptotically the lower bound on the mean-square angular error (MSAECRD). Numerical examples illustrate that the proposed ARL is practically computable and achievable with large data samples. Our analytical result can replace the commonly used ad hoc resolution limits in existing literature. [ABSTRACT FROM AUTHOR]

The article presents information on the estimation of parameters of life from progressively censored data using Burr-XII model. Based on progressively Type-II censored samples, the maximum likelihood, and Bayes estimators for some lifetime parameters including reliability, and hazard functions, as well as the parameters of the Burr-XII model, are derived. Some numerical results using simulation study concerning different sample sizes, and progressive censoring schemes have been reported.

An approach is presented for the joint segmentation and classification of a time series. The segmentation is on the basis of a menu of possible statistical models: each of these must be describable in terms of a sufficient statistic, but there is no need for these sufficient statistics to be the same and these can be as complex as fits. All that is needed is the probability density function of each sufficient statistic under its own assumed model-presumably this comes from training data and it is particularly appealing that there is no need at all for a joint statistical characterization of all the statistics.

We consider the problem of universal simulation of an unknown source from a certain parametric family of discrete memoryless sources, given a training vector X from that source and given a limited budget of purely random key bits. The goal is to generate a sequence of random vectors { Y[SUBi] }, all of the same dimension and the same probability law as the given training vector X, such that a certain, prescribed set of M statistical tests will be satisfied. In particular, for each statistical test, it is required that for a certain event, ∊[SUBℓ], 1≤ ℓ ≤ M, the relative frequency &frac1N; Σ[SUPN,SUBi=1] 1[SUB∊[SUBℓ]] (Y[SUBi]) (1[SUB∊] (·) being the indicator function of an event ∊), would converge, as N → ∞, to a random variable (depending on X), that is typically as close as possible to the expectation of 1[SUB∊[SUBℓ]] (X) with respect to (w.r.t.) the true unknown source, namely, to the probability of the event ∊[SUBℓ],. We characterize the minimum key rate needed for this purpose and demonstrate how this minimum can be approached in principle. [ABSTRACT FROM AUTHOR]

Program "testability" is, informally, the probability that a program will fail under test if it contains at least one fault. When a dependability assessment has to be derived from the observation of a series of failure-free test executions (a common need for software subject to "ultra-high reliability" requirements), measures of testability can-in theory-be used to draw inferences on program correctness (and hence on its probability of failure in operation). In this paper, we rigorously investigate the concept of testability and its use in dependability assessment, criticizing, and improving on, previously published results. We first give a general descriptive model of program execution and testing, on which the different measures of interest can be defined. We propose a more precise definition of program testability than that given by other authors, and discuss how to increase testing effectiveness without impairing program reliability in operation. We then study the mathematics of using testability to estimate, from test results: 1) the probability of program correctness and 2) the probability of failures. To derive the probability of program correctness, we use a Bayesian inference procedure and argue that this is more useful than deriving a classical "confidence level." We also show that a high testability is not an unconditionally desirable property for a program. In particular, for programs complex enough that they are unlikely to be completely fault-free, increasing testability may produce a program which will be less trustworthy, even after successful testing. [ABSTRACT FROM AUTHOR]

This paper introduces a statistical method to decide whether two blocks in a pair of images match reliably. The method ensures that the selected block matches are unlikely to have occurred “just by chance.” The new approach is based on the definition of a simple but faithful statistical background model for image blocks learned from the image itself. A theorem guarantees that under this model, not more than a fixed number of wrong matches occurs (on average) for the whole image. This fixed number (the number of false alarms) is the only method parameter. Furthermore, the number of false alarms associated with each match measures its reliability. This a contrario block-matching method, however, cannot rule out false matches due to the presence of periodic objects in the images. But it is successfully complemented by a parameterless self-similarity threshold. Experimental evidence shows that the proposed method also detects occlusions and incoherent motions due to vehicles and pedestrians in nonsimultaneous stereo. [ABSTRACT FROM AUTHOR]

In PET image reconstruction, it would be useful to obtain the entire posterior probability distribution of the image, because it allows for both estimating image intensity and assessing the uncertainty of the estimation, thus leading to more reliable interpretation. We propose a new entirely probabilistic model: the prior is a distribution over possible smooth regions (distance-driven Chinese restaurant process), and the posterior distribution is estimated using a Gibbs Markov chain Monte Carlo sampler. Data from other modalities (here one or several MR images) are introduced into the model as additional observed data, providing side information about likely smooth regions in the image. The reconstructed image is the posterior mean, and the uncertainty is presented as an image of the size of 95% posterior intervals. The reconstruction was compared with the maximum-likelihood expectation–maximization and OSEM algorithms, with and without post-smoothing, and with a penalized ML or MAP method that also uses additional images from other modalities. Qualitative and quantitative tests were performed on realistic simulated data with statistical replicates and on several clinical examinations presenting pathologies. The proposed method presents appealing properties in terms of obtained bias, variance, spatial regularization, and use of multimodal data, and produces, in addition, potentially valuable uncertainty information. [ABSTRACT FROM AUTHOR]

We consider the problem of fusing probability scores from a set of classifiers to estimate a final fused probability score. Our interest is in scenarios where the classifiers are statistically dependent. To that end, we propose a new classifier fusion approach that is data driven and founded on the statistical theory of copulas. Numerical results with both simulated and real data show that our copula based classifier fusion approach produces better probability scores than individual classifiers and outperforms existing probability score fusion approaches. [ABSTRACT FROM AUTHOR]