Scalar Estimates Research Articles

NEW RESULTS IN REDUCED ESTIMATION WITH SYSTEMATIC ERRORS IN MEASUREMENTS AND THEIR APPLICATION FOR THE FORMATION OF A GROUP TIME SCALE

The article deals with the behavior of reduced scalar estimates in the presence of systematic errors in the observational data. The proposed procedure with a different method of forming the reduction coefficient. A quasi-optimal variant of the compression parameter formation is considered. Simulation results for different conditions of application of the proposed algorithms are presented. Currently, one of the ways to improve the accuracy of the formation of the time scale in solving the problems of frequency-time customer support is the averaging of the readings of several generators. At the same time, this approach, as shown in the theory of statistical estimation, is effective for parrying the random component of the error of the estimated process. However, for frequency generators random error can be effectively compensated for a long range of observations, but the systematic component - frequency drift - is a serious problem, which can be eliminated by averaging only under certain conditions. Therefore, the article proposes a version of the reduced estimate, effective, as shown, to parry the departure of the time scale by introducing a shift in the implementation of compression, defined by the reduction procedure. The conditions in which the degree of the achieved positive effect has a practical sense are considered.

Iterative reconstruction of rank-one matrices in noise

Abstract We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and positivity that arise commonly in learning problems. We propose a family of algorithms that reduce the problem to a sequence of scalar estimation computations. These algorithms are similar to approximate message-passing techniques based on Gaussian approximations of loopy belief propagation that have been used recently in compressed sensing. Leveraging analysis methods by Bayati and Montanari, we show that the asymptotic behavior of the algorithm is described by a simple scalar equivalent model, where the distribution of the estimates at each iteration is identical to certain scalar estimates of the variables in Gaussian noise. Moreover, the effective Gaussian noise level is described by a set of state evolution equations. The proposed approach to deriving algorithms thus provides a computationally simple and general method for rank-one estimation problems with a precise analysis in certain high-dimensional settings.

Sensitivity Statistical Estimates for Local A Posteriori Inference Matrix-Vector Equations in Algebraic Bayesian Networks over Quantum Propositions

An approach to the sensitivity analysis of local a posteriori inference equations in algebraic Bayesian networks is proposed in this paper. Some basic definitions and formulations are briefly given and the development of the matrix-vector a posteriori inference approach is considered. Some cases of the propagation of deterministic and stochastic evidence in a knowledge pattern with scalar estimates of component truth probabilities over quantum propositions are described. For each of the considered cases, the necessary metrics are introduced, and some transformations resulting in four linear programming problems are performed. The solution of these problems gives the required estimates. In addition, two theorems postulating the covering estimates for the considered parameters are formulated. The results obtained in this work prove the correct application of models and create a basis for the sensitivity analysis of local and global probabilistic-logic inference equations.

A sharp scalar curvature estimate for CMC hypersurfaces satisfying an Okumura type inequality

We obtain a sharp estimate to the scalar curvature of stochastically complete hypersurfaces immersed with constant mean curvature in a locally symmetric Riemannian space obeying standard curvature constraints (which includes, in particular, a Riemannian space with constant sectional curvature). For this, we suppose that these hypersurfaces satisfy a suitable Okumura-type inequality recently introduced by Melendez (Bull Braz Math Soc 45:385–404, 2014), which is a weaker hypothesis than to assume that they have two distinct principal curvatures. Our approach is based on the equivalence between stochastic completeness and the validity of the weak version of the Omori–Yau’s generalized maximum principle, which was established by Pigola et al. (Proc Am Math Soc 131:1283–1288, 2002; Mem Am Math Soc 174:822, 2005).

Computational polarimetric microwave imaging

We propose a polarimetric microwave imaging technique that exploits recent advances in computational imaging. We utilize a frequency-diverse cavity-backed metasurface, allowing us to demonstrate high-resolution polarimetric imaging using a single transceiver and frequency sweep over the operational microwave bandwidth. The frequency-diverse metasurface imager greatly simplifies the system architecture compared with active arrays and other conventional microwave imaging approaches. We further develop the theoretical framework for computational polarimetric imaging and validate the approach experimentally using a multi-modal leaky cavity. The scalar approximation for the interaction between the radiated waves and the target- often applied in microwave computational imaging schemes-is thus extended to retrieve the susceptibility tensors, and hence provides additional information about the targets. Computational polarimetry has relevance for existing systems in the field that extract polarimetric imagery, and particular for ground observation. A growing number of short-range microwave imaging applications can also notably benefit from computational polarimetry, particularly for imaging objects that are difficult to reconstruct when assuming scalar estimations.

Development of a Measurement Complex with Intelligent Component

A method of constructing a selective measurement complex with variable structure is investigated. A measurement complex with intelligent component consisting of algorithms for the construction of predictive models and the comparison of a prediction with the current result of measurements is developed for precision determination of the parameters of a dynamic object. The algorithmic support of the complex is constructed on the basis of the Anokhin theory of functional systems with the use of a scalar estimation algorithm, self-organization algorithm with trend back-up, and criterion expressed as the degree of observability of the state variables. Models with elevated degrees of observability of the state variables are used in the information processing algorithms.

Multievent moment-tensor inversion for ill-conditioned geometries

Moment-tensor inversion under single monitoring well geometries becomes unstable due to the singularity of the inversion matrix. But microseismic events observed during hydraulic fracturing commonly show clusters of events with similar source mechanisms despite differences in the origin time and the magnitude. If the events with similar source mechanisms can be grouped and inverted for a single common moment tensor, the singularity can be eliminated. We have developed a normalized multievent moment-tensor inversion (NME-MTI) method, which does the MTI simultaneously for multiple events, to test the feasibility of this multievent approach. First, the scalar moment for each event was estimated using the far-field low-frequency level at each receiver. Then, the displacements measured at the receivers were normalized by the scalar moment and used to invert for the common moment tensor simultaneously for all the events in the group. We introduced a gradient search method to minimize the overall misfit by adjusting the scalar moment for each event to reduce the errors introduced by the scalar moment estimation. The algorithm was tested with a synthetic data set with four monitoring wells and a field data set with dual monitoring wells. It was proved that the NME-MTI method can retrieve the moment tensors of the event groups with data from a single monitoring well. The effects of uncertainties on the inversion were examined with data noise, scalar moment uncertainty, and event location uncertainty. The results showed that the ME-MTI result is much less sensitive to the data noise and the scalar moment uncertainty than the single-event approach. The results also determined that although the bias to the solutions increases when the event location uncertainty increases, the bias can be controlled by reducing the event location uncertainties using a more accurate location algorithm.

Multisensory decisions provide support for probabilistic number representations.

A large body of evidence suggests that an approximate number sense allows humans to estimate numerosity in sensory scenes. This ability is widely observed in humans, including those without formal mathematical training. Despite this, many outstanding questions remain about the nature of the numerosity representation in the brain. Specifically, it is not known whether approximate numbers are represented as scalar estimates of numerosity or, alternatively, as probability distributions over numerosity. In the present study, we used a multisensory decision task to distinguish these possibilities. We trained human subjects to decide whether a test stimulus had a larger or smaller numerosity compared with a fixed reference. Depending on the trial, the numerosity was presented as either a sequence of visual flashes or a sequence of auditory tones, or both. To test for a probabilistic representation, we varied the reliability of the stimulus by adding noise to the visual stimuli. In accordance with a probabilistic representation, we observed a significant improvement in multisensory compared with unisensory trials. Furthermore, a trial-by-trial analysis revealed that although individual subjects showed strategic differences in how they leveraged auditory and visual information, all subjects exploited the reliability of unisensory cues. An alternative, nonprobabilistic model, in which subjects combined cues without regard for reliability, was not able to account for these trial-by-trial choices. These findings provide evidence that the brain relies on a probabilistic representation for numerosity decisions.

Posteriori inference in tertiary polystructure of an algebraic Bayesian network.

There exist algorithms for determining the possibility of building an acyclic secondary structure of the network for its primary structure, and hence the possibility for effective carrying out of the posterior inference in the theory of algebraic Bayesian networks. Their presence allowed the introduction of a global posteriori algorithm for probabilistic inference, not based on the secondary structure. The coincidence of the results of using this algorithm and the known propagation algorithm using virtual evidences on the joint graph is proved for the case of scalar probability estimates.

Knowledge and reasoning with uncertainty modeling: matrix-and-vector calculus for local reconciliation of truth estimates

In the theory of algebraic Bayesian networks, there are four operations classified as a kind of local synthesis of consistent truth estimates: knowledge pattern consistency verification, knowledge pattern reconciliation, a posteriori inference, and knowledge pattern enclosing reconciliation. The paper presents a knowledge pattern model formalization based on the matrix-vector terms. The model itself is a conjuncts ideal with scalar or interval truth probabilistic estimates. A specification of all four operations of the local synthesis has been introduced in the matrix-vector terms.

Analysis of adaptive sampling techniques for underwater vehicles

A critical problem in planning sampling paths for autonomous underwater vehicles (AUVs) is correctly balancing two issues. First, obtaining an accurate scalar field estimation and second, efficiently utilizing the stored energy capacity of the sampling vehicle. Adaptive sampling approaches can only provide solutions when real time and a priori environmental data is available. In this paper we present an analysis of adaptive sampling methodologies for AUVs. In particular, we analyze various sampling path strategies including systematic and stratified random patterns within a wide range of sampling densities and their impact in the energy consumption of the vehicle through a cost-evaluation function. Our study demonstrates that a systematic spiral sampling path strategy is optimal for high-variance scalar fields for all sampling densities and low-variance scalar fields when sampling is sparse. In addition, our results show that the random spiral sampling path strategy is found to be optimal for low-variance scalar fields when sampling is dense.

Vector estimators of the Monte Carlo method with a finite variance

In this paper we study problems related to the finiteness of the variance of weighted Monte Carlo estimators for solving a system of second-kind integral equations. Modifications of the finiteness criterion for the variance of a weighted scalar estimator are based on the construction of an appropriate system of linear integral equations with ‘majorant’ kernels. A majorant criterion of the finiteness of a vector weighted estimator is given. This criterion uses a comparison of the estimator with a scalar estimator obtained by the method of randomization. It is shown that for the corresponding randomized algorithm the variance of the scalar estimator and the mean simulation time for a single trajectory are bounded if the original solution is bounded. The ability to use branching to construct a vector estimator of the solution to a system of integral equations is also studied.

Distance deviation measure of contouring variability

BackgroundSeveral methods that are currently used for contouring analysis have problems providing reliable and/or meaningful results. In this paper a solution to these problems is proposed in a form of a novel measure, which was developed based on requirements defined for contouring studies.Materials and methodsThe proposed distance deviation measure can be understood as an extension of the closest point measures in such a way that it does not measure only distances between points on contours but rather analyse deviation of distances to both/all contours from each image point/voxel. The obtained result is information rich, reliable and provided in a form of an image, enabling detailed topographic analysis. In addition to image representation, results can be further processed into angular representation for compact topographic analysis or into overall scalar estimates for quick assessment of contour disagreement.ResultsDistance deviation method is demonstrated on a multi observer contouring example with complex contour shapes, i.e., with pronounced extremes and void interior. The results are presented using the three proposed methods.ConclusionsThe proposed method can detect and measure contour variation irrespective of contour complexity and number of contour segments, while the obtained results are easy to interpret. It can be used in various situations, regarding the presence of reference contour or multiple test contours.

Tracking strategy analysis with multi underwater vehicles for ocean feature

Autonomous underwater vehicles (AUVs) are mobile platforms with excellent maneuverability, which are preferred for micro scale and meso scale ocean feature tracking in a near real time mode. With the feature extract analysis of ocean phenomena, autonomous control and tracking strategy of multi AUVs are designed for ocean feature tracking. Firstly, formation control is designed coordinately with the estimation of the ocean feature, and EKF (extended Klaman filter) is applied for ocean feature scalar estimation from the sample process noise and sample instrument noise. Secondly, the virtual leader-follow mode is utilized for multi AUVs formation control, and formation rotational is designed to adapt the variation of ocean phenomena. Lastly, the simulation platform is established for multi vehicles ocean feature tracking, and the simulation results are selected to verify the effectiveness of autonomous tracking strategy.

Coincidence of the sets of minimal and irreducible join graphs over primary structure of algebraic Bayesian networks

An algebraic Bayesian network (ABN) is a probabilistic-logic graphical model of bases of knowledge patterns with uncertainty. A primary structure of an ABN is a set of knowledge patterns, that are ideals of conjunctions of positive literals except the empty conjunction endowed with scalar or interval probability estimates. A secondary ABN structure is represented by a graph constructed over the primary structure, which is called a join graph. From the point of view of learning of a global ABN structure, of interest are join graphs with the minimum number of edges and irreducible join graphs.

Asymptotic Analysis of MAP Estimation via the Replica Method and Applications to Compressed Sensing

The replica method is a non-rigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method, under the assumption of replica symmetry, to study estimators that are maximum a posteriori (MAP) under a postulated prior distribution. It is shown that with random linear measurements and Gaussian noise, the replica-symmetric prediction of the asymptotic behavior of the postulated MAP estimate of an n-dimensional vector "decouples" as n scalar postulated MAP estimators. The result is based on applying a hardening argument to the replica analysis of postulated posterior mean estimators of Tanaka and of Guo and Verdu. The replica-symmetric postulated MAP analysis can be readily applied to many estimators used in compressed sensing, including basis pursuit, lasso, linear estimation with thresholding, and zero norm-regularized estimation. In the case of lasso estimation the scalar estimator reduces to a soft-thresholding operator, and for zero norm-regularized estimation it reduces to a hard-threshold. Among other benefits, the replica method provides a computationally-tractable method for precisely predicting various performance metrics including mean-squared error and sparsity pattern recovery probability.

Finite-volume complex surfaces without cuspidal Einstein metrics

We derive an obstruction to the existence of cuspidal Einstein metrics on finite-volume complex surfaces. This generalizes a theorem of LeBrun for compact complex surfaces. As in the compact case, such a result relies on a scalar curvature estimate. Finally, the obstruction is made explicit on some examples.

A comment on multidimensional poverty indices

The three papers on multidimensional poverty published in the 2011 June issue of the Journal of Economic Inequality [1–3] present strong cases in favor of their respective methodologies to capture and measure well-being and poverty. Ultimately the choice of preferred indicators, whether unidimensional or multidimensional (and, in the latter case, which dimensions to incorporate in such indicators), depends ultimately on the purposes they should serve. Money-metric (income or consumption based) poverty measures have been useful to the World Bank in estimating approximately the magnitude of global poverty as well as individual regions’ and countries’ progress towards the reduction of poverty. The Human Development Index has provided the development community with a broader measure of well-being—adding health and educational dimensions to income—and demonstrating that the correlation between the monetary and non-monetary dimensions of poverty within and across countries was far from perfect. Finally, multidimensional indicators such as the Alkire-Foster (A-F) measure respond to an effective demand for scalar estimates of poverty that could be used by policymakers in the allocation of funds to reduce poverty in an efficient and equitable way. Hence, notwithstanding their shortcomings, each of these indicators fulfills somewhat different yet important functions. A strong feature of the A-F methodology is that it is anchored on the joint distribution of the various dimensions of well-being and the resulting deprivations that poor people experience. It is therefore essential that all data come from the same household survey. It should be noted that this means that any given household information is available not only on possible deprivations in some dimensions but also on possible surpluses over and above the deprivation thresholds in other dimensions. This immediately raises the issue of possible trade-offs among dimensions.

Overlay measurements by Mueller polarimetry in back focal plane

Angle resolved Mueller polarimetry implemented as polarimetric imaging of a back focal plane of a high NA microscope objective has already demonstrated a good potential for CD metrology. Here we present the experimental and numerical results indicating that this technique may also be competitive for the measurements of overlay error δ. A series of samples of superimposed gratings with well controlled overlay errors have been manufactured and measured with the angle resolved Mueller polarimeter. The overlay targets were 20-μm wide. When the overlay error is δ is equal to 0, absolute values of elements of real 4×4 Mueller matrix M are invariant by matrix transposition. Otherwise this symmetry breaks down. Consequently, we define the following overlay estimator matrix as E = |M| − |M|t. The simulations show that matrix element E14 is the most sensitive to the overlay error. The scalar estimator of E14 was calculated by averaging the pixel values over a specifically chosen mask. This estimator is found to vary linearly with δ for overlay values up to 50 nm. Our technique allows entering small overlay marks (down to 5-μm wide). Only one target measurement is needed for each overlay direction. The actual overlay value can be determined without detailed simulation of the structure provided two calibrated overlay structures are available for each direction.

Particle Filter with Hybrid Proposal Distribution for Nonlinear State Estimation

Particle filters have been widely used in solving nonlinear filtering problems. Proposal Distribution design is a key issue for these methods and has vital effect on simulation results. Various proposal distributions have been proposed to improve the performance of particle filters, but practical situations have promoted the researchers to design better candidate for proposal distributions in order to gain better performance. This paper proposes a hybrid proposal distribution designed for particle filtering framework. The algorithm uses hybrid Kalman filter to generate the proposal distribution, which make efficient use of the latest observations and generate more closed approximation of the posterior probability density. The yielded algorithm is named as hybrid Kalman particle filter. In the experiments, we use a scalar estimation model and a real world application problem to evaluate the new algorithm. The experimental results show that the new algorithm outperforms other algorithms with different proposal distributions. In order to reduce the time consumption of the new algorithm, we propose an improvement strategy, namely partition-conquer strategy, in which the particles are partitioned into two parts, with one part drawn from the hybrid Kalman filter, another part from the transition prior. The validity of the strategy is verified through an experiment.