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Author: Grafiati

Published: 11 September 2023

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1

Utsugi, Akio, and Toru Kumagai. "Bayesian Analysis of Mixtures of Factor Analyzers." Neural Computation 13, no. 5 (May 1, 2001): 993–1002. http://dx.doi.org/10.1162/08997660151134299.

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For Bayesian inference on the mixture of factor analyzers, natural conjugate priors on the parameters are introduced, and then a Gibbs sampler that generates parameter samples following the posterior is constructed. In addition, a deterministic estimation algorithm is derived by taking modes instead of samples from the conditional posteriors used in the Gibbs sampler. This is regarded as a maximum a posteriori estimation algorithm with hyperparameter search. The behaviors of the Gibbs sampler and the deterministic algorithm are compared on a simulation experiment.

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2

Lee, Jun, and Jaejin Lee. "Modified maximum a posteriori decoding algorithm." Electronics Letters 37, no. 11 (2001): 698. http://dx.doi.org/10.1049/el:20010486.

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3

Xia, Meidong, Chengyou Wang, and Wenhan Ge. "Weights-Based Image Demosaicking Using Posteriori Gradients and the Correlation of R–B Channels in High Frequency." Symmetry 11, no. 5 (April 26, 2019): 600. http://dx.doi.org/10.3390/sym11050600.

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In this paper, we propose a weights-based image demosaicking algorithm which is based on the Bayer pattern color filter array (CFA). When reconstructing the missing G components, the proposed algorithm uses weights based on posteriori gradients to mitigate color artifacts and distortions. Furthermore, the proposed algorithm makes full use of the correlation of R–B channels in high frequency when interpolating R/B values at B/R positions. Experimental results show that the proposed algorithm is superior to previous similar algorithms in composite peak signal-to-noise ratio (CPSNR) and subjective visual effect. The biggest advantage of the proposed algorithm is the use of posteriori gradients and the correlation of R–B channels in high frequency.

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Tolpin, David, and Frank Wood. "Maximum a Posteriori Estimation by Search in Probabilistic Programs." Proceedings of the International Symposium on Combinatorial Search 6, no. 1 (September 1, 2021): 201–5. http://dx.doi.org/10.1609/socs.v6i1.18369.

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We introduce an approximate search algorithm for fast maximum a posteriori probability estimation in probabilistic programs, which we call Bayesian ascent Monte Carlo (BaMC). Probabilistic programs represent probabilistic models with varying number of mutually dependent finite, countable, and continuous random variables. BaMC is an anytime MAP search algorithm applicable to any combination of random variables and dependencies. We compare BaMC to other MAP estimation algorithms and show that BaMC is faster and more robust on a range of probabilistic models.

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Arar, Maher, Claude D'Amours, and Abbas Yongacoglu. "Simplified LLRs for the Decoding of Single Parity Check Turbo Product Codes Transmitted Using 16QAM." Research Letters in Communications 2007 (2007): 1–4. http://dx.doi.org/10.1155/2007/53517.

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Iterative soft-decision decoding algorithms require channel log-likelihood ratios (LLRs) which, when using 16QAM modulation, require intensive computations to be obtained. Therefore, we derive four simple approximate LLR expressions. When using the maximum a posteriori probability algorithm for decoding single parity check turbo product codes (SPC/TPCs), these LLRs can be simplified even further. We show through computer simulations that the bit-error-rate performance of(8,7)2and(8,7)3SPC/TPCs, transmitted using 16QAM and decoded using the maximum a posteriori algorithm with our simplified LLRs, is nearly identical to the one achieved by using the exact LLRs.

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Pan, Lu, Xiaoming He, and Tao Lü. "High Accuracy Combination Method for Solving the Systems of Nonlinear Volterra Integral and Integro-Differential Equations with Weakly Singular Kernels of the Second Kind." Mathematical Problems in Engineering 2010 (2010): 1–21. http://dx.doi.org/10.1155/2010/901587.

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This paper presents a high accuracy combination algorithm for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind. Two quadrature algorithms for solving the systems are discussed, which possess high accuracy order and the asymptotic expansion of the errors. By means of combination algorithm, we may obtain a numerical solution with higher accuracy order than the original two quadrature algorithms. Moreover an a posteriori error estimation for the algorithm is derived. Both of the theory and the numerical examples show that the algorithm is effective and saves storage capacity and computational cost.

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Karimi, Mohammad, Maryam Miriestahbanati, Hamed Esmaeeli, and Ciprian Alecsandru. "Multi-Objective Stochastic Optimization Algorithms to Calibrate Microsimulation Models." Transportation Research Record: Journal of the Transportation Research Board 2673, no. 4 (March 29, 2019): 743–52. http://dx.doi.org/10.1177/0361198119838260.

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The calibration process for microscopic models can be automatically undertaken using optimization algorithms. Because of the random nature of this problem, the corresponding objectives are not simple concave functions. Accordingly, such problems cannot easily be solved unless a stochastic optimization algorithm is used. In this study, two different objectives are proposed such that the simulation model reproduces real-world traffic more accurately, both in relation to longitudinal and lateral movements. When several objectives are defined for an optimization problem, one solution method may aggregate the objectives into a single-objective function by assigning weighting coefficients to each objective before running the algorithm (also known as an a priori method). However, this method does not capture the information exchange among the solutions during the calibration process, and may fail to minimize all the objectives at the same time. To address this limitation, an a posteriori method (multi-objective particle swarm optimization, MOPSO) is employed to calibrate a microscopic simulation model in one single step while minimizing the objectives functions simultaneously. A set of traffic data collected by video surveillance is used to simulate a real-world highway in VISSIM. The performance of the a posteriori-based MOPSO in the calibration process is compared with a priori-based optimization methods such as particle swarm optimization, genetic algorithm, and whale optimization algorithm. The optimization methodologies are implemented in MATLAB and connected to VISSIM using its COM interface. Based on the validation results, the a posteriori-based MOPSO leads to the most accurate solutions among the tested algorithms with respect to both objectives.

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8

Lee, Dongwook, and Rémi Bourgeois. "GP-MOOD: a positivity-preserving high-order finite volume method for hyperbolic conservation laws." Proceedings of the International Astronomical Union 16, S362 (June 2020): 373–79. http://dx.doi.org/10.1017/s1743921322001363.

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AbstractWe present an a posteriori shock-capturing finite volume method algorithm called GP-MOOD. The method solves a compressible hyperbolic conservative system at high-order solution accuracy in multiple spatial dimensions. The core design principle in GP-MOOD is to combine two recent numerical methods, the polynomial-free spatial reconstruction methods of GP (Gaussian Process) and the a posteriori detection algorithms of MOOD (Multidimensional Optimal Order Detection). We focus on extending GP’s flexible variability of spatial accuracy to an a posteriori detection formalism based on the MOOD approach. The resulting GP-MOOD method is a positivity-preserving method that delivers its solutions at high-order accuracy, selectable among three accuracy choices, including third-order, fifth-order, and seventh-order.

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9

Nguyen, Hoang Nguyen. "SYNTHESIS OF A RADAR RECOGNITION ALGORITHM WITH ABILITY TO MEET RELIABILITY OF DECISIONS." Journal of Science and Technique 14, no. 5 (April 26, 2021): 87–95. http://dx.doi.org/10.56651/lqdtu.jst.v14.n05.257.

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This paper is devoted to the variant of synthesis of a radar recognition algorithm with the ability to meet reliability of decisions. The algorithm is based on the theory of sequential analysis in combination with flexible change in the level of the classification detail when the observation time cannot be increased. Compared with one-step algorithms, the proposed algorithm allows guaranteeing “the posteriori probability of decisions is not smaller than the set value”. The proposed algorithm can be used in radar target recognition systems.

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10

Kang, Jiayi, Andrew Salmon, and Stephen S. T. Yau. "Log-Concave Posterior Densities Arising in Continuous Filtering and a Maximum A Posteriori Algorithm." SIAM Journal on Control and Optimization 61, no. 4 (August 4, 2023): 2407–24. http://dx.doi.org/10.1137/22m1508352.

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11

Ruszczak, Bogdan, and Dominika Boguszewska-Mańkowska. "Soil Moisture a Posteriori Measurements Enhancement Using Ensemble Learning." Sensors 22, no. 12 (June 17, 2022): 4591. http://dx.doi.org/10.3390/s22124591.

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This work aimed to assess the recalibration and accurate characterization of commonly used smart soil-moisture sensors using computational methods. The paper describes an ensemble learning algorithm that boosts the performance of potato root moisture estimation and increases the simple moisture sensors’ performance. It was prepared using several month-long everyday actual outdoor data and validated on the separated part of that dataset. To obtain conclusive results, two different potato varieties were grown on 24 separate plots on two distinct soil profiles and, besides natural precipitation, several different watering strategies were applied, and the experiment was monitored during the whole season. The acquisitions on every plot were performed using simple moisture sensors and were supplemented with reference manual gravimetric measurements and meteorological data. Next, a group of machine learning algorithms was tested to extract the information from this measurements dataset. The study showed the possibility of decreasing the median moisture estimation error from 2.035% for the baseline model to 0.808%, which was achieved using the Extra Trees algorithm.

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12

Bunch, J. R., R. C. Le Borne, and I. K. Proudler. "Analysis of the direct and indirecta posteriori RLSL algorithm." Numerical Linear Algebra with Applications 8, no. 6-7 (2001): 453–66. http://dx.doi.org/10.1002/nla.249.

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13

Jacobs, F. J., and P. A. G. van der Geest. "Spiking band‐limited traces with a relative‐entropy algorithm." GEOPHYSICS 56, no. 7 (July 1991): 1003–14. http://dx.doi.org/10.1190/1.1443109.

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A novel method for the inversion of band‐limited seismic traces to full bandwidth reflectivity traces, is based on a probabilistic spiky model of the reflectivity trace, in which position indicators and amplitudes of the spikes occur as random variables, and relies on relative entropy inference from information theory. First, an a priori model for general reflectivity traces in the prospect is derived from nearby wells. Second, the a priori distribution is updated into an a posteriori distribution for the specific trace being studied by the addition of the Fourier data of the seismic trace within a passband. Uncertainty about the Fourier coefficients can be accounted for by specification of a noise variance, which implicitly is infinite outside the passband. The update with relative entropy inference is justified because of its relationship with Bayesian inference. Application of maximum a posteriori (MAP) estimation to the a posteriori distribution results in the most likely spiky reflectivity trace of full bandwidth. A numerical algorithm for obtaining the MAP estimates of spike positions and spike amplitudes is derived from the concept of continuation and is described in detail. The algorithm avoids searching among all possible patterns of spike positions.

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Cordua, Knud Skou, Thomas Mejer Hansen, and Klaus Mosegaard. "Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information." GEOPHYSICS 77, no. 2 (March 2012): H19—H31. http://dx.doi.org/10.1190/geo2011-0170.1.

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We present a general Monte Carlo full-waveform inversion strategy that integrates a priori information described by geostatistical algorithms with Bayesian inverse problem theory. The extended Metropolis algorithm can be used to sample the a posteriori probability density of highly nonlinear inverse problems, such as full-waveform inversion. Sequential Gibbs sampling is a method that allows efficient sampling of a priori probability densities described by geostatistical algorithms based on either two-point (e.g., Gaussian) or multiple-point statistics. We outline the theoretical framework for a full-waveform inversion strategy that integrates the extended Metropolis algorithm with sequential Gibbs sampling such that arbitrary complex geostatistically defined a priori information can be included. At the same time we show how temporally and/or spatiallycorrelated data uncertainties can be taken into account during the inversion. The suggested inversion strategy is tested on synthetic tomographic crosshole ground-penetrating radar full-waveform data using multiple-point-based a priori information. This is, to our knowledge, the first example of obtaining a posteriori realizations of a full-waveform inverse problem. Benefits of the proposed methodology compared with deterministic inversion approaches include: (1) The a posteriori model variability reflects the states of information provided by the data uncertainties and a priori information, which provides a means of obtaining resolution analysis. (2) Based on a posteriori realizations, complicated statistical questions can be answered, such as the probability of connectivity across a layer. (3) Complex a priori information can be included through geostatistical algorithms. These benefits, however, require more computing resources than traditional methods do. Moreover, an adequate knowledge of data uncertainties and a priori information is required to obtain meaningful uncertainty estimates. The latter may be a key challenge when considering field experiments, which will not be addressed here.

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Pogorelov, V., and E. Chub. "Markov model of data measurement complex for track geometry car." E3S Web of Conferences 224 (2020): 02029. http://dx.doi.org/10.1051/e3sconf/202022402029.

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A stochastic model of a nonadjustable data measurement complex platform for track geometry cars is introduced. A state vector evaluation algorithm based on the approximation of a posteriori probability density by the system of a posteriori moments is also offered.

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16

Miazio, Łukasz, and Grzegorz Zboiński. "A Posteriori Detection of Numerical Locking in hpq-Adaptive Finite Element Analysis." Applied Sciences 10, no. 22 (November 20, 2020): 8247. http://dx.doi.org/10.3390/app10228247.

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The proposed detection algorithms are assigned for the hpq-adaptive finite element analysis of the solid mechanics problems affected by the locking phenomena. The algorithms are combined with the M- and hpq-adaptive finite element method, where M is the element model, h denotes the element size parameter, and p and q stand for the longitudinal and transverse approximation orders within an element. The applied adaptive scheme is extended with the additional step where the locking phenomena are a posteriori detected, assessed and resolved. The detection can be applied to shear, membrane, or shear–membrane locking phenomena. The removal of the undesired influence of the numerical locking on the problem solution is based on p-enrichment of the mesh. The detection algorithm is also enriched with the locking assessment algorithm which is capable of determination of the optimized value of p which is sufficient for the phenomena removal. The detection and assessment algorithms are based on a simple sensitivity analysis performed locally for the finite elements of the thin-walled domain. The sensitivity analysis lies in comparison of the element solutions corresponding to two values of the order p, namely current and potentially eliminating the locking. The local solutions are obtained from the element residual method. The elaborated algorithms are original, relatively simple, extremely reliable, and highly effective.

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17

Wan, Yang, Shouyong Wang, and Xing Qin. "IMM Iterated Extended Particle Filter Algorithm." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/970158.

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In order to solve the tracking problem of radar maneuvering target in nonlinear system model and non-Gaussian noise background, this paper puts forward one interacting multiple model (IMM) iterated extended particle filter algorithm (IMM-IEHPF). The algorithm makes use of multiple modes to model the target motion form to track any maneuvering target and each mode uses iterated extended particle filter (IEHPF) to deal with the state estimation problem of nonlinear non-Gaussian system. IEHPF is an improved particle filter algorithm, which utilizes iterated extended filter (IEHF) to obtain the mean value and covariance of each particle and describes importance density function as a combination of Gaussian distribution. Then according to the function, draw particles to approximate the state posteriori density of each mode. Due to the high filter accuracy of IEHF and the adaptation of system noise with arbitrary distribution as well as strong robustness, the importance density function generated by this method is more approximate to the true sate posteriori density. Finally, a numerical example is included to illustrate the effectiveness of the proposed methods.

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18

Yang, Lei, Xiaohui Yang, Yue Wu, and Xiaoping Liu. "Applied Research on Distributed Generation Optimal Allocation Based on Improved Estimation of Distribution Algorithm." Energies 11, no. 9 (September 7, 2018): 2363. http://dx.doi.org/10.3390/en11092363.

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Most of the current algorithms used to solve the optimal configuration problem in the distributed generation (DG) of electricity depend heavily on control parameters, which may lead to local optimal solutions. To achieve a rapid and effective algorithm of optimized configuration for distributed generation, a hybrid approach combined with Bayesian statistical-inference and distribution estimation is proposed. Specifically, a probability distribution estimation model based on the theory of Bayesian inference is established, then a posteriori probability model with the prior distribution and the conditional distribution is generated, and new individual generators are formed into a dominant group. The information of each individual of this dominant group is used to update the probability model and the updated posteriori probability is used for sampling until the optimal solution is obtained. Finally, the 12 bus, 34 bus and 69 bus radial distribution system is used as an example and comparison is performed to show the effectiveness of the proposed algorithm.

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19

Botti, Michele, and Rita Riedlbeck. "Equilibrated Stress Tensor Reconstruction and A Posteriori Error Estimation for Nonlinear Elasticity." Computational Methods in Applied Mathematics 20, no. 1 (January 1, 2020): 39–59. http://dx.doi.org/10.1515/cmam-2018-0012.

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AbstractWe consider hyperelastic problems and their numerical solution using a conforming finite element discretization and iterative linearization algorithms. For these problems, we present equilibrated, weakly symmetric, {H(\mathrm{div)}}-conforming stress tensor reconstructions, obtained from local problems on patches around vertices using the Arnold–Falk–Winther finite element spaces. We distinguish two stress reconstructions: one for the discrete stress and one representing the linearization error. The reconstructions are independent of the mechanical behavior law. Based on these stress tensor reconstructions, we derive an a posteriori error estimate distinguishing the discretization, linearization, and quadrature error estimates, and propose an adaptive algorithm balancing these different error sources. We prove the efficiency of the estimate, and confirm it on a numerical test with an analytical solution. We then apply the adaptive algorithm to a more application-oriented test, considering the Hencky–Mises and an isotropic damage model.

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Liu, Gang, Wensen Feng, Runpu Chen, and Yunfeng Shao. "Interferogram noise reduction algorithm base on maximum A Posteriori estimate." Journal of Electronics (China) 31, no. 3 (June 2014): 200–207. http://dx.doi.org/10.1007/s11767-014-4076-8.

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Yu, Yuanyuan, Yidu Yang, and Jiayu Han. "An Adaptive Nonconforming Finite Element Algorithm for Laplace Eigenvalue Problem." Abstract and Applied Analysis 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/189490.

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We establish Crouzeix-Raviart element adaptive algorithm based on Rayleigh quotient iteration and give its a priori/a posteriori error estimates. Our algorithm is performed under the package of Chen, and satisfactory numerical results are obtained.

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Chen, Yu, and Zhe-min Duan. "Congested Link Inference Algorithms in Dynamic Routing IP Network." Mathematical Problems in Engineering 2017 (2017): 1–17. http://dx.doi.org/10.1155/2017/6342421.

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The performance descending of current congested link inference algorithms is obviously in dynamic routing IP network, such as the most classical algorithm CLINK. To overcome this problem, based on the assumptions of Markov property and time homogeneity, we build a kind of Variable Structure Discrete Dynamic Bayesian (VSDDB) network simplified model of dynamic routing IP network. Under the simplified VSDDB model, based on the Bayesian Maximum A Posteriori (BMAP) and Rest Bayesian Network Model (RBNM), we proposed an Improved CLINK (ICLINK) algorithm. Considering the concurrent phenomenon of multiple link congestion usually happens, we also proposed algorithm CLILRS (Congested Link Inference algorithm based on Lagrangian Relaxation Subgradient) to infer the set of congested links. We validated our results by the experiments of analogy, simulation, and actual Internet.

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23

Li, Feiyan, and Hai Bi. "A Type of Multigrid Method Based on the Fixed-Shift Inverse Iteration for the Steklov Eigenvalue Problem." Advances in Mathematical Physics 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/4691759.

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For the Steklov eigenvalue problem, we establish a type of multigrid discretizations based on the fixed-shift inverse iteration and study in depth its a priori/a posteriori error estimates. In addition, we also propose an adaptive algorithm on the basis of the a posteriori error estimates. Finally, we present some numerical examples to validate the efficiency of our method.

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Cen, Zhongdi, Jian Huang, and Aimin Xu. "A posteriori grid method for a time-fractional Black-Scholes equation." AIMS Mathematics 7, no. 12 (2022): 20962–78. http://dx.doi.org/10.3934/math.20221148.

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<abstract><p>In this paper, a posteriori grid method for solving a time-fractional Black-Scholes equation governing European options is studied. The possible singularity of the exact solution complicates the construction of the discretization scheme for the time-fractional Black-Scholes equation. The $ L1 $ method on an arbitrary grid is used to discretize the time-fractional derivative and the central difference method on a piecewise uniform grid is used to discretize the spatial derivatives. Stability properties and a posteriori error analysis for the discrete scheme are studied. Then, an adapted a posteriori grid is constructed by using a grid generation algorithm based on a posteriori error analysis. Numerical experiments show that the $ L1 $ method on an adapted a posteriori grid is more accurate than the method on the uniform grid.</p></abstract>

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Merle, Fabian, and Andreas Prohl. "An adaptive time-stepping method based on a posteriori weak error analysis for large SDE systems." Numerische Mathematik 149, no. 2 (October 2021): 417–62. http://dx.doi.org/10.1007/s00211-021-01233-4.

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AbstractWe develop an adaptive algorithm for large SDE systems, which automatically selects (quasi-)deterministic time steps for the semi-implicit Euler method, based on an a posteriori weak error estimate. Main tools to construct the a posteriori estimator are the representation of the weak approximation error via Kolmogorov’s backward equation, a priori bounds for its solution and the Clark–Ocone formula. For a certain class of SDE systems, we validate optimal weak convergence order 1 of the a posteriori estimator, and termination of the adaptive method based on it within $${{\mathcal {O}}}(\mathtt{Tol}^{-1})$$ O ( Tol - 1 ) steps.

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Ghesmati, Arezou, Wolfgang Bangerth, and Bruno Turcksin. "Residual-based a posteriori error estimation for hp-adaptive finite element methods for the Stokes equations." Journal of Numerical Mathematics 27, no. 4 (December 18, 2019): 237–52. http://dx.doi.org/10.1515/jnma-2018-0047.

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AbstractWe derive a residual-based a posteriori error estimator for the conforminghp-Adaptive Finite Element Method (hp-AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is obtained by extending the idea of a posteriori error estimation for the classicalh-version of AFEM. We also establish the reliability and efficiency of the error estimator. The proofs are based on the well-known Clément-type interpolation operator introduced in [27] in the context of thehp-AFEM. Numerical experiments show the performance of an adaptivehp-FEM algorithm using the proposed a posteriori error estimator.

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Kikin, I. S. "ALGORITHMIC METHOD OF AUTONOMOUS CORRECTION MEASUREMENT ERRORS IN SYSTEMS AUTOMATIC CONTROL AND REGULATION." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 207 (September 2021): 3–10. http://dx.doi.org/10.14489/vkit.2021.09.pp.003-010.

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A method of autonomous a posteriori estimation of control target’s state coordinates is demonstrated. The method’s accuracy does not depend on automatic control system sensors errors. An algorithmic implementation of the method is proposed – an algorithm for processing the array of data on the control target observed inputs and outputs, obtained by passive information accumulation during the observation interval of the control target normal functioning. At the final stage of the estimation algorithm, the implemented control process is simulated with complete a priori information about the conditions for its implementation (simulation estimation method). The algorithm execution time should be negligible in relation to the duration of the observation interval (instantaneous a posteriori estimation of the control target’s state). The proposed method allows to cyclically correct instrumental errors of automatic control and regulation systems without using external sources of information.

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Chub, E. G., and V. A. Pogorelov. "Identification algorithm for telecommunication systems with uncertain parameters of their vector of state stochastic model." Journal of Physics: Conference Series 2131, no. 2 (December 1, 2021): 022090. http://dx.doi.org/10.1088/1742-6596/2131/2/022090.

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Abstract The described method of structure identification of the state vector of a telecommunication system stochastic model is based on a posteriori probability density approximation (APDA) by a system of a posteriori moments. An assumption of possible APDA approximation by a class of Pearson distributions resulted in a closed system of moment equations. Implementation of optimal non-linear stochastic object control techniques helped to solve the problem of structural identification. Introduction of the proposed approach into contemporary telecommunication systems will not impose additional requirements on the calculating equipment, thus making this method well-suited for a wide range of applications.

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29

Lu, Kezhong, Xiaohua Xiang, Dian Zhang, Rui Mao, and Yuhong Feng. "Localization Algorithm Based on Maximum a Posteriori in Wireless Sensor Networks." International Journal of Distributed Sensor Networks 8, no. 1 (December 15, 2011): 260302. http://dx.doi.org/10.1155/2012/260302.

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Many applications and protocols in wireless sensor networks need to know the locations of sensor nodes. A low-cost method to localize sensor nodes is to use received signal strength indication (RSSI) ranging technique together with the least-squares trilateration. However, the average localization error of this method is large due to the large ranging error of RSSI ranging technique. To reduce the average localization error, we propose a localization algorithm based on maximum a posteriori. This algorithm uses the Baye's formula to deduce the probability density of each sensor node's distribution in the target region from RSSI values. Then, each sensor node takes the point with the maximum probability density as its estimated location. Through simulation studies, we show that this algorithm outperforms the least-squares trilateration with respect to the average localization error.

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30

Binding, Jonas, Shawn Mikula, and Winfried Denk. "Low-Dosage Maximum-A-Posteriori Focusing and Stigmation." Microscopy and Microanalysis 19, no. 1 (February 2013): 38–55. http://dx.doi.org/10.1017/s1431927612013852.

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AbstractRadiation damage is often an issue during high-resolution imaging, making low-dose focusing and stigmation essential, in particular when no part of the sample can be “sacrificed” for this. An example is serial block-face electron microscopy, where the imaging resolution must be kept optimal during automated acquisition that can last months. Here, we present an algorithm, which we call “Maximum-A-Posteriori Focusing and Stigmation (MAPFoSt),” that was designed to make optimal use of the available signal. We show that MAPFoSt outperforms the built-in focusing algorithm of a commercial scanning electron microscope even at a tenfold reduced total dose. MAPFoSt estimates multiple aberration modes (focus and the two astigmatism coefficients) using just two test images taken at different focus settings. Using an incident electron dose density of 2,500 electrons/pixel and a signal-to-noise ratio of about one, all three coefficients could be estimated to within <7% of the depth of focus, using 19 detected secondary electrons per pixel. A generalization to higher-order aberrations and to other forms of imaging in both two and three dimensions appears possible.

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31

Huang, Yung‐Dar. "Maximum a posteriori probability direction finding and the dynamic programming algorithm." Journal of the Chinese Institute of Engineers 18, no. 4 (June 1995): 509–17. http://dx.doi.org/10.1080/02533839.1995.9677715.

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32

Takeda, Koujin, and Yoshiyuki Kabashima. "Reconstruction algorithm in compressed sensing based on maximum a posteriori estimation." Journal of Physics: Conference Series 473 (December 16, 2013): 012003. http://dx.doi.org/10.1088/1742-6596/473/1/012003.

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33

Lalush, David S., and Benjamin M. W. Tsui. "A fast and stable maximum a posteriori conjugate gradient reconstruction algorithm." Medical Physics 22, no. 8 (August 1995): 1273–84. http://dx.doi.org/10.1118/1.597614.

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34

Wang, Zhoufeng, and Lingxue Zhu. "An Adaptive CIP-FEM for the Polygonal-Line Grating Problem." International Journal of Computational Methods 16, no. 04 (May 13, 2019): 1850096. http://dx.doi.org/10.1142/s0219876218500962.

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This paper is concerned with the diffraction by a polygonal-line grating. We develop a continuous interior penalty finite element method based on the truncation of the nonlocal boundary operators for solving the problem. An a posteriori error estimate is derived for the method. The truncation parameter is determined through the truncation error of the a posteriori error estimate. Numerical experiments are also presented to show the efficiency and robustness of the proposed adaptive algorithm.

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Kienle, F., H. Michel, F. Gilbert, and N. Wehn. "Efficient MAP-algorithm implementation on programmable architectures." Advances in Radio Science 1 (May 5, 2003): 259–63. http://dx.doi.org/10.5194/ars-1-259-2003.

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Abstract. Maximum-A-Posteriori (MAP) decoding algorithms are important HW/SW building blocks in advanced communication systems due to their ability to provide soft-output informations which can be efficiently exploited in iterative channel decoding schemes like Turbo-Codes. Multi-standards demand flexible implementations on programmable platforms. In this paper we analyze a quantized turbo-decoder based on a Max-Log-MAP algorithm with Extrinsic Scaling Factor (ESF). Its communication performance approximate to a Turbo-Decoder with a Log-MAP algorithm and is less sensitive to quantization effects. We present Turbo-Decoder implementations on state-of-the-art DSPs and show that only a Max-Log-MAP implementation fulfills a throughput requirement of ~2 Mbit/s. The negligible overhead for the ESF implementation strengthen the use of Max-Log-MAP with ESF implementation on programmable platforms.

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Fan, Xue Ping, Sen Wang, and Yue Fei Liu. "Bridge Resistance Updating Based on the General Particle Simulation Algorithms of Complex Bayesian Formulas." Advanced Engineering Forum 43 (November 16, 2021): 111–22. http://dx.doi.org/10.4028/www.scientific.net/aef.43.111.

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The existing bridges are subjected to time-variant loading and resistance degradation processes. How to update resistance probability distribution functions with resistance degradation model and proof load effects has become one of the research hotspots in bridge engineering field. To solve with the above issue, this paper proposed the general particle simulation algorithms of complex Bayesian formulas for bridge resistance updating. Firstly, the complex Bayesian formulas for updating resistance probability model are built. For overcoming the difficulty for the analytic calculation of complex Bayesian formulas, the general particle simulation methods are provided to obtain the particles of complex Bayesian formulas; then, with the improved expectation maximization optimization algorithm obtained with the combination of K-MEANS algorithm and Expectation Maximization (EM) algorithm, the above simulated particles can be used to estimate the posteriori probability density functions of resistance probability model; finally, a numerical example is provided to illustrate the feasibility and application of the proposed algorithms.

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Cen, Zhongdi, Jian Huang, and Aimin Xu. "A posteriori mesh method for a system of singularly perturbed initial value problems." AIMS Mathematics 7, no. 9 (2022): 16719–32. http://dx.doi.org/10.3934/math.2022917.

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<abstract><p>A system of singularly perturbed initial value problems with weak constrained conditions on the coefficients is considered. First the system of second-order singularly perturbed problems is transformed into a system of first-order singularly perturbed problems with integral terms, which facilitates the subsequent stability and a posteriori error analyses. Then a hybrid difference method with the use of interpolating quadrature rules is utilized to approximate the transformed system. Next a posteriori error analysis for the discretization scheme on an arbitrary mesh is presented. A solution-adaptive algorithm based on a posteriori error estimation is devised to generate a posteriori mesh and obtain approximation solution. Finally numerical experiments show a uniform convergence behavior of second-order for the scheme, which improves the previous results and achieves the optimal convergence order under the given discrete scheme.</p></abstract>

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Mai, Xiongfa, Ciwen Zhu, and Libin Liu. "An adaptive grid method for a singularly perturbed convection-diffusion equation with a discontinuous convection coefficient." Networks and Heterogeneous Media 18, no. 4 (2023): 1528–38. http://dx.doi.org/10.3934/nhm.2023067.

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<abstract><p>In this paper, an adaptive grid method is put forward to solve a singularly perturbed convection-diffusion problem with a discontinuous convection coefficient. First, this problem is discretized by using an upwind finite difference scheme on an arbitrary nonuniform grid except the fixed jump point. Then, a first-order maximum norm a posterior error estimate is derived. Further, based on this a posteriori error estimation and the mesh equidistribution principle, an adaptive grid generation algorithm is constructed. Finally, some numerical experiments are presented that support our theoretical estimate.</p></abstract>

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Ahmadian, Yashar, Jonathan W. Pillow, and Liam Paninski. "Efficient Markov Chain Monte Carlo Methods for Decoding Neural Spike Trains." Neural Computation 23, no. 1 (January 2011): 46–96. http://dx.doi.org/10.1162/neco_a_00059.

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Stimulus reconstruction or decoding methods provide an important tool for understanding how sensory and motor information is represented in neural activity. We discuss Bayesian decoding methods based on an encoding generalized linear model (GLM) that accurately describes how stimuli are transformed into the spike trains of a group of neurons. The form of the GLM likelihood ensures that the posterior distribution over the stimuli that caused an observed set of spike trains is log concave so long as the prior is. This allows the maximum a posteriori (MAP) stimulus estimate to be obtained using efficient optimization algorithms. Unfortunately, the MAP estimate can have a relatively large average error when the posterior is highly nongaussian. Here we compare several Markov chain Monte Carlo (MCMC) algorithms that allow for the calculation of general Bayesian estimators involving posterior expectations (conditional on model parameters). An efficient version of the hybrid Monte Carlo (HMC) algorithm was significantly superior to other MCMC methods for gaussian priors. When the prior distribution has sharp edges and corners, on the other hand, the “hit-and-run” algorithm performed better than other MCMC methods. Using these algorithms, we show that for this latter class of priors, the posterior mean estimate can have a considerably lower average error than MAP, whereas for gaussian priors, the two estimators have roughly equal efficiency. We also address the application of MCMC methods for extracting nonmarginal properties of the posterior distribution. For example, by using MCMC to calculate the mutual information between the stimulus and response, we verify the validity of a computationally efficient Laplace approximation to this quantity for gaussian priors in a wide range of model parameters; this makes direct model-based computation of the mutual information tractable even in the case of large observed neural populations, where methods based on binning the spike train fail. Finally, we consider the effect of uncertainty in the GLM parameters on the posterior estimators.

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Míchal, Jan, and Josef Dobeš. "Parallelized A Posteriori Multiobjective Optimization in RF Design." Electronics 12, no. 10 (May 22, 2023): 2343. http://dx.doi.org/10.3390/electronics12102343.

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A posteriori multiobjective optimization relies on a series of mutually independent single-objective optimization subproblems, which can be run in parallel, thus making full use of a multiprocessor (or multicore) computer. This paper presents a parallel process launching scheme, such that practically no computing capacity gets wasted. This is achieved using standard Windows API kernel objects for process synchronization of the semaphore and mutex types. The algorithm used was further modified to inherently generate the desired Pareto front in the convenient form of a contour plot.

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Coene, W. "A practical algorithm for maximum-likelihood HREM image reconstruction." Proceedings, annual meeting, Electron Microscopy Society of America 50, no. 2 (August 1992): 986–87. http://dx.doi.org/10.1017/s0424820100129565.

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Reconstruction in HREM of the complex wave function at the exit face of a crystal foil out of a focal series of HREM images, and with correction for the microscope's aberrations, can be performed with a variety of algorithms depending on the approximations involved for the HREM image formation. The maximum-a-posteriori (MAP) recursive reconstruction algorithm of Kirkland is the most general one with the full benefit of the effects of non-linear imaging and partial coherence, which are correctly treated in terms of a transmission-cross-coefficient (TCC). However, the routine application of the Kirkland algorithm has thusfar been hampered by its enormous computational demands, especially when large image frame sizes (5122) and a large number of HREM images (≥20) are aimed at. In this paper, we present a modified version of the Kirkland method within a maximum-likelihood (MAL) framework, and with a new numerical implementation yielding a workable algorithm with a much higher computational efficiency.

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Cochez-Dhondt, Sarah, and Serge Nicaise. "A Posteriori Error Estimators Based on Equilibrated Fluxes." Computational Methods in Applied Mathematics 10, no. 1 (2010): 49–68. http://dx.doi.org/10.2478/cmam-2010-0002.

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Abstract We consider the conforming of finite element approximations of reactiondiffusion problems. We propose new a posteriori error estimators based on H(div)- conforming finite elements and equilibrated fluxes. It is shown that these estimators give rise to an upper bound where the constant is one in front of the indicator, up to higher order terms. Lower bounds can also be established with constants depending on the shape regularity of the mesh and the local variation of the coefficients. We further analyze the convergence of an adaptive algorithm. The reliability and efficiency of the proposed estimators are confirmed by various numerical tests.

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Endtmayer, Bernhard, Ulrich Langer, and Thomas Wick. "Reliability and Efficiency of DWR-Type A Posteriori Error Estimates with Smart Sensitivity Weight Recovering." Computational Methods in Applied Mathematics 21, no. 2 (January 9, 2021): 351–71. http://dx.doi.org/10.1515/cmam-2020-0036.

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Abstract We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [B. Endtmayer, U. Langer and T. Wick, Two-side a posteriori error estimates for the dual-weighted residual method, SIAM J. Sci. Comput. 42 2020, 1, A371–A394], we showed efficiency and reliability for error estimators based on enriched finite element spaces. However, the solution of problems on an enriched finite element space is expensive. In the literature, it is well known that one can use some higher-order interpolation to overcome this bottleneck. Using a saturation assumption, we extend the proofs of efficiency and reliability to such higher-order interpolations. The results can be used to create a new family of algorithms, where one of them is tested on three numerical examples (Poisson problem, p-Laplace equation, Navier–Stokes benchmark), and is compared to our previous algorithm.

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Chen, Wen, Xiang-zhong Fang, and Yan Cheng. "A maximum a posteriori super resolution algorithm based on multidimensional Lorentzian distribution." Journal of Zhejiang University-SCIENCE A 10, no. 12 (December 2009): 1705–13. http://dx.doi.org/10.1631/jzus.a0920013.

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Escribano, F. J., L. López, and M. A. F. Sanjuán. "Exploiting symbolic dynamics in chaos coded communications with maximum a posteriori algorithm." Electronics Letters 42, no. 17 (2006): 984. http://dx.doi.org/10.1049/el:20060649.

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Kim, J., J. Kim, H. Park, B. Kim, and S. Park. "Modified enhanced max-log-maximum a posteriori algorithm using variable scaling factor." IET Communications 1, no. 5 (2007): 1061. http://dx.doi.org/10.1049/iet-com:20060632.

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Arribas, J. I., and J. Cid-Sueiro. "A Model Selection Algorithm for a Posteriori Probability Estimation With Neural Networks." IEEE Transactions on Neural Networks 16, no. 4 (July 2005): 799–809. http://dx.doi.org/10.1109/tnn.2005.849826.

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Chen, Guangzhou, Lifeng Jiao, and Xinhai Li. "Sensitivity Analysis and Identification of Parameters to the Van Genuchten Equation." Journal of Chemistry 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/9879537.

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Van Genuchten equation is the soil water characteristic curve equation used commonly, and identifying (estimating) accurately its parameters plays an important role in the study on the movement of soil water. Selecting the desorption and absorption experimental data of silt loam from a northwest region in China as an instance, Monte-Carlo method was firstly applied to analyze sensitivity of the parameters and uncertainty of model so as to get the key parameters and posteriori parameter distribution to guide subsequent parameter identification. Then, the optimization model of the parameters was set up, and a new type of intelligent algorithm-difference search algorithm was employed to identify them. In order to overcome the fault that the base difference search algorithm needed more iterations and to further enhance the optimization performance, a hybrid algorithm, which coupled the difference search algorithm with simplex method, was employed to identification of the parameters. By comparison with other optimization algorithms, the results show that the difference search algorithm has the following characteristics: good optimization performance, the simple principle, easy implement, short program code, and less control parameters required to run the algorithm. In addition, the proposed hybrid algorithm outperforms the basic difference search algorithm on the comprehensive performance of algorithm.

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Zheng, Na, Yanli Du, and Qinghua Bai. "Robot Navigation Algorithm Based on Sensor Technology and Iterative Maximum a Posteriori Estimation." Journal of Advanced Computational Intelligence and Intelligent Informatics 23, no. 2 (March 20, 2019): 282–86. http://dx.doi.org/10.20965/jaciii.2019.p0282.

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The hybrid sensor network is mainly composed of static and dynamic sensor nodes. The dynamic node is the mobile robot with wireless sensor module installed. This paper proposes a robot navigation algorithm based on sensor technology and iterative maximum a posteriori estimation. It uses Kalman filter and least-squares fitting to improve RSSI measurement accuracy and the mobile robot only needs to use the received signal strength (RSSI) and odometer information to realize autonomous navigation in the sensing area. Moreover, static nodes are randomly deployed in the sensing area without a priori location information. Therefore, this algorithm has the advantages of low cost and ease of deployment. Both simulation and outdoor field experiments show the performance and effectiveness of the algorithm.

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Zhang, Yuan, Shao Chen Kang, Peng Wang, and Shi Wei Yin. "Vision Monitoring Algorithm for Work Condition of NC Processing." Applied Mechanics and Materials 16-19 (October 2009): 920–24. http://dx.doi.org/10.4028/www.scientific.net/amm.16-19.920.

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Aim at the problem of work condition monitoring in high speed NC processing, a new method is proposed based on video analysis technology. It puts forward a segmentation model with maximum a posteriori and Markov random field for NC processing image sequence. Moreover, the best segmentation is obtained by optimization immunity algorithm to monitor tool and work piece effectively. The experiment shows that this method can achieve accurate and real time monitoring and demonstrate the validity and robust of the solution for barrier work piece.

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