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Spatial Bayesian inversion with localized likelihoods: An exact sampling alternative to MCMC

JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH 2014年第7期119卷 5741-5761页

作者： Walker, Matthew Curtis, Andrew Univ Edinburgh Grant Inst Sch GeoSci Edinburgh Midlothian Scotland

Geoscientists often use spatially discretized cellular models of the Earth where data in each grid cell provide independent information about the model parameters of interest at that location. In Bayesian inference this information is given as a set of likelihoods describing the (unnormalized) probability of the parameters, given only the data in each cell. Preexisting information about the model parameters' values and their spatial correlations may be described by a prior probability distribution. The prior, likelihoods, and Bayes' rule together specify a posterior probability distribution that describes the resultant state of information over all model parameters. However, due to the high dimensionality of typical models, the posterior is usually only known up to a multiplicative constant and only at specific, numerically evaluated points in the model space (i.e., it is not known analytically). Markov chain Monte Carlo (MCMC) methods are typically used to produce an ensemble of correlated samples from the posterior. These ensembles are slow to converge in distribution to the posterior;indeed, they may not converge in finite time, and detecting their state of convergence is often impossible in practice. Thus, estimates of the posterior obtained in this way may be biased. We derive a recursive algorithm which samples the posterior exactly, so as to avoid these convergence issues. Its computational cost scales with the size of the parameters' sample space, the prior's spatial range of dependency, and the shortest edge dimension of the grid. We develop an approximation to the algorithm such that it may be used on large 2-D (and potentially 3-D) model grids. We apply it to synthetic seismic attribute data and obtain results which compare favorably to the results of MCMC (Gibbs) sampling-which exhibits convergence problems.

关键词： Bayesian inversion McMC spatial priors recursive algorithm high-dimensional inverse problem gridded data

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Systematic modeling of a chain of N-flexible link manipulators connected by revolute-prismatic joints using recursive Gibbs-Appell formulation

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ARCHIVE OF APPLIED MECHANICS 2014年第2期84卷 187-206页

作者： Korayem, M. H. Shafei, A. M. Dehkordi, S. F. Iran Univ Sci & Technol Sch Mech Engn Dept Mech EngnRobot Res Lab Ctr Excellence Expt Solid Mech & Dynam Tehran 16846 Iran

The main intent of this paper is to represent a systematic algorithm capable of deriving the equations of motion of N-flexible link manipulators with revolute-prismatic joints. The existence of the prismatic joints together with the revolute ones makes the derivation of governing equations difficult. Also, the variations of the flexible parts of the links, with respect to time cause the associated mode shapes of the links to vary instantaneously. So, to derive the kinematic and dynamic equations of motion for such a complex system, the recursive Gibbs-Appell formulation is applied. For a comprehensive and accurate modeling of the system, the coupling effects due to the simultaneous rotating and reciprocating motions of the flexible arms as well as the dynamic interactions between large movements and small deflections are also included. In this study, the links are modeled based on the Euler-Bernoulli beam theory and the assumed mode method. Also, the effects of gravity as well as the longitudinal, transversal and torsional vibrations have been considered in the formulations. Moreover, a recursive algorithm based on 3 x 3 rotational matrices has been applied in order to derive the system's dynamic equations of motion, symbolically and systematically. Finally, a numerical simulation has been performed by means of a developed computer program in order to demonstrate the ability of this algorithm in deriving and solving the equations of motion related to such systems.

关键词： Revolute-prismatic joint Gibbs-Appell recursive algorithm Flexible link

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recursive Estimation of Conditional Spatial Medians and Conditional Quantiles

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SEQUENTIAL ANALYSIS-DESIGN METHODS AND APPLICATIONS 2014年第4期33卷 519-538页

作者： Belitser, Eduard Serra, Paulo Vrije Univ Amsterdam Dept Math Amsterdam Netherlands Univ Gottingen Inst Math Stochast D-37077 Gottingen Germany

We consider the problem of constructing an on-line (recursive) algorithm for tracking a conditional spatial median, a center of a multivariate distribution. In the one-dimensional case we also track conditional quantiles of arbitrary level. We establish a nonasymptotic upper bound for the L-p-risk of the algorithm, which is then minimized under different assumptions on the magnitude of the variation of the spatial median or quantile. We derive convergence rates for the examples we consider.

关键词： Conditional spatial median Convergence rate Half-space symmetric distributions recursive algorithm Sequential estimation 62L12 62G20 62L20

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recursive computational formulas of the least squares criterion functions for scalar system identification

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APPLIED MATHEMATICAL MODELLING 2014年第1期38卷 1-11页

作者： Ma, Junxia Ding, Rui Jiangnan Univ Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Peoples R China Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Peoples R China

The paper discusses recursive computation problems of the criterion functions of several least squares type parameter estimation methods for linear regression models, including the well-known recursive least squares (RLS) algorithm, the weighted RLS algorithm, the forgetting factor RLS algorithm and the finite-data-window RLS algorithm without or with a forgetting factor. The recursive computation formulas of the criterion functions are derived by using the recursive parameter estimation equations. The proposed recursive computation formulas can be extended to the estimation algorithms of the pseudo-linear regression models for equation error systems and output error systems. Finally, the simulation example is provided. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Numerical algorithm Least squares System modeling Criterion function recursive algorithm Parameter estimation

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Reliability evaluation of non-reparable three-state systems using Markov model and its comparison with the UGF and the recursive methods

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2014年第Sep.期129卷 29-35页

作者： Guilani, Pedram Pourkarim Sharifi, Mani Niaki, S. T. A. Zaretalab, Arash Islamic Azad Univ Fac Ind & Mech Engn Qazvin Branch Qazvin Iran Sharif Univ Technol Dept Ind Engn Tehran *** Iran

In multi-state systems (MSS) reliability problems, it is assumed that the components of each subsystem have different performance rates with certain probabilities. This leads into extensive computational efforts involved in using the commonly employed universal generation function (UGF) and the recursive algorithm to obtain reliability of systems consisting of a large number of components. This research deals with evaluating non-repairable three-state systems reliability and proposes a novel method based on a Markov process for which an appropriate state definition is provided. It is shown that solving the derived differential equations significantly reduces the computational time compared to the UGF and the recursive algorithm. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Reliability Multi-state systems Three-state components UGF Markov process recursive algorithm

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APPROXIMATION OF A LINEAR DYNAMIC PROCESS MODEL USING THE FREQUENCY APPROACH AND A NON-QUADRATIC MEASURE OF THE MODEL ERROR

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INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE 2014年第1期24卷 99-109页

作者： Janiszowski, Krzysztof B. Warsaw Univ Technol Inst Automat Control & Robot PL-02525 Warsaw Poland

The paper presents a novel approach to approximation of a linear transfer function model, based on dynamic properties represented by a frequency response, e. g., determined as a result of discrete-time identification. The approximation is derived for minimization of a non-quadratic performance index. This index can be determined as an exponent or absolute norm of an error. Two algorithms for determination of the approximation coefficients are considered, a batch processing one and a recursive scheme, based on the well-known on-line identification algorithm. The proposed approach is not sensitive to local outliers present in the original frequency response. Application of the approach and its features are presented on examples of two simple dynamic systems.

关键词： approximation method frequency domain non-quadratic criterion recursive algorithm

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recursive Identification of Continuous Two-Dimensional Systems in the Presence of Additive Colored Noise

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IETE JOURNAL OF RESEARCH 2014年第1期60卷 74-84页

作者： Shafieirad, Mohsen Shafiee, Masoud Abedi, Mehrdad Amirkabir Univ Technol Dept Elect Engn Tehran Iran Amirkabir Univ Technol SIC Res Inst Tehran Iran

In this paper, a recursive algorithm is developed to estimate the parameters of a partial differential equation as a continuous two-dimensional (2-D) system in the presence of additive colored noise. The system is modelled as hybrid Box-Jenkins model. No comprehensive algorithm for identification of continuous 2-D systems simultaneous with noise process parameter estimation has been proposed so far. Also, there is no recursive method to identify the continuous 2-D systems. The proposed algorithm estimates the noise-free system parameters and colored noise process parameters based on the instrumental variable method simultaneously. Finally, the performance of the proposed method is evaluated by a numerical example.

关键词： Two-dimensional continuous systems recursive algorithm Instrumental variable Stochastic estimation

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Pade-type approximation method for two dimensional Fredholm integral equations of the second kind

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APPLIED MATHEMATICS AND COMPUTATION 2014年 246卷 71-78页

作者： Tao, Youtian Wang, Dongyin Chaohu Coll Dept Math Chaohu 238000 Peoples R China Univ Sci & Technol China Sch Math Sci Hefei 230026 Peoples R China Anhui Fuhuang Steel Struct Chaohu 238076 Peoples R China

Two dimensional Fredholm integral equation of the second kind (2DF-II) on a bounded domain D is regarded as the problem with characteristic values. A two dimensional function-valued Pade-type approximation(2DFPTA) is defined. Its error formulas and convergence theorems are presented. To obtain higher order 2DFPTA, a determinantal expression and its recursive algorithm are given. In the end three numerical examples are tested, where one on the unit triangle of vertices (0, 0), (0, 1), (1, 0) and the other two on the square. The testing results show that 2DFPTA method is more accurate. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Pade-type approximation Fredholm integral equation recursive algorithm

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Estimation Applied to a Third Stochastic Process Order

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REVISTA IBEROAMERICANA DE AUTOMATICA E INFORMATICA INDUSTRIAL 2014年第4期11卷 389-394页

作者： Medel J, Jesus Urbieta P, Romeo Garcia, Juan C., I Ctr Invest Comp Mexico City 07738 DF Mexico Escuela Prof Ingn Mecan & Elect Mexico City DF Mexico

This paper presents the estimation considering the Second Probability Moment applied to a simplified Third Order Stochastic Process. Model commonly used to describe smoothing systems as a synchronous motor. Its values used into the model describe and estimate the Black Box system behavior. In the design three parameters based on covariance P-k and Q(k) are calculated The stochastic variable depends on the three gains and three functional estimation errors, respectively, developing the stochastic identification by a reference model that converges in almost all points with 10 iterations in recursive estimation. The results demonstrate a theoretical experiment using the Matlab (R) obtaining the parameters and the third order model to converge in accordance to the reference signal. The accuracy achieved in thousandths was in a Supermartingale sense and. implementation performed as a function of recursive estimation.

关键词： Probability Identification Filtering recursive algorithm

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Complexity Analysis via Approach Spaces

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APPLIED CATEGORICAL STRUCTURES 2014年第1期22卷 119-136页

作者： Colebunders, E. De Wachter, S. Schellekens, M. Vrije Univ Brussel Dept Math B-1050 Brussels Belgium Natl Univ Ireland Univ Coll Cork CEOL Cork Ireland

Complexity of a recursive algorithm typically is related to the solution to a recurrence equation based on its recursive structure. For a broad class of recursive algorithms we model their complexity in what we call the complexity approach space, the space of all functions in X = ]0, aaEuro parts per thousand] (Y) , where Y can be a more dimensional input space. The set X, which is a dcpo for the pointwise order, moreover carries the complexity approach structure. There is an associated selfmap I broken vertical bar on the complexity approach space X such that the problem of solving the recurrence equation is reduced to finding a fixed point for I broken vertical bar. We will prove a general fixed point theorem that relies on the presence of the limit operator of the complexity approach space X and on a given well founded relation on Y. Our fixed point theorem deals with monotone selfmaps I broken vertical bar that need not be contractive. We formulate conditions describing a class of recursive algorithms that can be treated in this way.

关键词： recursive algorithm Complexity approach space Complexity Fixed point Monotone map

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