a new nonlinear robust disturbance observer abstract this paper presents a new nonlinear robust disturbance observer by using only the input output information for minimum phase dynamical systems with arbitrarily relative degrees the model uncertainties the nonlinear parts of the system are merged into the disturbance term and are regarded as a part of the disturbance the disturbance is assumed bounded however the upper and lower bounds are assumed unknown the new disturbance observer is inspired by the vss control theory whereas the upper and lower bounds of the disturbance are adaptively updated the estimation error of the disturbance can be made as small as necessary by choosing the design parameters the attraction of the proposed method lies in its robustness to disturbance and easiness to be implemented example and simulation results show the effectiveness of the proposed algorithm

implicit finite difference approximation for time fractional diffusion equations time fractional diffusion equations are used when attempting to describe transport processes with long memory where the rate of diffusion is inconsistent with the classical brownian motion model in this paper we develop an implicit unconditionally stable numerical method to solve the one dimensional linear time fractional diffusion equation formulated with caputo s fractional derivative on a finite slab several numerical examples of interest are also included

self similar transport in incomplete chaos particle chaotic dynamics along a stochastic web is studied for three dimensional hamiltonian flow with hexagonal symmetry in a plane two different classes of dynamical motion obtained by different values of a control parameter and corresponding to normal and anomalous diffusion have been considered and compared it is shown that the anomalous transport can be characterized by powerlike wings of the distribution function of displacement flights which are similar to l evy flights approximate trappings of orbits near the boundary layer of islands and anomalous behavior of the moments of a distribution function considered as a function of the number of the moment the main result is related to the self similar properties of different topological and dynamical characteristics of the particle motion this self similarity appears in the weierstrass like random walk process that is responsible for the anomalous transport exponent in the mean moment dependence on t this exponent can be expressed as a ratio of fractal dimensions of space and time sets in the weierstrass like process an explicit form for the expression of the anomalous transport exponent through the local topological properties of orbits has been given

order restricted score parameters in association models for contingency tables abstract the row effects and column effects models for two way contingency tables have parameters for the row and column categories pertaining to the association between the variables for classifications having ordered categories it is often reasonable to assume that the association parameters have a corresponding ordering this article proposes order restricted estimates of the association parameters in these models the maximum likelihood solution can be determined by the solution of a simple isotonic regression of some of the model sufficient statistics the models are primarily log linear in form and can be expressed in terms of odds ratios for 2 2 subtables consisting of adjacent rows and adjacent columns for the order restricted solution these local log odds ratios have uniform sign goodness of fit statistics for this solution are related to corresponding statistics for collapsed tables and to statistics for testing equality of sets of the parameters the row effects model discussed in this art

a second order accurate numerical approximation for the fractional diffusion equation fractional order diffusion equations are generalizations of classical diffusion equations treating super diffusive flow processes in this paper we examine a practical numerical method which is second order accurate in time and in space to solve a class of initial boundary value fractional diffusive equations with variable coefficients on a finite domain an approach based on the classical crank nicholson method combined with spatial extrapolation is used to obtain temporally and spatially second order accurate numerical estimates stability consistency and therefore convergence of the method are examined it is shown that the fractional crank nicholson method based on the shifted grunwald formula is unconditionally stable a numerical example is presented and compared with the exact analytical solution for its order of convergence

compact finite difference method for the fractional diffusion equation high order compact finite difference scheme for solving one dimensional fractional diffusion equation is considered in this paper after approximating the second order derivative with respect to space by the compact finite difference we use the grunwald letnikov discretization of the riemann liouville derivative to obtain a fully discrete implicit scheme we analyze the local truncation error and discuss the stability using the fourier method then we prove that the compact finite difference scheme converges with the spatial accuracy of fourth order using matrix analysis numerical results are provided to verify the accuracy and efficiency of the proposed algorithm

the order restricted rc model for ordered contingency tables estimation and testing for fit the rc model has been proposed as a model for ordered contingency tables it involves parametric scores that are assigned to the rows and columns of the table so that these scores reflect the ordinality of the row and column categories efficient estimation of these parameters subject to order constraints remained an open problem mainly due to severe difficulties in computing these estimates and difficulties in deriving an appropriate asymptotic goodness of fit test a nonstandard yet very simple algorithm is derived which produces the desired order restricted maximum likelihood estimates with probability converging to 1 testing the order restricted rc model for fit is also discussed

numerical solution of the space fractional fokker planck equation the traditional second order fokker planck equation may not adequately describe the movement of solute in an aquifer because of large deviation from the dynamics of brownian motion densities of stable type have been used to describe the probability distribution of these motions the resulting governing equation of these motions is similar to the traditional fokker planck equation except that the order of the highest derivative is fractional in this paper a space fractional fokker planck equation sffpe with instantaneous source is considered a numerical scheme for solving sffpe is presented using the riemann liouville and grunwald letnikov definitions of fractional derivatives the sffpe is transformed into a system of ordinary differential equations ode then the ode system is solved by a method of lines numerical results for sffpe with a constant diffusion coefficient are evaluated for comparison with the known analytical solution the numerical approximation of sffpe with a time dependent diffusion coefficient is also used to simulate levy motion with stable densities we will show that the numerical method of sffpe is able to more accurately model these heavy tailed motions

a geometric combination estimator for d dimensional ordinal sparse contingency tables a geometric combination estimator is proposed for d dimensional ordinal contingency tables the proposed estimator is nonnegative it is shown that assuming sufficient smoothness and boundary conditions for the underlying probabilities the rate of convergence of mean summed squared error msse of this estimator is o k 1 n 8 d 8 for d dimensional tables d 4 with k cells and sample size n this rate is optimal under the smoothness assumptions and is faster than that attained by nonnegative kernel estimates boundary kernels for multidimensional tables are also developed for the proposed estimator to relax restrictive boundary conditions resulting in summed squared error sse being of order o p k 1 n 8 d 8 for all d 1 the behavior of the new estimator is investigated through simulations and applications to real data it is shown that even for relatively small tables these estimators are superior to nonnegative kernel estimators in sharp contrast to the relatively unimpressive performance of such estimators for continuous data

analysis of contingency tables by correspondence models subject to order constraints abstract inferential correspondence analysis which has gained much attention in recent years is applied here to contingency tables with ordered categories to reflect such order the parameters of the underlying correspondence models are constrained to follow the order induced by the categories of the analyzed table a reparameterization of the correspondence model in terms of a latent variable model is presented this allows a simple and straightforward use of the em algorithm to obtain efficient order restricted estimates a goodness of fit test is also discussed and an example is analyzed a small monte carlo example is presented

bayesian measures of model complexity and fit summary we consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined using an information theoretic argument we derive a measure pd for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest in general pd approximately corresponds to the trace of the product of fisher s information and the posterior covariance which in normal models is the trace of the hat matrix projecting observations onto fitted values its properties in exponential families are explored the posterior mean deviance is suggested as a bayesian measure of fit or adequacy and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages adding pd to the posterior mean deviance gives a deviance information criterion for comparing models which is related to other information criteria and has an approximate decision theoretic justification the procedure is illustrated in some examples and comparisons are drawn with alternative bayesian and classical proposals throughout it is emphasized that the quantities required are trivial to compute in a markov chain monte carlo analysis

the fractional order governing equation of levy motion a governing equation of stable random walks is developed in one dimension this fokker planck equation is similar to and contains as a subset the second order advection dispersion equation ade except that the order a of the highest derivative is fractional e g the 1 65th derivative fundamental solutions are levy s a stable densities that resemble the gaussian except that they spread proportional to time 1 a have heavier tails and incorporate any degree of skewness the measured variance of a plume undergoing levy motion would grow faster than fickian plume at a rate of time 2 a where 0 a 2 the equation is parsimonious since the parameters are not functions of time or distance the scaling behavior of plumes that undergo levy motion is accounted for by the fractional derivatives which are appropriate measures of fractal functions in real space the fractional derivatives are integrodifferential operators so the fractional ade describes a spatially nonlocal process that is ergodic and has analytic solutions for all time and space

a class of second order difference approximations for solving space fractional diffusion equations a class of second order approximations called the weighted and shifted grunwald difference wsgd operators are proposed for riemann liouville fractional derivatives with their effective applications to numerically solving space fractional diffusion equations in one and two dimensions the stability and convergence of our difference schemes for space fractional diffusion equations with constant coefficients in one and two dimensions are theoretically established several numerical examples are implemented to test the efficiency of the numerical schemes and confirm the convergence order and the numerical results for variable coefficients problem are also presented

numerical solutions for fractional reaction diffusion equations fractional diffusion equations are useful for applications in which a cloud of particles spreads faster than predicted by the classical equation in a fractional diffusion equation the second derivative in the spatial variable is replaced by a fractional derivative of order less than two the resulting solutions spread faster than the classical solutions and may exhibit asymmetry depending on the fractional derivative used fractional reaction diffusion equations combine the fractional diffusion with a classical reaction term in this paper we develop a practical method for numerical solution of fractional reaction diffusion equations based on operator splitting then we present results of numerical simulations to illustrate the method and investigate properties of numerical solutions we also discuss applications to biology where the reaction term models species growth and the diffusion term accounts for movements

the accuracy and stability of an implicit solution method for the fractional diffusion equation we have investigated the accuracy and stability of an implicit numerical scheme for solving the fractional diffusion equation this model equation governs the evolution for the probability density function that describes anomalously diffusing particles anomalous diffusion is ubiquitous in physical and biological systems where trapping and binding of particles can occur the implicit numerical scheme that we have investigated is based on finite difference approximations and is straightforward to implement the accuracy of the scheme is o dx 2 in the spatial grid size and o dt 1 c in the fractional time step where 0 email protected 1 is the order of the fractional derivative and c 1 is standard diffusion we have provided algebraic and numerical evidence that the scheme is unconditionally stable for 0 c 1

numerical approximation of a time dependent nonlinear space fractional diffusion equation in this article we analyze a fully discrete numerical approximation to a time dependent fractional order diffusion equation which contains a nonlocal quadratic nonlinearity the analysis is performed for a general fractional order diffusion operator the nonlinear term studied is a product of the unknown function and a convolution operator of order 0 convergence of the approximation and a priori error estimates are given numerical computations are included which confirm the theoretical predictions

multigrid method for fractional diffusion equations the fractional diffusion equation is discretized by the implicit finite difference scheme with the shifted grunwald formula the scheme is unconditionally stable and the coefficient matrix possesses the toeplitz like structure a multigrid method is proposed to solve the resulting system meanwhile the fast toeplitz matrix vector multiplication is utilized to lower the computational cost with only o nlogn complexity where n is the number of the grid points numerical experiments are given to demonstrate the efficiency of the method

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

finite difference approximations for fractional advection dispersion flow equations fractional advection dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium in this paper we develop practical numerical methods to solve one dimensional fractional advection dispersion equations with variable coefficients on a finite domain the practical application of these results is illustrated by modeling a radial flow problem use of the fractional derivative allows the model equations to capture the early arrival of tracer observed at a field site

regression and ordered categorical variables read before the royal statistical society by professor r l plackett on behalf of the late professor anderson at a meeting organized by the research section on wednesday october 5th 1983 professor j b copas in the chair summary a general approach to regression modelling for ordered categorical response variables y is given which is equally applicable to ordered and unordered y the regressor variables xt xi x may be continuous or categorical the method is based on the logistic family which contains a hierarchy of regression models ranging from ordered to unordered models ordered properties of the former the stereotype model are established the choice between models is made empirically on the basis of model fit this is particularly important for assessed ordered categorical response variables where it is not obvious a priori whether or not the ordering is relevant to the regression relationship model simplification is investigated in terms of whether or not the response categories are distinguishable with respect to x the models are fitted iteratively using the method of maximum likelihood examples are given

lyapunov based adaptive state estimation for a class of nonlinear stochastic systems this paper is concerned with an adaptive state estimation problem for a class of nonlinear stochastic systems with unknown constant parameters these nonlinear systems have a linear in parameter structure and the nonlinearity is assumed to be bounded in a lipschitz like manner using stochastic counterparts of lyapunov stability theory we present adaptive state and parameter estimators with ultimately exponentially bounded estimator errors in the sense of mean square for both continuous time and discrete time nonlinear stochastic systems sufficient conditions are given in terms of the solvability of lmis moreover we also introduce a suboptimal design approach to optimizing the upper bound of the mean square error of parameter estimation this suboptimal design procedure is also realized by lmi computations by a martingale method we also show that the related lyapunov function has a non negative lyapunov exponent

observer matrix gain optimization for stochastic continuous time nonlinear systems it is shown that for a class of stationary stochastic nonlinear systems satisfying a global lipschitz condition the high gain observer with a constant gain matrix may guarantee an upper bound for the averaged quadratic error of state estimation the nonlinearity is assumed to be a priory known the main contribution of this paper consists in designing of a numerical procedure for the optimal gain matrix minimizing this upper bound the convergence analysis of this procedure is presented as well as an example illustrating its finite steps workability it is shown that within a neighborhood of the optimal matrix gain the others provide lower estimation performance

multigrid method for ill conditioned symmetric toeplitz systems in this paper we consider solutions of toeplitz systems anu b where the toeplitz matrices an are generated by nonnegative functions with zeros since the matrices an are ill conditioned the convergence factor of classical iterative methods such as the damped jacobi method will approach one as the size n of the matrices becomes large here we propose to solve the systems by the multigrid method the cost per iteration for the method is of o n log n operations for a class of toeplitz matrices which includes weakly diagonally dominant toeplitz matrices we show that the convergence factor of the two grid method is uniformly bounded below one independent of n and the full multigrid method has convergence factor depending only on the number of levels numerical results are given to illustrate the rate of convergence

finite element method for the space and time fractional fokker planck equation we develop the finite element method for the numerical resolution of the space and time fractional fokker planck equation which is an effective tool for describing a process with both traps and flights the time fractional derivative of the equation is used to characterize the traps and the flights are depicted by the space fractional derivative the stability and error estimates are rigorously established and we prove that the convergent order is o k 2 alpha h mu where k is the time step size and h the space step size numerical computations are presented which demonstrate the effectiveness of the method and confirm the theoretical claims

log multiplicative association models as item response models log multiplicative association lma models which are special cases of log linear models have interpretations in terms of latent continuous variables two theoretical derivations of lma models based on item response theory irt arguments are presented first we show that anderson and colleagues anderson vermunt 2000 anderson bockenholt 2000 anderson 2002 who derived lma models from statistical graphical models made the equivalent assumptions as holland 1990 when deriving models for the manifest probabilities of response patterns based on an irt approach we also present a second derivation of lma models where item response functions are specified as functions of rest scores these various connections provide insights into the behavior of lma models as item response models and point out philosophical issues with the use of lma models as item response models we show that even for short tests lma and standard irt models yield very similar to nearly identical results when data arise from standard irt models log multiplicative association models can be used as item response models and do not require numerical integration for estimation

fractional order anisotropic diffusion for image denoising this paper introduces a new class of fractional order anisotropic diffusion equations for noise removal these equations are euler lagrange equations of a cost functional which is an increasing function of the absolute value of the fractional derivative of the image intensity function so the proposed equations can be seen as generalizations of second order and fourth order anisotropic diffusion equations we use the discrete fourier transform to implement the numerical algorithm and give an iterative scheme in the frequency domain it is one important aspect of the algorithm that it considers the input image as a periodic image to overcome this problem we use a folded algorithm by extending the image symmetrically about its borders finally we list various numerical results on denoising real images experiments show that the proposed fractional order anisotropic diffusion equations yield good visual effects and better signal to noise ratio

modeling and forecasting u s mortality abstract time series methods are used to make long run forecasts with confidence intervals of age specific mortality in the united states from 1990 to 2065 first the logs of the age specific death rates are modeled as a linear function of an unobserved period specific intensity index with parameters depending on age this model is fit to the matrix of u s death rates 1933 to 1987 using the singular value decomposition svd method it accounts for almost all the variance over time in age specific death rates as a group whereas e 0 has risen at a decreasing rate over the century and has decreasing variability k t declines at a roughly constant rate and has roughly constant variability facilitating forecasting k t which indexes the intensity of mortality is next modeled as a time series specifically a random walk with drift and forecast the method performs very well on within sample forecasts and the forecasts are insensitive to reductions in the length of the base period from 90 to 30

association models and canonical correlation in the analysis of cross classifications having ordered categories abstract the association models considered in goodman 1979a for the analysis of cross classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach both the association models and the canonical correlation approach can provide meaningful scores for the row and column categories and these scores can be used to partition into relevant components the usual chi squared statistic for testing the null hypothesis of statistical independence between the row classification and column classification however while the usual procedure for testing the statistical significance of chi squared components is invalid when these components are based on the canonical correlations a corresponding procedure is valid when these components are obtained with the association models the components of association obtained with the association mo

the order restricted association model two estimation algorithms and issues in testing this paper presents a row column rc association model in which the estimated row and column scores are forced to be in agreement with an a priori specified ordering two efficient algorithms for finding the order restricted maximum likelihood ml estimates are proposed and their reliability under different degrees of association is investigated by a simulation study we propose testing order restricted rc models using a parametric bootstrap procedure which turns out to yield reliablep values except for situations in which the association between the two variables is very weak the use of order restricted rc models is illustrated by means of an empirical example

preconditioning techniques for diagonal times toeplitz matrices in fractional diffusion equations the fractional diffusion equation is discretized by an implicit finite difference scheme with the shifted grunwald formula which is unconditionally stable the coefficient matrix of the discretized linear system is equal to the sum of a scaled identity matrix and two diagonal times toeplitz matrices standard circulant preconditioners may not work for such toeplitz like linear systems the main aim of this paper is to propose and develop approximate inverse preconditioners for such toeplitz like matrices an approximate inverse preconditioner is constructed to approximate the inverses of weighted toeplitz matrices by circulant matrices and then combine them together row by row because of toeplitz structure both the discretized coefficient matrix and the preconditioner can be implemented very efficiently by using fast fourier transforms theoretically we show that the spectra of the resulting preconditioned matrices are clustered around one thus krylov subspace methods with the proposed preconditione

on bayesian analysis of mixtures with an unknown number of components discussion author s reply new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

limited information goodness of fit testing in multidimensional contingency tables we introduce a family of goodness of fit statistics for testing composite null hypotheses in multidimensional contingency tables these statistics are quadratic forms in marginal residuals up to order r they are asymptotically chi square under the null hypothesis when parameters are estimated using any asymptotically normal consistent estimator for a widely used item response model when r is small and multidimensional tables are sparse the proposed statistics have accurate empirical type i errors unlike pearson s x2 for this model in nonsparse situations the proposed statistics are also more powerful than x2 in addition the proposed statistics are asymptotically chi square when applied to subtables and can be used for a piecewise goodness of fit assessment to determine the source of misfit in poorly fitting models

fast matrix splitting preconditioners for higher dimensional spatial fractional diffusion equations abstract the discretizations of two and three dimensional spatial fractional diffusion equations with the shifted finite difference formulas of the grunwald letnikov type can result in discrete linear systems whose coefficient matrices are of the form d t where d is a nonnegative diagonal matrix and t is a block toeplitz with toeplitz block matrix or a block toeplitz with each block being block toeplitz with toeplitz block matrix for these discrete spatial fractional diffusion matrices we construct diagonal and block circulant with circulant block splitting preconditioner for the two dimensional case and diagonal and block circulant with each block being block circulant with circulant block splitting preconditioner for the three dimensional case to further accelerate the convergence rates of krylov subspace iteration methods and we analyze the eigenvalue distributions for the corresponding preconditioned matrices theoretical results show that except for a small number of outliners the eigenvalues of the preconditioned matrices are located within a complex disk centered at 1 with the radius being exactly less than 1 and numerical experiments demonstrate that these structured preconditioners can significantly improve the convergence behavior of the krylov subspace iteration methods moreover this approach is superior to the geometric multigrid method and the preconditioned conjugate gradient methods incorporated with the approximate inverse circulant plus diagonal preconditioners in both iteration counts and computing times

a direct o nlog2n finite difference method for fractional diffusion equations fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not be modeled accurately by the second order diffusion equations because of the nonlocal property of fractional differential operators the numerical methods have full coefficient matrices which require storage of o n 2 and computational cost of o n 3 where n is the number of grid points in this paper we develop a fast finite difference method for fractional diffusion equations which only requires storage of o n and computational cost of o nlog 2n while retaining the same accuracy and approximation property as the regular finite difference method numerical experiments are presented to show the utility of the method

a fourth order approximation of fractional derivatives with its applications a new fourth order difference approximation is derived for the space fractional derivatives by using the weighted average of the shifted grunwald formulae combining the compact technique the properties of proposed fractional difference quotient operator are presented and proved then the new approximation formula is applied to solve the space fractional diffusion equations by the energy method the proposed quasi compact difference scheme is proved to be unconditionally stable and convergent in l2 norm for both 1d and 2d cases several numerical examples are given to confirm the theoretical results

a meshless method based on point interpolation method pim for the space fractional diffusion equation this paper aims to develop a meshless approach based on the point interpolation method pim for numerical simulation of a space fractional diffusion equation two fully discrete schemes for the one dimensional space fractional diffusion equation are obtained by using the pim and the strong forms of the space diffusion equation numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

discussion to bayesian measures of model complexity and fit by spiegelhalter d j best n g carlin b p and van der linde a

application of a fractional advection dispersion equation abstract a transport equation that uses fractional order dispersion derivatives hasfundamental solutions that are le vy s a stable densities these densities represent plumesthat spread proportional to time 1 a have heavy tails and incorporate any degree ofskewness the equation is parsimonious since the dispersion parameter is not a functionof time or distance the scaling behavior of plumes that undergo le vy motion isaccounted for by the fractional derivative a laboratory tracer test is described by adispersion term of order 1 55 while the cape cod bromide plume is modeled by anequation of order 1 65 to 1 8 1 introduction anomalous or non fickian dispersion has been an activearea of research in the physics community since the introduc tion of continuous time random walks ctrw by montrolland weiss 1965 these random walks extended the predictivecapability of models built on the stochastic process of brown ian motion which is the basis for the classical advection dispersion equation ade the ctrw assign a joint space time distribution called the transition density to individualparticle motions when the tails are heavy enough i e powerlaw non fickian dispersion results for all time scales andspace scales

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

bayesian model comparison for the order restricted rc association model association models constitute an attractive alternative to the usual log linear models for modeling the dependence between classification variables they impose special structure on the underlying association by assigning scores on the levels of each classification variable which can be fixed or parametric under the general row column rc association model both row and column scores are unknown parameters without any restriction concerning their ordinality however when the classification variables are ordinal order restrictions on the scores arise naturally under such restrictions we adopt an alternative parameterization and draw inferences about the equality of adjacent scores using the bayesian approach to achieve that we have constructed a reversible jump markov chain monte carlo algorithm for moving across models of different dimension and estimate accurately the posterior model probabilities which can be used either for model comparison or for model averaging the proposed methodology is evaluated through a simulation study and illustrated using actual datasets

computing symmetric solutions of general sylvester matrix equations via lanczos version of biconjugate residual algorithm abstract many problems in control theory can be studied by obtaining the symmetric solution of linear matrix equations in this investigation we deal with the symmetric solutions x y and z of the general sylvester matrix equations a 1 x b 1 c 1 y d 1 e 1 z f 1 g 1 a 2 x b 2 c 2 y d 2 e 2 z f 2 g 2 a t x b t c t y d t e t z f t g t the lanczos version of biconjugate residual bcr algorithm is generalized to compute the symmetric solutions of the general sylvester matrix equations the convergence properties of this algorithm are discussed and it is proven that it smoothly converges to the symmetric solutions of the general sylvester matrix equations in a finite number of iterations in the absence of round off errors finally the comparative numerical results are carried out to support that the current algorithm may be more efficient than other iterative algorithms

a receding horizon kalman fir filter for linear continuous time systems a receding horizon kalman finite impulse response fir filter is suggested for continuous time systems combining the kalman filter with the receding horizon strategy in the suggested filter the horizon initial state is assumed to be unknown it can always be obtained irrespective of unknown information on the horizon initial state the filter may be the first stochastic fir form for continuous time systems that may have many good inherent properties the suggested filter can be represented in an iterative form and also in a standard fir form the suggested filter turns out to be a remarkable deadbeat observer the validity of the suggested filter is illustrated by numerical examples

extended rc association models allowing for order restrictions and marginal modeling in the context of two way contingency tables the rc model may be seen as a way of modeling the set of log odds ratios for adjacent 2 2 subtables through row and column scores this article presents an extended class of rc models that allows simultaneous modeling of the marginal distributions and the association between two categorical variables these components are parameterized with logits and log odds ratios that may be of different types e g global or continuation to suit the nature of the data and the type of dependence of interest an algorithm for maximum likelihood estimation under equality and inequality constraints is presented the asymptotic distribution of the likelihood ratio statistic to test some interesting hypotheses is derived and extensions to multiway tables are outlined three examples are presented to highlight the features of the new approach

some models for the analysis of association in multiway cross classifications having ordered categories abstract goodman recently presented a class of models for the analysis of association between two discrete ordinal variables the association was measured in terms of the odds ratios in 2 2 subtables formed from adjacent rows and adjacent columns of the cross classification and models were devised that allowed the odds ratios to depend on an overall effect on row effects on column effects and on other effects this article presents some generalizations of this approach appropriate for multiway cross classifications including a models for the analysis of conditional association b models for the analysis of partial association and c models for the analysis of symmetric association three cross classifications are analyzed with these models and methods and rather simple interpretations of the association in each are provided

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

a note on the convergence of the two grid method for toeplitz systems abstract in this paper we consider solutions of toeplitz systems au b where the toeplitz matrices a are generated by nonnegative functions with zeros since the matrices a are ill conditioned the convergence factor of classical iterative methods such as the richardson method will approach 1 as the size n of the matrices becomes large in 1 2 convergence of the two grid method with richardson method as smoother was proved for band matrices and it was conjectured that this convergence result can be carried to toeplitz systems in this paper we show that the two grid method with richardson smoother indeed converges for toeplitz systems that are generated by functions with zeros provided that the order of the zeros are less than or equal to 2 however we illustrate by examples that the convergence results of the two grid method cannot be readily extended to multigrid method for n that are not of the form 2 l 1

a multigrid method for linear systems arising from time dependent two dimensional space fractional diffusion equations abstract in this paper we study a v cycle multigrid method for linear systems arising from time dependent two dimensional space fractional diffusion equations the coefficient matrices of the linear systems are structured such that their matrix vector multiplications can be computed efficiently the main advantage using the multigrid method is to handle the space fractional diffusion equations on non rectangular domains and to solve the linear systems with non constant coefficients more effectively the main idea of the proposed multigrid method is to employ two banded splitting iteration schemes as pre smoother and post smoother the pre smoother and the post smoother take banded splitting of the coefficient matrix under the x dominant ordering and the y dominant ordering respectively we prove the convergence of the proposed two banded splitting iteration schemes in the sense of infinity norm results of numerical experiments for time dependent two dimensional space fractional diffusion equations on rectangular l shape and u shape domains are reported to demonstrate that both computational time and iteration number required by the proposed method are significantly smaller than those of the other tested methods