optimization of type 2 fuzzy systems based on bio inspired methods a concise review a review of the optimization methods used in the design of type 2 fuzzy systems which are relatively novel models of imprecision has been considered in this work the fundamental focus of the work has been based on the basic reasons of the need for optimizing type 2 fuzzy systems for different areas of application recently bio inspired methods have emerged as powerful optimization algorithms for solving complex problems in the case of designing type 2 fuzzy systems for particular applications the use of bio inspired optimization methods have helped in the complex task of finding the appropriate parameter values and structure of the fuzzy systems in this review we consider the application of genetic algorithms particle swarm optimization and ant colony optimization as three different paradigms that help in the design of optimal type 2 fuzzy systems we also provide a comparison of the different optimization methods for the case of designing type 2 fuzzy systems

analytical and numerical solutions of a one dimensional fractional in space diffusion equation in a composite medium in this paper a one dimensional space fractional diffusion equation in a composite medium consisting of two layers in contact is studied both analytically and numerically since domain decomposition is the only approach available to solve this problem we at first investigate analytical and numerical strategies for a composite medium with the same fractal dimension in each layer to ascertain which domain decomposition approach is the most accurate and consistent with a global solution methodology which is available in this case we utilise a matrix representation of the fractional in space operator to generate a system of linear odes with the matrix raised to the same fractional exponent we show that the global and domain decomposition numerical strategies for this problem produce simulation results that are in good agreement with their analytic counterparts and conclude that the domain decomposition that imposes the neumann condition at the interface produces the most consistent results finally we carry this finding to study the composite problem with different fractal dimensions where we again favourably compare analytic and numerical solutions the resulting method can be naturally extended to space fractional diffusion in a composite medium consisting of more than two layers

approximate likelihood for large irregularly spaced spatial data likelihood approaches for large irregularly spaced spatial datasets are often very difficult if not infeasible to implement due to computational limitations even when we can assume normality exact calculations of the likelihood for a gaussian spatial process observed at n locations requires o n3 operations we present a version of whittle s approximation to the gaussian log likelihood for spatial regular lattices with missing values and for irregularly spaced datasets this method requires o nlog2n operations and does not involve calculating determinants we present simulations and theoretical results to show the benefits and the performance of the spatial likelihood approximation method presented here for spatial irregularly spaced datasets and lattices with missing values we apply these methods to estimate the spatial structure of sea surface temperatures using satellite data with missing values

an investigation of the small slope approximation for scattering from rough surfaces part i theory the small slope approximation ssa of voronovich sov phys jetp 62 65 70 1985 is a promising method for application to scattering from many natural surfaces the theory gives a systematic expansion that can be interpreted as a series in generalized surface slope the ssa series for the t matrix satisfies the appropriate reciprocity condition at each order and reduces to the standard perturbation series for small surface roughness in this paper we examine in detail the derivation of the ssa for surfaces subject to the dirichlet zero field boundary condition a number of points are discussed including the requirements for determining the series terms in addition questions have been raised recently about the ssa it has been argued that 1 an assumption in the derivation contradicts the exact formulation of the problem and 2 there is an arbitrariness in determining the series terms these two points are refuted and the assumptions needed to determine the series terms unambiguously are clarified the meaning of slope orders in the ssa series expansion are examined and the concept of generalized slope is discussed a future companion paper part ii numerical studies will present an investigation of the accuracy of the ssa through comparison with exact results

physical and geometrical optics for 2 d rough surfaces with power law height spectra random rough surfaces with slowly decaying power spectral density can have infinite slope variance such surfaces do not satisfy the classical curvature criterion for validity of the physical optics po approximation and the infinite frequency geometrical optics limit or specular point scattering model breaks down we show for two dimensional surfaces with infinite slope variance that the gaussian form of the classical geometrical limit generalizes to a stable distribution function we also show that the po integral is insensitive to surface components with spatial frequency above a cutoff wavenumber which explains past observations that po can be accurate for surfaces with power law spectra this result leads to a general validity condition for the po approximation in the backscattering direction for power law surfaces which in the case of a k sup 4 spectrum requires that the significant slope of the surface be less than 0 03

hierarchical spatial process models for multiple traits in large genetic trials this article expands upon recent interest in bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets of multiple traits of interest direct application of such multivariate models to large spatial datasets is often computationally infeasible because of cubic order matrix algorithms involved in estimation the situation is even worse in markov chain monte carlo mcmc contexts where such computations are performed for several thousand iterations here we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling for genetic effects we demonstrate how an initial spectral decomposition of the relationship matrices negates the expensive matrix inversions required in previously proposed mcmc methods for spatial effects we discuss a multivariate predictive process that reduces the computational burden by projecting th

analytical solution for the time fractional telegraph equation by the method of separating variables in this paper a method of separating variables is effectively implemented for solving a time fractional telegraph equation tfte we discuss and derive the analytical solution of the tfte with three kinds of nonhomogeneous boundary conditions namely dirichlet neumann and robin boundary conditions

simulations of rough interface scattering this paper describes numerical simulations of rough interface scattering both dirichlet and fluid solid boundary conditions are treated the rayleigh fourier method is used to compute exact plane wave scattering amplitudes and results are compared to various approximations the small slope approximation of voronovich performs remarkably well while the tangent plane approximation is shown to miss some essential physics of scattering it is observed that at the rayleigh angle there is a peak in the backscattering amplitude even for plane wave incidence it is argued that the statistics of plane wave scattering amplitudes are gaussian

defuzzification of the discretised generalised type 2 fuzzy set experimental evaluation the work reported in this paper addresses the challenge of the efficient and accurate defuzzification of discretised generalised type 2 fuzzy sets as created by the inference stage of a mamdani fuzzy inferencing system the exhaustive method of defuzzification for type 2 fuzzy sets is extremely slow owing to its enormous computational complexity several approximate methods have been devised in response to this defuzzification bottleneck in this paper we begin by surveying the main alternative strategies for defuzzifying a generalised type 2 fuzzy set 1 vertical slice centroid type reduction 2 the sampling method 3 the elite sampling method and 4 the a planes method we then evaluate the different methods experimentally for accuracy and efficiency for accuracy the exhaustive method is used as the standard the test results are analysed statistically by means of the wilcoxon nonparametric test and the elite sampling method shown to be the most accurate in regards to efficiency vertical slice centroid type reduction is demonstrated to be the fastest technique

joint composite estimating functions in spatiotemporal models summary modelling of spatiotemporal processes has received considerable attention in recent statistical research however owing to the high dimensionality of the data the joint modelling of spatial and temporal processes presents a great computational challenge in both likelihood based and bayesian approaches we propose a joint composite estimating function approach to estimating spatiotemporal covariance structures this substantially reduces the computational complexity and is more efficient than existing composite likelihood methods the novelty of the proposed joint composite estimating function is rooted in the construction of three sets of estimating functions from spatial temporal and spatiotemporal cross pairs which results in overidentified estimating functions thus we form a joint inference function in a spirit that is similar to hansen s generalized method of moments we show that under practical scenarios the estimator proposed is consistent and asymptotically normal simulation studies prove that our method performs well in finite samples finally we illustrate the joint composite estimating function method by estimating the spatiotemporal dependence structure of airborne particulates pm10 in the north eastern usa over a 32 month period

on a class of random field models which allows long range dependence summary in this note it is shown how a convenient class of random field models with rational spectral densities can be augmented to incorporate the possibility of long range dependence

footprint of uncertainty for type 2 fuzzy sets in the paper a new and comprehensible definition is proposed for type 2 fuzzy sets t2 fss and the primary and secondary memberships function are defined respectively by using multi valued mapping a new definition and formula for the footprint of uncertainty fou is presented and based on the new definitions the relation between fou and the original definition of t2 fs is discussed finally the partition method of fou is provided to represent the primary membership grade the fou and the interval type 2 fuzzy sets it2 fs when the upper and lower membership functions umf lmf of fou are given

fitting continuous arma models to unequally spaced spatial data abstract methods for fitting continuous spatial autoregressive moving average arma models to unequally spaced observations in two dimensions are reviewed and extended these are models with rational two dimensional spectra assuming gaussian input noise and observational errors maximum likelihood methods are used to estimate the arma parameters and the regression coefficients of the deterministic trend when the number of observations is too large for exact maximum likelihood estimation approximate maximum likelihood estimation is used based on nearest neighbors comparisons of nearest neighbor methods with exact likelihood methods are presented predictions of the height of the field at unobserved points can be calculated with confidence intervals

convection diffusion equations with random initial conditions abstract we consider an evolution equation generalising the viscous burgers equation supplemented by an initial condition which is a homogeneous random field we develop a non linear framework enabling us to show the existence and regularity of solutions as well as their long time behaviour

renormalization and homogenization of fractional diffusion equations with random data this paper presents a renormalization and homogenization theory for fractional in space or in time diffusion equations with singular random initial conditions the spectral representations for the solutions of these equations are provided gaussian and non gaussian limiting distributions of the renormalized solutions of these equations are then described in terms of multiple stochastic integral representations

compressing an ensemble with statistical models an algorithm for global 3d spatio temporal temperature one of the main challenges when working with modern climate model ensembles is the increasingly larger size of the data produced and the consequent difficulty in storing large amounts of spatio temporally resolved information many compression algorithms can be used to mitigate this problem but since they are designed to compress generic scientific datasets they do not account for the nature of climate model output and they compress only individual simulations in this work we propose a different statistics based approach that explicitly accounts for the space time dependence of the data for annual global three dimensional temperature fields in an initial condition ensemble the set of estimated parameters is small compared to the data size and can be regarded as a summary of the essential structure of the ensemble output therefore it can be used to instantaneously reproduce the temperature fields in an ensemble with a substantial saving in storage and time the statistical model exploits the gri

diffusion on multifractals abstract we introduce a class of random fields with variable mean square regularity order defined on multifractal domains the local singularity order of these random fields then depends on the initial variable mean square regularity order and on the variable local singularity exponent of the multifractal measure defining the local dimension of the domain considered the theory is developed in a generalized framework through the covariance factorization using the tools of reproducing kernel hilbert spaces and fractional sobolev spaces of variable order

serial correlation in unequally spaced longitudinal data summary serial correlation in the within subject error structure in longitudinal data with unequally spaced observations is modelled using continuous time autoregressive moving averages the models considered have both fixed and random effects in addition to serially correlated within subject errors two approaches are presented for calculating the exact likelihood for a model when the errors are gaussian the first calculates the covariance matrices for each subject for assumed values of the unknown parameters and estimates the fixed parameters by weighted least squares the second uses a state space model and the kalman filter to calculate the exact likelihood both methods involve the use of complex arithmetic nonlinear optimization is used to obtain maximum likelihood estimates of the parameters

covariance tapering for likelihood based estimation in large spatial data sets maximum likelihood is an attractive method of estimating covariance parameters in spatial models based on gaussian processes but calculating the likelihood can be computationally infeasible for large data sets requiring o n3 calculations for a data set with n observations this article proposes the method of covariance tapering to approximate the likelihood in this setting in this approach covariance matrixes are tapered or multiplied element wise by a sparse correlation matrix the resulting matrixes can then be manipulated using efficient sparse matrix algorithms we propose two approximations to the gaussian likelihood using tapering one of these approximations simply replaces the model covariance with a tapered version whereas the other is motivated by the theory of unbiased estimating equations focusing on the particular case of the matern class of covariance functions we give conditions under which estimators maximizing the tapering approximations are like the maximum likelihood estimat

spectral analysis of fractional kinetic equations with random data we present a spectral representation of the mean square solution of the fractional kinetic equation also known as fractional diffusion equation with random initial condition gaussian and non gaussian limiting distributions of the renormalized solution of the fractional in time and in space kinetic equation are described in terms of multiple stochastic integral representations

the sampling method of defuzzification for type 2 fuzzy sets experimental evaluation for generalised type 2 fuzzy sets the defuzzification process has historically been slow and inefficient this has hampered the development of type 2 fuzzy inferencing systems for real applications and therefore no advantage has been taken of the ability of type 2 fuzzy sets to model higher levels of uncertainty the research reported here provides a novel approach for improving the speed of defuzzification for discretised generalised type 2 fuzzy sets the traditional type reduction method requires every embedded type 2 fuzzy set to be processed the high level of redundancy in the huge number of embedded sets inspired the development of our sampling method which randomly samples the embedded sets and processes only the sample the paper presents detailed experimental results for defuzzification of constructed sets of known defuzzified value the sampling defuzzifier is compared on aggregated type 2 fuzzy sets resulting from the inferencing stage of a fis in terms of accuracy and speed with other methods including the exhaustive and techniques based on the a planes representation the results indicate that by taking only a sample of the embedded sets we are able to dramatically reduce the time taken to process a type 2 fuzzy set with very little loss in accuracy

stratified structure of the universe and burgers equation a probabilistic approach the model of the potential turbulence described by the 3 dimensional burgers equation with random initial data was developped by zeldovich and shandarin in order to explain the existing large scale structure of the universe most of the recent probabilistic investigations of large time asymptotics of the solution deal with the central limit type results the gaussian scenario under suitable moment assumptions on the initial velocity field these results and some open questions are discussed in sect 2 where we concentrate on the gaussian model and the shot noise model in sect 3 we construct a probabilistic model of strong initial fluctuations a zero range shot noise field with high amplitudes which reveals an intermittent large time behaviour with the velocity vec v t x determined by the position of the largest initial fluctuation discounted by the heat kernelg t x in a neighborhood ofx the asymptoties of such local maximum ast can be analyzed with the help of the theory of records sect 4 finally in sect 5 we introduce a global definition of a point process oft local maxima and show the weak convergence of the suitably rescaled process to a non trivial limit ast

an explicit link between gaussian fields and gaussian markov random fields the stochastic partial differential equation approach continuously indexed gaussian fields gfs are the most important ingredient in spatial statistical modelling and geostatistics the specification through the covariance function gives an intuitive interpretation of the field properties on the computational side gfs are hampered with the big n problem since the cost of factorizing dense matrices is cubic in the dimension although computational power today is at an all time high this fact seems still to be a computational bottleneck in many applications along with gfs there is the class of gaussian markov random fields gmrfs which are discretely indexed the markov property makes the precision matrix involved sparse which enables the use of numerical algorithms for sparse matrices that for fields in r 2 only use the square root of the time required by general algorithms the specification of a gmrf is through its full conditional distributions but its marginal properties are not transparent in such a parameterization we show that using an approximate stochastic weak solution to linear stochastic partial differential equations we can for some gfs in the matern class provide an explicit link for any triangulation of r d between gfs and gmrfs formulated as a basis function representation the consequence is that we can take the best from the two worlds and do the modelling by using gfs but do the computations by using gmrfs perhaps more importantly our approach generalizes to other covariance functions generated by spdes including oscillating and non stationary gfs as well as gfs on manifolds we illustrate our approach by analysing global temperature data with a non stationary model defined on a sphere less

a new indirect approach to the type 2 fuzzy systems modeling and design this paper proposes a new method for designing interval type 2 fuzzy logic systems it2 flss considering two issues first quality of clustering the output space and secondly approximating the output of the it2 fls based on a new output processing method based on these two issues we present a new cluster validity index capable of being used for type 1 fuzzy c means fcms interval type 2 fcm it2 fcm and possibilistic c means pcms clustering algorithms this validity index is highly efficient in determining clusters with the least similarity between them and the highest similarity between data vectors in each cluster then a new definition for uncertainty bounds is presented in order to eliminate the type reduction process in it2 flss and to increase accuracy of the existing uncertainty bounds in the literature finally effectiveness of the proposed approaches compared to several well known existing methods has been investigated computational results have verified accuracy and effectiveness of the proposed method

kriging nonstationary data abstract spatial data modeled to have come from a random function with a nonstationary mean are considered the spatial prediction method known as kriging exploits second order spatial correlation structure to obtain minimum variance predictions of certain average values of the random function but to do so it must be assumed that either the mean function the drift is known up to a constant or the second order structure the variogram is known exactly knowledge of the drift allows the stationary variogram to be estimated and leads to ordinary kriging knowledge of the variogram allows the drift to be estimated and leads to universal kriging more usually neither is known this article shows how median polish of gridded spatial data provides a resistant and relatively bias free way of kriging in the presence of drift yet yields results as good as the mathematically optimal but operationally difficult universal kriging comparisons are performed on two data sets

statistical estimation of polynomial generalized covariance functions and hydrologic applications minimum variance unbiased linear estimation theory has found many applications in the analysis of spatial rainfall and hydrogeologic data estimation of point values or areal averages calculation of variances of estimation error and network design however the important problem of inferring the spatial structure or interdependence of the function of interest has received relatively less attention three methods for the estimation of the parameters of matheron s polynomial generalized covariance function a useful model for nonstationary functions are presented and evaluated maximum likelihood ml minimum variance unbiased quadratic mvuq and minimum norm least squares the estimation error covariance matrix of the parameters is calculated with each of these methods ml and mvuq estimation have very good properties and for reasonably large samples give very similar results minimum norm estimation is appropriate for preliminary data analysis the application of these methodologies is illustrated with a set of rainfall data and problems of implementation are discussed it is shown that the estimation of the parameters of the covariance function involves sizeable errors it is suggested that in practice it may be rather difficult to identify the parameters of all but simple models it is important that future research evaluate the effects of parameter uncertainty in the circulation of estimation error variances of point or areal averages and in the design of hydrologic data collection networks

examination of coherent surface reflection coefficient csrc approximations in shallow water propagation the parabolic wave equation pe code of rosenberg j acoust soc am 105 144 153 1999 is used as a benchmark to study acoustic propagation in an ocean waveguide with a rough air water interface the pe results allow a close examination of the ability of a ray code i e gaussian ray bundle grab to accurately estimate coherent field propagation using a coherent reflection coefficient derived from scattering theory comparison with pe implies that the beckmann spizzichino model as given within the grab software package does not give accurate predictions of the coherent field at long ranges three other coherent reflection coefficient approximations are tested the perturbation the small slope and the kirchhoff approximations the small slope approximation is the most accurate of the models tested however the kirchhoff approximation is perhaps accurate enough for some purposes and would be simpler to implement as a module within grab

minimum norm quadratic estimation of spatial variograms abstract the estimation of spatial variograms a measure of spatial correlation is a critical problem in the implementation of kriging a method for interpolating random fields we consider the use of minimum norm quadratic estimators of the variogram when it is specified up to a finite number of linear parameters we investigate the asymptotic behavior of such estimators for gaussian processes as the number of observations within some bounded region increases the basic conclusion is that we can estimate consistently those functions of the parameters and only those functions that have a nonnegligible impact asymptotically on the kriging procedure in general the behavior of the variogram over relatively short distances is the only aspect of the variogram that is asymptotically important as an example consider a gaussian process z on the real line with unknown constant mean and where is known as the semivariogram of the process and is a finite vector of unknown parameters suppose for 0

stochastic analysis of three dimensional flow in a bounded domain a commonly accepted first order approximation of the equation for steady state flow in a fully saturated spatially random medium has the form of poisson s equation this form allows for the advantageous use of green s functions to solve for the random output hydraulic heads in terms of a convolution over the random input the logarithm of hydraulic conductivity a solution for steady state three dimensional flow in an aquifer bounded above and below is presented consideration of these boundaries is made possible by use of green s functions to solve poisson s equation within the bounded domain the medium hydraulic conductivity is assumed to be a second order stationary random process as represented by a simple three dimensional covariance function upper and lower boundaries are taken to be no flow boundaries the mean flow vector lies entirely in the horizontal dimensions the resulting hydraulic head covariance function exhibits nonstationary effects resulting from the imposition of boundary conditions comparisons are made with existing infinite domain solutions

simulation of moisture deficits and areal interpolation by universal cokriging simulation models for calculating moisture deficits for areas of land require interpolation procedures to arrive from point observations to area covering statements we use both 1 calculate first interpolate later ci procedures which interpolate calculated model results for test locations and 2 procedures which interpolate basic soil data toward test locations followed by model calculations interpolate first calculate later ic procedures in this study several ci and ic procedures which simulate moisture deficits are compared by means of a test set of 100 observations yielding the mean standard error mse ci procedures consistently produced lower mse values than ic procedures parameters of the pseudocovariance function pcf which models the spatial structure of bivariate increments in universal cokriging were estimated by means of the restricted maximum likelihood procedure compared to universal kriging universal cokriging yielded comparable mse values but a lower mean variance of the prediction error best results in this study were obtained by pointwise simulation model calculations followed by statistical interpolations

a multi resolution approximation for massive spatial datasets abstractautomated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high resolution observations of spatial fields over large spatial regions if these datasets can be efficiently exploited they can provide new insights on a wide variety of issues however traditional spatial statistical techniques such as kriging are not computationally feasible for big datasets we propose a multi resolution approximation m ra of gaussian processes observed at irregular locations in space the m ra process is specified as a linear combination of basis functions at multiple levels of spatial resolution which can capture spatial structure from very fine to very large scales the basis functions are automatically chosen to approximate a given covariance function which can be nonstationary all computations involving the m ra including parameter inference and prediction are highly scalable for massive datasets crucially the inference algorithms can also be parallelize

statistical methods for regular monitoring data summary meteorological and environmental data that are collected at regular time intervals on a fixed monitoring network can be usefully studied combining ideas from multiple time series and spatial statistics particularly when there are little or no missing data this work investigates methods for modelling such data and ways of approximating the associated likelihood functions models for processes on the sphere crossed with time are emphasized especially models that are not fully symmetric in space time two approaches to obtaining such models are described the first is to consider a rotated version of fully symmetric models for which we have explicit expressions for the covariance function the second is based on a representation of space time covariance functions that is spectral in just the time domain and is shown to lead to natural partially nonparametric asymmetric models on the sphere crossed with time various models are applied to a data set of daily winds at 11 sites in ireland over 18 years spectral and space time domain diagnostic procedures are used to assess the quality of the fits the spectral in time modelling approach is shown to yield a good fit to many properties of the data and can be applied in a routine fashion relative to finding elaborate parametric models that describe the space time dependences of the data about as well

simulation of first and second order scattering by rough surfaces with a sound ray formalism the sound ray technique is developed to simulate rough surfaces scattering processes which are consistent with the kirchhoff approximation ka theory it is first proved that both approaches ka and sound rays lead to the same theoretical expression of the first order scattered intensity an algorithm based on the random generation of surfaces slopes is proposed together with some results computed for gaussian rough surfaces this algorithm could be used in room acoustics more as a physical substitute for the cosine lambert law of diffusion the method is then extended to the analysis of second order scattering effects which are not taken into account by ka this new approach does not require the generation of several profiles of rough surface however some assumptions must be made in order to derive a useful mathematical expression of the second order scattered intensity the first results obtained are fairly consistent with the present knowledge of multiple scattering effects e g enhanced backscattering for very rough surfaces but further work is needed to test the assumptions and to improve the method

an investigation of the small slope approximation for scattering from rough surfaces part ii numerical studies broschat s l and e i thorsos an investigation of the small slope approximation for scattering from rough surfaces part ii numerical studies j acoust soc am vol 101 no 5 2615 2625 may 1997 http dx doi org 10 1121 1 418502

a note on composite likelihood inference and model selection a composite likelihood consists of a combination of valid likelihood objects usually related to small subsets of data the merit of composite likelihood is to reduce the computational complexity so that it is possible to deal with large datasets and very complex models even when the use of standard likelihood or bayesian methods is not feasible in this paper we aim to suggest an integrated general approach to inference and model selection using composite likelihood methods in particular we introduce an information criterion for model selection based on composite likelihood we also describe applications to the modelling of time series of counts through dynamic generalised linear models and to the analysis of the well known old faithful geyser dataset

use of kriging models to approximate deterministic computer models the use of kriging models for approximation and metamodel based design and optimization has been steadily on the rise in the past decade the widespread usage of kriging models appears to be hampered by 1 the lack of guidance in selecting the appropriate form of the kriging model 2 computationally efficient algorithms for estimating the model s parameters and 3 an effective method to assess the resulting model s quality in this paper we compare 1 maximum likelihood estimation mle and cross validation cv parameter estimation methods for selecting a kriging model s parameters given its form and 2 and an r 2 of prediction and the corrected akaike information criterion for assessing the quality of the created kriging model permitting the comparison of different forms of a kriging model these methods are demonstrated with six test problems finally different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models

fourier analysis of irregularly spaced data on rd summary the purpose of the paper is to propose a frequency domain approach for irregularly spaced data on rd we extend the original definition of a periodogram for time series to that for irregularly spaced data and define non parametric and parametric spectral density estimators in a way that is similar to the classical approach introduction of the mixed asymptotics which are one of the asymptotics for irregularly spaced data makes it possible to provide asymptotic theories to the spectral estimators the asymptotic result for the parametric estimator is regarded as a natural extension of the classical result for regularly spaced data to that for irregularly spaced data empirical studies are also included to illustrate the frequency domain approach in comparisons with the existing spatial and frequency domain approaches

nonparametric estimation of nonstationary spatial covariance structure abstract estimation of the covariance structure of spatial processes is a fundamental prerequisite for problems of spatial interpolation and the design of monitoring networks we introduce a nonparametric approach to global estimation of the spatial covariance structure of a random function z x t observed repeatedly at times ti i 1 t at a finite number of sampling stations xi i 1 2 n in the plane our analyses assume temporal stationarity but do not assume spatial stationarity or isotropy we analyze the spatial dispersions var z xi t z xj t as a natural metric for the spatial covariance structure and model these as a general smooth function of the geographic coordinates of station pairs xi xj the model is constructed in two steps first using nonmetric multidimensional scaling mds we compute a two dimensional representation of the sampling stations for which a monotone function of interpoint distances ij approximates the spatial dispersions mds transforms the problem

the method of normalized correlations a fast parameter estimation method for random processes and isotropic random fields that focuses on short range dependence we focus on the inference of covariance parameters from spatial or temporal data using the method of normalized correlations monc we compare the monc with maximum likelihood estimation and weighted least squares using simulated data as well as gridded and scattered real data for the synthetic experiments none of the methods considered performed uniformly better than the others in terms of estimation accuracy and precision however for regularly spaced data the monc was significantly faster and practically insensitive to sample size for scattered data the monc s speed was reduced but still competitive potential applications of the monc include those involving large data sets and fast preconditioning

approximating likelihoods for large spatial data sets summary likelihood methods are often difficult to use with large irregularly sited spatial data sets owing to the computational burden even for gaussian models exact calculations of the likelihood for n observations require o n3 operations since any joint density can be written as a product of conditional densities based on some ordering of the observations one way to lessen the computations is to condition on only some of the past observations when computing the conditional densities we show how this approach can be adapted to approximate the restricted likelihood and we demonstrate how an estimating equations approach allows us to judge the efficacy of the resulting approximation previous work has suggested conditioning on those past observations that are closest to the observation whose conditional density we are approximating through theoretical numerical and practical examples we show that there can often be considerable benefit in conditioning on some distant observations as well

gaussian predictive process models for large spatial data sets with scientific data available at geocoded locations investigators are increasingly turning to spatial process models for carrying out statistical inference over the last decade hierarchical models implemented through markov chain monte carlo methods have become especially popular for spatial modelling given their flexibility and power to fit models that would be infeasible with classical methods as well as their avoidance of possibly inappropriate asymptotics however fitting hierarchical spatial models often involves expensive matrix decompositions whose computational complexity increases in cubic order with the number of spatial locations rendering such models infeasible for large spatial data sets this computational burden is exacerbated in multivariate settings with several spatially dependent response variables it is also aggravated when data are collected at frequent time points and spatiotemporal process models are used with regard to this challenge our contribution is to work with what we call predictive process models for spatial and spatiotemporal data every spatial or spatiotemporal process induces a predictive process model in fact arbitrarily many of them the latter models project process realizations of the former to a lower dimensional subspace thereby reducing the computational burden hence we achieve the flexibility to accommodate non stationary non gaussian possibly multivariate possibly spatiotemporal processes in the context of large data sets we discuss attractive theoretical properties of these predictive processes we also provide a computational template encompassing these diverse settings finally we illustrate the approach with simulated and real data sets

the validity of the perturbation approximation for rough surface scattering using a gaussian roughness spectrum the validity of the perturbation approximation for rough surface scattering is examined 1 by comparison with exact results obtained by solving an integral equation and 2 through comparison of low order perturbation predictions with higher order predictions the pressure release boundary condition is assumed and the field quantity calculated is the bistatic scattering cross section a gaussian roughness spectrum is used and the surfaces have height variations in only one direction it is found in general that the condition kh 1 k is the acoustic wavenumber h is the rms surface height is insufficient to guarantee the accuracy of first order or higher order perturbation theory when the surface correlation length l becomes too large or too small with h held fixed higher order perturbation terms can make larger contributions to the scattering cross section than lower order terms an explanation for this result is given the regions of validity for low order perturbation theory are also given th

stochastic analysis of spatial variability in two dimensional steady groundwater flow assuming stationary and nonstationary heads two dimensional steady groundwater flow in a confined aquifer with spatially variable transmissivity t is analyzed stochastically using spectral analysis and the theory of intrinsic random functions conditions that ensure a stationary statistically homogeneous head process are derived and using two convenient forms for the covariance function of the ln t process the head covariance function is studied in addition the head variogram is obtained for a particular nonstationary case and the asymptotic head variogram is derived under very general conditions results are compared to those obtained by gelhar 1976 for one and two dimensional phreatic flow and bakr et al 1978 for one and three dimensional confined flow multidimensional flow analysis results in a significantly reduced head variance the head correlation remains high over much greater distances than the ln t correlation the variogram obtained when stationary heads are assumed is identical to that obtained for nonstationary heads for dimensionless lag distances up to 2 times the correlation scale of the log transmissivity the variogram for nonstationary heads continues to grow logarithmically as lag distance increases independent of the form of the input covariance in the nonstationary case the conditions for stationarity are contrasted with the corresponding results obtained for the one and three dimensional cases of gutjahr and gelhar 1981 the head variance calculated from the stationary theory is found to agree with that of previous monte carlo simulations

a full scale approximation of covariance functions for large spatial data sets summary gaussian process models have been widely used in spatial statistics but face tremendous computational challenges for very large data sets the model fitting and spatial prediction of such models typically require o n3 operations for a data set of size n various approximations of the covariance functions have been introduced to reduce the computational cost however most existing approximations cannot simultaneously capture both the large and the small scale spatial dependence a new approximation scheme is developed to provide a high quality approximation to the covariance function at both the large and the small spatial scales the new approximation is the summation of two parts a reduced rank covariance and a compactly supported covariance obtained by tapering the covariance of the residual of the reduced rank approximation whereas the former part mainly captures the large scale spatial variation the latter part captures the small scale local variation that is unexplained by the former part by combining the reduced rank representation and sparse matrix techniques our approach allows for efficient computation for maximum likelihood estimation spatial prediction and bayesian inference we illustrate the new approach with simulated and real data sets

estimation and model identification for continuous spatial processes summary formal parameter estimation and model identification procedures for continuous domain spatial processes are introduced the processes are assumed to be adequately described by a linear model with residuals that follow a second order stationary gaussian random field and data are assumed to consist of noisy observations of the process at arbitrary sampling locations a general class of two dimensional rational spectral density functions with elliptic contours is used to model the spatial covariance function an iterative estimation procedure alleviates many of the computational difficulties of conventional maximum likelihood estimation for non lattice data the procedure is applied to several generated data sets and to an actual ground water data set

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

fractional derivative quantum fields at positive temperature abstract this paper considers fractional generalization of finite temperature klein gordon kg field and vector potential in covariant gauge and static temporal gauge fractional derivative quantum field at positive temperature can be regarded as a collection of infinite number of fractional thermal oscillators generalized riemann zeta function regularization and heat kernel techniques are used to obtain the high temperature expansion of free energy associated with the fractional kg field we also show that quantization of the fractional derivative fields can be carried out by using the parisi wu stochastic quantization

nondeterministic fuzzy automata to handle fuzzy uncertainty in system modeling nondeterministic finite automata have been generalized into fuzzy automata after a reexamination of the notions of fuzzy automata in the literature we ascertain that the fundamental property nondeterminism in nondeterministic finite automata has not been well embodied in the generalization in order to reflect nondeterminism in fuzzy automata we introduce nondeterministic fuzzy automata with or without e moves and fuzzy languages recognized by them like nondeterministic finite automata nondeterministic fuzzy automata provide a mathematical representation of nondeterministic dynamic fuzzy systems moreover we show that deterministic fuzzy automata nondeterministic fuzzy automata and nondeterministic fuzzy automata with e moves are all equivalent in the sense that they recognize the same class of fuzzy languages which is an extension of the well known equivalence among finite automata nondeterministic finite automata and nondeterministic finite automata with e moves

estimating space and space time covariance functions for large data sets a weighted composite likelihood approach in this article we propose two methods for estimating space and space time covariance functions from a gaussian random field based on the composite likelihood idea the first method relies on the maximization of a weighted version of the composite likelihood function while the second one is based on the solution of a weighted composite score equation this last scheme is quite general and could be applied to any kind of composite likelihood an information criterion for model selection based on the first estimation method is also introduced the methods are useful for practitioners looking for a good balance between computational complexity and statistical efficiency the effectiveness of the methods is illustrated through examples simulation experiments and by analyzing a dataset on ozone measurements

indirect adaptive type 2 fuzzy impulsive control of nonlinear systems in this paper a novel indirect adaptive interval type 2 fuzzy tracking control is proposed strategy with impulsive and lyapunov synthesis approach it handles the training data corrupted by noise or rule uncertainties for linear and nonlinear systems involving external disturbances in comparison with conventional methods the advocated approach guarantees closed loop stability the output tracking error of the overall system will converge to zero asymptotically by the generalized barbalat s lemma numerical simulations are given to illustrate the effectiveness of the proposed techniques

preaveraged localized orthogonal polynomial estimators for surface smoothing and partial differentiation abstract we propose a multivariate smoothing method based on products of localized orthogonal polynomial series estimators for a smooth regression surface in the fixed design regression model the estimation of partial derivatives is included the proposed method provides for automatic and efficient boundary modifications near the edges of the surface assuming that the boundary of the support of the regression function satisfies some regularity conditions by allowing for a preaveraging step the corresponding algorithms are speeded up considerably and are easy to implement computation of special boundary kernels as required by the kernel method to avoid edge effects is not necessary it is shown that under sufficient smoothness assumptions the global average mean squared error has the same optimal rate of convergence as the mean squared error at an interior point that is the boundary correction is asymptotically effective the method depends on two smoothing parameters one determining the amount

reduction methods of type 2 uncertain variables and their applications to solid transportation problem uncertainty theory is a branch of mathematics for dealing with realistic uncertainties arising out of complexity changeability and non decidability of practical environments an uncertain variable is defined as a function from the uncertainty space to the set of real numbers and is characterized by an uncertainty distribution this paper proposes the definition of type 2 uncertain variables within the framework of uncertainty theory through introduction of generalized uncertain measures and focuses on more complex twofold uncertainties some uncertainty reduction methods associated with type 2 uncertain variables are also proposed for convenience of applicability including reduction of optimistic value pessimistic value and expected value moreover four classes of type 2 uncertain variables are reduced to type 1 uncertain variables with specific uncertainty distributions type 2 uncertain optimization methods are applied to solving the fixed charge solid transportation problem with the type 2 uncertain parameters where the solution methods are also provided for the proposed models finally numerical experiments are implemented to demonstrate application and sensitivity analysis of the proposed approaches

speeding up neighborhood search in local gaussian process prediction recent implementations of local approximate gaussian process models have pushed computational boundaries for nonlinear nonparametric prediction problems particularly when deployed as emulators for computer experiments their flavor of spatially independent computation accommodates massive parallelization meaning that they can handle designs two or more orders of magnitude larger than previously however accomplishing that feat can still require massive computational horsepower here we aim to ease that burden we study how predictive variance is reduced as local designs are built up for prediction we then observe how the exhaustive and discrete nature of an important search subroutine involved in building such local designs may be overly conservative rather we suggest that searching the space radially that is continuously along rays emanating from the predictive location of interest is a far thriftier alternative our empirical work demonstrates that ray based search yields predictors with accur

non nested testing of spatial correlation we develop non nested tests in a general spatial spatio temporal or panel data context the spatial aspect can be interpreted quite generally in either a geographical sense or employing notions of economic distance or when parametric modelling arises in part from a common factor or other structure in the former case observations may be regularly spaced across one or more dimensions as is typical with much spatio temporal data or irregularly spaced across all dimensions both isotropic models and non isotropic models can be considered and a wide variety of correlation structures in the second case models involving spatial weight matrices are covered such as spatial autoregressive models the setting is sufficiently general to potentially cover other parametric structures such as certain factor models and vector valued observations and here our preliminary asymptotic theory for parameter estimates is of some independent value the test statistic is based on a gaussian pseudo likelihood ratio and is shown to have an asymptotic standard normal distribution under the null hypothesis that one of the two models is correct this limit theory rests strongly on a central limit theorem for the gaussian pseudo maximum likelihood parameter estimates a small monte carlo study of finite sample performance is included

the inviscid burgers equation with brownian initial velocity the law of the hopf cole solution of the inviscid burgers equation with brownian initial velocity is made explicit as examples of applications we investigate the smoothness of the solution the statistical distribution of the shocks we determine the exact hausdorff function of the lagrangian regular points and investigate the existence of lagrangian regular points in a fixed borel set

a new method of prediction for spatial regression models with correlated errors summary this paper deals with minimum mean squared error unbiased linear interpolation of a continuous domain spatial process based on a sparse set of irregularly spaced observations the process is assumed to be governed by a linear regression model with errors that follow a second order stationary gaussian random field a new method of prediction is developed that is compatible with the parameter estimation procedures of vecchia the result is a new likelihood based method for joint parameter estimation and prediction that can be applied to large or small data sets with irregularly spaced data simulated and observed data sets are analysed to illustrate the methods

approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations summary structured additive regression models are perhaps the most commonly used class of models in statistical applications it includes among others generalized linear models generalized additive models smoothing spline models state space models semiparametric regression spatial and spatiotemporal models log gaussian cox processes and geostatistical and geoadditive models we consider approximate bayesian inference in a popular subset of structured additive regression models latent gaussian models where the latent field is gaussian controlled by a few hyperparameters and with non gaussian response variables the posterior marginals are not available in closed form owing to the non gaussian response variables for such models markov chain monte carlo methods can be implemented but they are not without problems in terms of both convergence and computational time in some practical applications the extent of these problems is such that markov chain monte carlo sampling is simply not an appropriate tool for routine analysis we show that by using an integrated nested laplace approximation and its simplified version we can directly compute very accurate approximations to the posterior marginals the main benefit of these approximations is computational where markov chain monte carlo algorithms need hours or days to run our approximations provide more precise estimates in seconds or minutes another advantage with our approach is its generality which makes it possible to perform bayesian analysis in an automatic streamlined way and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged

simulation of the bird age structured population growth based on an interval type 2 fuzzy cellular structure in this paper an age structured population growth model based on a fuzzy cellular structure is proposed an age structured population growth model enables a better description of population dynamics in this paper the dynamics of a particular bird species is considered the dynamics is governed by the variation of natality mortality and emigration rates which in this work are evaluated using an interval type 2 fuzzy logic system the use of type 2 fuzzy logic enables handling the effects caused by environment heterogeneity on the population a set of fuzzy rules about population growth are derived from the interpretation of the ecological laws and the bird life cycle the proposed model is formulated using discrete mathematics within the framework of a fuzzy cellular structure the fuzzy cellular structure allows us to visualize the evolution of the population s spatial dynamics the spatial distribution of the population has a deep effect on its dynamics moreover the model enables not only to estimate the percentage of occupation on the cellular space when the species reaches its stable equilibrium level but also to observe the occupation patterns

fuzzy interpolative reasoning based on the ratio of fuzziness of rough fuzzy sets in this paper we propose a method to construct a polygonal rough fuzzy set from a set of polygonal fuzzy sets representing the aggregation of multiple experts opinions and propose a new fuzzy interpolative reasoning method for sparse fuzzy rule based systems based on the ratio of fuzziness of the constructed polygonal rough fuzzy sets where the values of the antecedent variables and the consequence variable appearing in the fuzzy rules are represented by the constructed polygonal rough fuzzy sets the proposed fuzzy interpolative reasoning method can overcome the drawbacks of the existing method due to the fact that it can deal with fuzzy interpolative reasoning using polygonal rough fuzzy sets and it gets more reasonable fuzzy interpolative reasoning results than the existing method

interval valued fuzzy sets representation on multiple antecedent fuzzy s implications and reasoning abstract interval valued fuzzy sets are used to represent multiple antecedent s implications based on normal forms where linguistic connectives antecedents and consequents are assumed to be fuzzy these intervals are represented equivalently with their lower and upper bounds general forms are given for the bounds of multiple antecedent fuzzy s implications bounds for multiple antecedent reasoning are also investigated based on the bounds of multiple antecedent s implications it is suggested that modification functions utilized in approximation analogical reasoning aar be determined in such a way that consequents deduced by aar fall within the bounds of the reasoning an example is given to show how the bounds might be used to choose a modification scheme in aar

a hybrid approach for image recognition combining type 2 fuzzy logic modular neural networks and the sugeno integral in this paper a hybrid approach for image recognition combining type 2 fuzzy logic modular neural networks and the sugeno integral is described interval type 2 fuzzy inference systems are used to perform edge detection and to calculate fuzzy densities for the decision process a type 2 fuzzy system is used for edge detection which is a pre processing applied to the training data for better use in the neural networks another type 2 fuzzy system calculates the fuzzy densities necessary for the sugeno integral which is used to integrate results of the neural network modules in this case fuzzy logic is shown to be a good methodology to improve the results of a neural system facilitating the representation of the human perception a comparative study is also made to verify that the proposed approach is better than existing approaches and improves the performance over type 1 fuzzy logic

accelerating asymptotically exact mcmc for computationally intensive models via local approximations abstractwe construct a new framework for accelerating markov chain monte carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood or of numerical models embedded therein our approach introduces local approximations of these models into the metropolis hastings kernel borrowing ideas from deterministic approximation theory optimization and experimental design previous efforts at integrating approximate models into inference typically sacrifice either the sampler s exactness or efficiency our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations we prove the ergodicity of our approximate markov chain showing that it samples asymptotically from the exact posterior distribution of interest we describe variations of the algorithm that employ either local polynomial approximations or local gaussian process regressors our theoretical results reinforce the key observation underlying this

a resampling based stochastic approximation method for analysis of large geostatistical data the gaussian geostatistical model has been widely used in modeling of spatial data however it is challenging to computationally implement this method because it requires the inversion of a large covariance matrix particularly when there is a large number of observations this article proposes a resampling based stochastic approximation method to address this challenge at each iteration of the proposed method a small subsample is drawn from the full dataset and then the current estimate of the parameters is updated accordingly under the framework of stochastic approximation since the proposed method makes use of only a small proportion of the data at each iteration it avoids inverting large covariance matrices and thus is scalable to large datasets the proposed method also leads to a general parameter estimation approach maximum mean log likelihood estimation which includes the popular maximum log likelihood estimation mle approach as a special case and is expected to play an important role

applications of type 2 fuzzy logic systems to forecasting of time series abstract in this paper we begin with a type 1 fuzzy logic system fls trained with noisy data we then demonstrate how information about the noise in the training data can be incorporated into a type 2 fls which can be used to obtain bounds within which the true noisefree output is likely to lie we do this with the example of a one step predictor for the mackey glass chaotic time series m c mackey l glass oscillation and chaos in physiological control systems science 197 1977 287 280 we also demonstrate how a type 2 fls can be used to obtain better predictions than those obtained with a type 1 fls

an interval type 2 fuzzy linmap method with approximate ideal solutions for multiple criteria decision analysis the purpose of this paper is to develop a linear programming technique for multidimensional analysis of preference linmap to address multiple criteria decision analysis problems within the interval type 2 fuzzy environment based on interval type 2 trapezoidal fuzzy numbers considering the issue of anchor dependency we use multiple anchor points in the decision making process and employ approximate positive ideal and negative ideal solutions as the points of reference selected useful properties of the approximate ideal solutions are also investigated in contrast to the classical linmap methods this paper directly generates approximate ideal solutions from the characteristics of all alternatives next this work presents the concept of closeness based indices using minkowski distances with approximate ideal solutions to develop a new approach for determining measurements of consistency and inconsistency under incomplete preference information on paired comparisons of the alternatives this paper provides a novel method that uses the concept of comprehensive closeness based indices to measure the poorness of fit and the goodness of fit by applying the consistency indices and inconsistency indices this work formulates an optimization problem that can be solved for the optimal weights of the criteria and thus acquires the best compromise alternative additionally this paper explores the problem of supplier selection and conducts a comparative discussion to validate the effectiveness and applicability of the proposed interval type 2 fuzzy linmap method with approximate ideal solutions furthermore the proposed method is applied to address a marketplace decision difficulty mpdd prone decision making problem to provide additional contributions for practical implications

scaling laws for the multidimensional burgers equation with quadratic external potential the reordering of the multidimensional exponential quadratic operator in coordinate momentum space see x wang c h oh and l c kwek 1998 j phys a math gen 31 4329 4336 is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions the solution to the multidimensional burgers equation with quadratic external potential under gaussian strongly dependent scenarios is also obtained via the hopf cole transformation the limiting distributions of scaling solutions to the multidimensional heat and burgers equations with quadratic external potential are then obtained under such scenarios

stochastic partial differential equation based modelling of large space time data sets summary increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data we show that the solution of a stochastic advection diffusion partial differential equation provides a flexible model class for spatiotemporal processes which is computationally feasible also for large data sets the gaussian process defined through the stochastic partial differential equation has in general a non separable covariance structure its parameters can be physically interpreted as explicitly modelling phenomena such as transport and diffusion that occur in many natural processes in diverse fields ranging from environmental sciences to ecology to obtain computationally efficient statistical algorithms we use spectral methods to solve the stochastic partial differential equation this has the advantage that approximation errors do not accumulate over time and that in the spectral space the computational cost grows linearly with the dimension the total computational cost of bayesian or frequentist inference being dominated by the fast fourier transform the model proposed is applied to post processing of precipitation forecasts from a numerical weather prediction model for northern switzerland in contrast with the raw forecasts from the numerical model the post processed forecasts are calibrated and quantify prediction uncertainty moreover they outperform the raw forecasts in the sense that they have a lower mean absolute error

type 1 and type 2 fuzzy inference systems as integration methods in modular neural networks for multimodal biometry and its optimization with genetic algorithms we describe in this paper a comparative study between fuzzy inference systems as methods of integration in modular neural networks for multimodal biometry these methods of integration are based on techniques of type 1 fuzzy logic and type 2 fuzzy logic also the fuzzy systems are optimized with simple genetic algorithms with the goal of having optimized versions of both types of fuzzy systems first we considered the use of type 1 fuzzy logic and later the approach with type 2 fuzzy logic the fuzzy systems were developed using genetic algorithms to handle fuzzy inference systems with different membership functions like the triangular trapezoidal and gaussian since these algorithms can generate fuzzy systems automatically then the response integration of the modular neural network was tested with the optimized fuzzy systems of integration the comparative study of the type 1 and type 2 fuzzy inference systems was made to observe the behavior of the two different integration methods for modular neural networks for multimodal biometry

maximum likelihood estimation of models for residual covariance in spatial regression we describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters observations are assumed to be gaussian we give conditions which ensure consistency and asymptotic normality of the estimators our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small sample behaviour of estimators we also discuss an application of the spectral approximation to the likelihood for processes on a lattice

spectral density estimation for random fields via periodic embeddings we introduce methods for estimating the spectral density of a random field on a formula see text dimensional lattice from incomplete gridded data data are iteratively imputed onto an expanded lattice according to a model with a periodic covariance function the imputations are convenient computationally in that circulant embedding and preconditioned conjugate gradient methods can produce imputations in formula see text time and formula see text memory however these so called periodic imputations are motivated mainly by their ability to produce accurate spectral density estimates in addition we introduce a parametric filtering method that is designed to reduce periodogram smoothing bias the paper contains theoretical results on properties of the imputed data periodogram and numerical and simulation studies comparing the performance of the proposed methods to existing approaches in a number of scenarios we present an application to a gridded satellite surface temperature dataset with missing values

compressed gaussian process for manifold regression nonparametric regression for large numbers of features p is an increasingly important problem if the sample size n is massive a common strategy is to partition the feature space and then separately apply simple models to each partition set this is not ideal when n is modest relative to p and we propose an alternative approach relying on random compression of the feature vector combined with gaussian process regression the proposed approach is particularly motivated by the setting in which the response is conditionally independent of the features given the projection to a low dimensional manifold conditionally on the random compression matrix and a smoothness parameter the posterior distribution for the regression surface and posterior predictive distributions are available analytically running the analysis in parallel for many random compression matrices and smoothness parameters model averaging is used to combine the results the algorithm can be implemented rapidly even in very large p and moderately large n nonparametric regression has strong theoretical justification and is found to yield state of the art predictive performance

a hybrid learning algorithm for a class of interval type 2 fuzzy neural networks in real life information about the world is uncertain and imprecise the cause of this uncertainty is due to deficiencies on given information the fuzzy nature of our perception of events and objects and on the limitations of the models we use to explain the world the development of new methods for dealing with information with uncertainty is crucial for solving real life problems in this paper three interval type 2 fuzzy neural network it2fnn architectures are proposed with hybrid learning algorithm techniques gradient descent backpropagation and gradient descent with adaptive learning rate backpropagation at the antecedents layer a interval type 2 fuzzy neuron it2fn model is used and in case of the consequents layer an interval type 1 fuzzy neuron model it1fn in order to fuzzify the rule s antecedents and consequents of an interval type 2 takagi sugeno kang fuzzy inference system it2 tsk fis it2 tsk fis is integrated in an adaptive neural network in order to take advantage the best of both models this provides a high order intuitive mechanism for representing imperfect information by means of use of fuzzy if then rules in addition to handling uncertainty and imprecision on the other hand neural networks are highly adaptable with learning and generalization capabilities experimental results are divided in two kinds in the first one a non linear identification problem for control systems is simulated here a comparative analysis of learning architectures it2fnn and anfis is done for the second kind a non linear mackey glass chaotic time series prediction problem with uncertainty sources is studied finally it2fnn proved to be more efficient mechanism for modeling real world problems

higher order spectral densities of fractional random fields this paper presents the second and higher order spectral densities of stationary in space random fields arising as approximations of rescaled solutions of the heat and fractional heat equations with singular initial conditions the development is based on the diagram formalism and the riesz composition formula our results are the first step to full parametrization of higher order spectra of some classes of fractional random fields

spectral properties of burgers and kpz turbulence this paper presents the higher order spectral densities of non gaussian random fields arising as scaling limits in the burgers and kpz turbulence problems with strongly dependent non gaussian initial conditions

on semiparametric inference of geostatistical models via local karhunen loeve expansion summary we develop a semiparametric approach to geostatistical modelling and inference in particular we consider a geostatistical model with additive components where the form of the covariance function of the spatial random error is not prespecified and thus is flexible a novel local karhunen loeve expansion is developed and a likelihood based method is devised for estimating the model parameters and statistical inference a simulation study demonstrates sound finite sample properties and a real data example is given for illustration finally the theoretical properties of the estimates are explored and in particular consistency results are established

the collapsing method of defuzzification for discretised interval type 2 fuzzy sets this paper proposes a new approach for defuzzification of interval type 2 fuzzy sets the collapsing method converts an interval type 2 fuzzy set into a type 1 representative embedded set res whose defuzzified values closely approximates that of the type 2 set as a type 1 set the res can then be defuzzified straightforwardly the novel representative embedded set approximation resa to which the method is inextricably linked is expounded stated and proved within this paper it is presented in two forms simple resa this approximation deals with the most simple interval fou in which a vertical slice is discretised into 2 points interval resa this approximation concerns the case in which a vertical slice is discretised into 2 or more points the collapsing method simple resa version was tested for accuracy and speed with excellent results on both criteria the collapsing method proved more accurate than the karnik mendel iterative procedure kmip for an asymmetric test set for both a symmetric and an asymmetric test set the collapsing method outperformed the kmip in relation to speed