bayesian guided pattern search for robust local optimization optimization for complex systems in engineering often involves the use of expensive computer simulation by combining statistical emulation using treed gaussian processes with pattern search optimization we are able to perform robust local optimization more efficiently and effectively than when using either method alone our approach is based on the augmentation of local search patterns with location sets generated through improvement prediction over the input space we further develop a computational framework for asynchronous parallel implementation of the optimization algorithm we demonstrate our methods on two standard test problems and our motivating example of calibrating a circuit device simulator

a new approach to multipath correction of constant modulus signals an adaptive digital filtering algorithm that can compensate for both frequency selective multipath and interference on constant envelope modulated signals is presented the method exploits the fact that multipath reception and various interference sources generate incidental amplitude modulation on the received signal a class of so called constant modulus performance functions is developed which sense this am term but are insensitive to the angle modulation simple adaptive algorithms for finite impulse response fir digital filters are developed which employ a gradient search of the performance function one of the resulting algorithms is simulated for the example of an fm signal degraded by specular multipath propagation substantial improvements in noise power ratio npr are observed e g 25 db with moderately rapid convergence time these results are then extended to include tonal interference on a fm signal and intersymbol interference on a qpsk data signal

a nonparametric multidimensional latent class irt model in a bayesian framework we propose a nonparametric item response theory model for dichotomously scored items in a bayesian framework the model is based on a latent class lc formulation and it is multidimensional with dimensions corresponding to a partition of the items in homogenous groups that are specified on the basis of inequality constraints among the conditional success probabilities given the latent class moreover an innovative system of prior distributions is proposed following the encompassing approach in which the largest model is the unconstrained lc model a reversible jump type algorithm is described for sampling from the joint posterior distribution of the model parameters of the encompassing model by suitably post processing its output we then make inference on the number of dimensions i e number of groups of items measuring the same latent trait and we cluster items according to the dimensions when unidimensionality is violated the approach is illustrated by two examples on simulated data and two applications based on educational and quality of life data

on the non existence of undesirable equilibria of godard blind equalizers existing results in the literature have proved that particular blind equalization algorithms including godard algorithms are globally convergent in an ideal and nonimplementable setting where a doubly infinite dimensional equalizer is available for adaptation contrary to popular conjectures it is shown that implementable finite dimensional equalizers which attempt to approximate the ideal setting generally fail to have global convergence to acceptable equalizer parameter settings without the use of special remedial measures a theory based on the channel convolution matrix nullspace is proposed to explain the failure of godard algorithms for such practical blind equalization situations this nullspace theory is supported by a simple example showing ill convergence of the godard algorithm

fast and low complexity blind equalization via subgradient projections we propose a novel blind equalization method based on subgradient search over a convex cost surface this is an alternative to the existing iterative blind equalization approaches such as the constant modulus algorithm cma which often suffer from the convergence problems caused by their nonconvex cost functions the proposed method is an iterative algorithm called subgradient based blind algorithm sgba for both real and complex constellations with a very simple update rule it is based on the minimization of the l sub spl infin norm of the equalizer output under a linear constraint on the equalizer coefficients using subgradient iterations the algorithm has a nice convergence behavior attributed to the convex l sub spl infin cost surface as well as the step size selection rules associated with the subgradient search we illustrate the performance of the algorithm using examples with both complex and real constellations where we show that the proposed algorithm s convergence is less sensitive to initial point selection and a fast convergence behavior can be achieved with a judicious selection of step sizes furthermore the amount of data required for the training of the equalizer is significantly lower than most of the existing schemes

a fast linear programming algorithm for blind equalization a fast implementation of a special non mse cost function for blind equalization is presented here this baud rate equalization algorithm is based on a convex cost function coupled with a simple linear constraint on the equalizer parameters for a generic class of channels with persistently exciting quadrature amplitude modulation input signals this new algorithm allows the convergence of equalizer parameters to a unique global minimum achieving intersymbol interference suppression and carrier phase recovery

a quadratic programming approach to blind equalization and signal separation blind equalization and signal separation are two well established signal processing problems in this paper we present a quadratic programming algorithm for fast blind equalization and signal separation by introducing a special non mean square error mse objective function we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem based on a clear geometric interpretation and a formal proof we show that a perfect equalization solution is obtained at every local optimum of the quadratic program because blind source separation is by nature and mathematically a closely related problem we also generalize the algorithm for blind signal separation we show that by enforcing source orthogonalization through successive processing the quadratic programming approach can be applied effectively moreover the quadratic program is easily extendible to incorporate additional practical conditions such as jamming suppression constraints we also provide evidence of good performance through computer simulations

a linear programming receiver for blind detection of full rate space time block codes we present a new approach to the blind detection of full rate space time block coded transmissions our method is based on linear programming and is globally convergent we exploit the implicit structure of space time block codes to cast the problem as linear programming to be solved efficiently unlike several known methods the proposed technique is applicable to full rate space time block codes such as the popular alamouti orthogonal code and the quasi orthogonal space time code moreover we utilize the code structure of these full rate codes to achieve simultaneous detection of all coded data streams without relying on successive schemes that are prone to error propagation for orthogonal space time codes our algorithm allows near maximum likelihood detection of orthogonal codes without channel knowledge we also can generalize the application of the proposed receiver to be used with nonorthogonal codes our proposed algorithm can provide performance competitive with existing techniques without imposing any conditions on the number of receive antennas

an efficient method to determine the diagonal loading factor using the constant modulus feature the diagonal loading method is a simple and efficient method that improves the robustness of beamformers however determining an ideal diagonal loading factor dlf is not a trivial problem one that still has not been adequately addressed although beamformers are widely used in radar sonar and many other applications in this correspondence we consider a beamformer used only for digital communication applications in digital communications user information is coded into a sequence with the constant modulus cm in the baseband obviously if the beamformer can cancel interference sufficiently well the outputs of the beamformer should satisfy the cm condition more precisely therefore minimizing cm errors can act as a natural criterion for determining dlfs in this correspondence we present a cost function based on the criterion we also propose a direct search algorithm for dlf determination by minimizing the cost function numerical experiments show the effectiveness of the proposed method

joint detection and decoding in ldpc based space time coded mimo ofdm systems via linear programming this work proposes a novel linear programming approach for the joint detection and decoding of ldpc based space time st coded signals in multi antenna orthogonal frequency division multiplexing ofdm systems while traditional receivers typically decouple the detection and decoding processes as two disjunctive blocks or require iterative turbo exchange of extrinsic information between the soft detector and decoder we formulate a joint linear program lp by exploiting the constraints imposed on the data symbols training symbols noise subspace as well as channel code in consideration of the vast amount of ldpc parity check inequalities we further present an adaptive procedure to significantly reduce the complexity of the joint lp receiver our lp based receivers outperform existing receivers with substantial performance gains moreover the proposed joint lp receiver demonstrates strong robustness when pilot symbols are sparsely arranged on subcarriers

periodic solutions of lagrangian systems on a compact manifold abstract let m be a smooth n dimensional manifold and let tm be its tangent bundle we consider a time periodic lagrangian of period t l t tm r and we seek t periodic solutions of the lagrange equations which in local coordinates are d dt l q t q q l q t q q 0 i 1 n our main result states that if the fundamental group of m is finite then has infinitely many t periodic solutions provided that l t satisfies certain physically reasonable assumptions

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

stochastic identification of imperfections in a submerged shell structure abstract accurate predictions of the buckling load in imperfection sensitive shell structures requires precise knowledge of the location and magnitude of any geometric imperfections in the shell e g dents this work describes a non contact approach to identifying such imperfections in a submerged shell structure by monitoring the acoustic pressure field at discrete points proximal to a shell structure excited by a cyclic membrane i e in plane loading it is noticed that parameters describing small scale denting can be identified in order to perform the identification a fluid structure model that predicts the spatio temporal pressure field is required this model is described in detail and includes the predicted effects of the imperfection on the observations a bayesian markov chain monte carlo approach is then used to generate the imperfection parameter estimates and quantify the uncertainty in those estimates additionally for cases involving the occurrence of an unknown number of dents reversible jump markov chain monte carlo rjmcmc methods are employed in this work

branches of forced oscillations for periodically perturbed second order autonomous odes on manifolds where h tm r and f r tm r are continuous vector fields tangent to a differentiable manifold m embedded in some euclidean space r and f is t periodic in t here x represents the component of the acceleration parallel to m this equation governs the motion of a constrained mechanical system with configuration space m acted on by the sum of two forces an autonomous one h and a periodic perturbation f this motion problem reduces to that of 3 and 2 when h 0 nevertheless our results do not include those of 3 unless the manifold m is compact as in 2 we investigate the properties of the set x of t pairs of 1 i e of those pairs x 0 c t m with x a t periodic solution of 1 in article id jdeq 1998 3557 available online at http www idealibrary com on

bayesian wavelet networks for nonparametric regression radial wavelet networks have been proposed previously as a method for nonparametric regression we analyze their performance within a bayesian framework we derive probability distributions over both the dimension of the networks and the network coefficients by placing a prior on the degrees of freedom of the model this process bypasses the need to test or select a finite number of networks during the modeling process predictions are formed by mixing over many models of varying dimension and parameterization we show that the complexity of the models adapts to the complexity of the data and produces good results on a number of benchmark test series

convergence analysis of self adaptive equalizers a theoretical analysis of self adaptive equalization for data transmission is carried out starting from known convergence results for the corresponding trained adaptive filter the development relies on a suitable ergodicity model for the sequence of observations at the output of the transmission channel thanks to the boundedness of the decision function used for data recovery it can be proved that the algorithm is bounded strong convergence results can be reached when a perfect noiseless equalizer exists the algorithm will converge to it if the eye pattern is initially open otherwise convergence may take place towards certain other stationary points of the algorithm for which domains of attraction have been defined some of them will result in a poor error rate the case of a noisy channel exhibits limit points for the algorithm that differ from those of the classical trained algorithm the stronger the noise the greater the difference is one of the principal results of this study is the proof of the stability of the usual decision feedback algorithms once the learning period is over

robust full bayesian learning for radial basis networks we propose a hierarchical full bayesian model for radial basis networks this model treats the model dimension number of neurons model parameters regularization parameters and noise parameters as unknown random variables we develop a reversible jump markov chain monte carlo mcmc method to perform the bayesian computation we find that the results obtained using this method are not only better than the ones reported previously but also appear to be robust with respect to the prior specification in addition we propose a novel and computationally efficient reversible jump mcmc simulated annealing algorithm to optimize neural networks this algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis function it performs a global search in the joint space of the parameters and number of parameters thereby surmounting the problem of local minima to a large extent we show that by calibrating the full hierarchical bayesian prior we can obtain the classical akaike information criterion bayesian information criterion and minimum description length model selection criteria within a penalized likelihood framework finally we present a geometric convergence theorem for the algorithm with homogeneous transition kernel and a convergence theorem for the reversible jump mcmc simulated annealing method

forced oscillations of a massive point on a compact surface with a boundary abstract we present sufficient conditions for the existence of a periodic solution for a class of systems describing the periodically forced motion of a massive point on a compact surface with a boundary

product partition models for change point problems product partition models assume that observations in different components of a random partition of the data are independent if the probability distribution of random partitions is in a certain product form prior to making the observations it is also in product form given the observations the product model thus provides a convenient machinery for allowing the data to weight the partitions likely to hold and inference about particular future observations may then be made by first conditioning on the partition and then averaging over all partitions these models apply with special computational simplicity to change point problems where the partitions divide the sequence of observations into components within which different regimes hold we show with appropriate selection of prior product models that the observations can eventually determine approximately the true partition

applications of convex optimization in signal processing and digital communication in the last two decades the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization these advances have recently started to significantly impact various fields of applied sciences and engineering where computational efficiency is essential this paper focuses on two such fields digital signal processing and communication in the past the widely used optimization methods in both fields had been the gradient descent or least squares methods both of which are known to suffer from the usual headaches of stepsize selection algorithm initialization and local minima with the recent advances in conic and robust optimization the opportunity is ripe to use the newly developed interior point optimization techniques and highly efficient software tools to help advance the fields of signal processing and digital communication this paper surveys recent successes of applying interior point and robust optimization to solve some core problems in these two fields the successful applications considered in this paper include adaptive filtering robust beamforming design and analysis of multi user communication system channel equalization decoding and detection throughout our emphasis is on how to exploit the hidden convexity convex reformulation of semi infinite constraints analysis of convergence complexity and performance as well as efficient practical implementation

moment conditions and bayesian non parametrics models phrased through moment conditions are central to much of modern inference here these moment conditions are embedded within a non parametric bayesian set up handling such a model is not probabilistically straightforward as the posterior has support on a manifold we solve the relevant issues building new probability and computational tools by using hausdorff measures to analyse them on real and simulated data these new methods which involve simulating on a manifold can be applied widely including providing bayesian analysis of quasi likelihoods linear and non linear regression missing data and hierarchical models

finite mixture varying coefficient models for analyzing longitudinal heterogenous data this paper aims to develop a mixture model to study heterogeneous longitudinal data on the treatment effect of heroin use from a california civil addict program each component of the mixture is characterized by a varying coefficient mixed effect model we use the bayesian p splines approach to approximate the varying coefficient functions we develop markov chain monte carlo algorithms to estimate the smooth functions unknown parameters and latent variables in the model we use modified deviance information criterion to determine the number of components in the mixture a simulation study demonstrates that the modified deviance information criterion selects the correct number of components and the estimation of unknown quantities is accurate we apply the proposed model to the heroin treatment study furthermore we identify heterogeneous longitudinal patterns copyright 2011 john wiley sons ltd

modeling a poisson forest in variable elevations a nonparametric bayesian approach summary a nonparametric bayesian formulation is given to the problem of modeling nonhomogeneous spatial point patterns influenced by concomitant variables only incomplete information on the concomitant variables is assumed consisting of a relatively small number of point measurements residual variation caused by other unmeasured influential factors is modeled in terms of a spatially varying baseline intensity function a markov chain monte carlo scheme is proposed for the simultaneous nonparametric estimation of each unknown function in the model the suggested method is illustrated by reanalysing a data set in rathbun 1996 biometrics52 226 242 and the estimated models are compared with those obtained by rathbun

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

bayesian survival analysis using a mars model a bayesian multivariate adaptive regression spline fitting approach is used to model univariate and multivariate survival data with censoring the possible models contain the proportional hazards model as a subclass and automatically detect departures from this a reversible jump markov chain monte carlo algorithm is described to obtain the estimate of the hazard function as well as the survival curve

bayesian nonparametric modeling using mixtures of triangular distributions nonparametric modeling is an indispensable tool in many applications and its formulation in an hierarchical bayesian context using the entire posterior distribution rather than particular expectations increases its flexibility in this article the focus is on nonparametric estimation through a mixture of triangular distributions the optimality of this methodology is addressed and bounds on the accuracy of this approximation are derived although our approach is more widely applicable we focus for simplicity on estimation of a monotone nondecreasing regression on 0 1 with additive error effectively approximating the function of interest by a function having a piecewise linear derivative computationally accessible methods of estimation are described through an amalgamation of existing markov chain monte carlo algorithms simulations and examples illustrate the approach

screening based on the risk of cancer calculation from bayesian hierarchical changepoint and mixture models of longitudinal markers the standard approach to early detection of disease with a quantitative marker is to set a population based fixed reference level for making further individual screening or referral decisions for many types of disease including prostate and ovarian cancer additional information is contained in the subject specific temporal behavior of the marker which exhibits a characteristic alteration early in the course of the disease in this article we derive a bayesian approach to screening based on calculation of the posterior probability of disease given longitudinal marker levels the method is motivated by a randomized ovarian cancer screening trial in the united kingdom comprising 22 000 women screened over 4 years with an additional 5 years of follow up on average levels of the antigen ca125 were recorded annually in the screened arm ca125 profiles of cases and controls from the u k trial are modeled using hierarchical changepoint and mixture models posterior distributions are calculated using markov

on the set of harmonic solutions of periodically perturbed autonomous differential equations on manifolds where g m r and f r m r are continuous vector fields tangent to a not necessarily closed boundaryless differentiable manifold m r with f t periodic with respect to the first variable we investigate the structure of the set of solution pairs of 1 i e of those pairs x 0 ct m such that x is a necessarily t periodic solution of 1 we give conditions ensuring the existence of a non compact connected component of solution pairs x of 1 which emanates from the set of constant solutions of the unperturbed equation

a bayesian analysis for change point problems a sequence of observations undergoes sudden changes at unknown times we model the process by supposing that there is an underlying sequence of parameters partitioned into contiguous blocks of equal parameter values the beginning of each block is said to be a change point observations are then assumed to be independent in different blocks given the sequence of parameters in a bayesian analysis it is necessary to give probability distributions to both the change points and the parameters we use product partition models barry and hartigan 1992 which assume that the probability of any partition is proportional to a product of prior cohesions one for each block in the partition and that given the blocks the parameters in different blocks have independent prior distributions given the observations a new product partition model holds with posterior cohesions for the blocks and new independent block posterior distributions for parameters the product model thus provides a convenient machinery for allo

sequential tests for large scale learning we argue that when faced with big data sets learning and inference algorithms should compute updates using only subsets of data items we introduce algorithms that use sequential hypothesis tests to adaptively select such a subset of data points the statistical properties of this subsampling process can be used to control the efficiency and accuracy of learning or inference in the context of learning by optimization we test for the probability that the update direction is no more than 90 degrees in the wrong direction in the context of posterior inference using markov chain monte carlo we test for the probability that our decision to accept or reject a sample is wrong we experimentally evaluate our algorithms on a number of models and data sets

convex cost functions in blind equalization existing blind adaptive equalizers that use nonconvex cost functions and stochastic gradient descent suffer from lack of global convergence to an equalizer setup that removes sufficient isi when an fir equalizer is used the authors impose convexity on the cost function and anchoring of the equalizer away from the all zero setup they establish that there exists a globally convergent blind equalization strategy for 1d pulse amplitude modulation pam systems with bounded input data discrete or continuous even when the equalizer is truncated the resulting cost function is a constrained l sub 1 norm of the joint impulse response of the channel and the equalizer the results apply to arbitrary linear channels provided there are no unit circle zeros and apply regardless of the initial isi that is whether the eye is initially open or closed they also show a globally convergent stochastic gradient scheme based on an implementable approximation of the l sub 1 cost function

solving the meg inverse problem a robust two way regularization method magnetoencephalography meg is a common noninvasive imaging modality for instantly measuring whole brain activities one challenge in meg data analysis is how to minimize the impact of the outliers that commonly exist in the images in this article we propose a robust two way regularization approach to solve the important meg inverse problem that is reconstructing neuronal activities using the measured meg signals the proposed method is based on the distributed source model and produces a spatio temporal solution for all the dipoles simultaneously unlike the traditional methods that use the squared error loss function our proposal uses a robust loss function which improves the robustness of the results against outliers to impose desirable spatial focality and temporal smoothness we then penalize the robust loss through appropriate spatial temporal two way regularization furthermore an alternating reweighted least squares algorithm is developed to optimize the penalized model fitting criterion

bayesian analysis of quantitative trait locus data using reversible jump markov chain monte carlo the advent of molecular markers has created a great potential for the understanding of quantitative inheritance in plants as well as in animals taking the newly available data into account biometric models have been constructed for the mapping of quantitative trait loci qtls in current approaches the lack of knowledge on the number and location of the most important qtls contributing to a trait is a major problem in this paper we utilize reversible jump markov chain monte carlo methodology green 1995 biometrika 82 711 732 in order to compute the posterior quantities required for fully bayesian inference it yields posterior densities not only for the parameters given the number of qtl but also for the number of qtl itself as an example the algorithm is applied to simulated data according to a standard design in plant breeding

reformulation of linearly constrained adaptation and its application to blind equalization this work introduces a reformulation of general linearly constrained equalization using a fixed prefilter plus adaptive equalizer subject to a single constrained tap this connection is exploited to simplify and improve an early result of lucky 1965 on equalization and to derive an optimum though nonblind linear constraint for a broad class of cost functions based on the insights gained we briefly suggest that a globally convergent adaptation scheme can be formulated by either generalizing the parameter constraint or generalizing the specific cost to a general convex cost and also note that such a scheme may be applied to blind equalization

model determination for categorical data with factor level merging we deal with contingency table data that are used to examine the relationships between a set of categorical variables or factors we assume that such relationships can be adequately described by the conditional independence structure that is imposed by an undirected graphical model if the contingency table is large a desirable simplified interpretation can be achieved by combining some categories or levels of the factors we introduce conditions under which such an operation does not alter the markov properties of the graph implementation of these conditions leads to bayesian model uncertainty procedures based on reversible jump markov chain monte carlo methods the methodology is illustrated on a 2 x 3 x 4 and up to a 4 x 5 x 5 x 2 x 2 contingency table

joint bayesian model selection and parameter estimation of the generalized extreme value model with covariates using birth death markov chain monte carlo 1 this paper describes bayesian estimation of the parameters of the generalized extreme value gev model with covariates for this model the parameters of the gev distribution are functions of covariates allowing for dependent parameters and or trends a markov chain monte carlo mcmc algorithm is generally used to estimate the posterior distributions of the parameters in a bayesian framework in this paper the birth death mcmc bdmcmc procedure is developed in order to carry out both parameter estimation and bayesian model selection the bdmcmc methods allow the jump between models of different dimensions the general algorithm consists of two types of sampling steps the first one involves dimension changing moves and the second is conditional on a fixed model parameters are estimated in a fully bayesian framework and the model is selected by the length of time that the mcmc chain remains in that model real and simulated data sets illustrate the usefulness of the proposed methodology

combining minimax shrinkage estimators abstract when one estimates a multivariate normal mean the use of stein estimation entails both the grouping of coordinates and the selection of a set of targets toward which to shrink each group in this article we propose new minimax multiple shrinkage estimators that allow for multiple specifications of these aspects we provide examples that are evaluated on real and simulated data including an estimator that adaptively resolves the issue of combining possibly related estimation problems and an adaptive clustering shrinkage estimator the construction and properties of these estimators are shown to follow from the application of the multiple shrinkage results of george 1986a to general partitioned shrinkage estimators

variational learning for finite dirichlet mixture models and applications in this paper we focus on the variational learning of finite dirichlet mixture models compared to other algorithms that are commonly used for mixture models such as expectation maximization our approach has several advantages first the problem of over fitting is prevented furthermore the complexity of the mixture model i e the number of components can be determined automatically and simultaneously with the parameters estimation as part of the bayesian inference procedure finally since the whole inference process is analytically tractable with closed form solutions it may scale well to large applications both synthetic and real data generated from real life challenging applications namely image databases categorization and anomaly intrusion detection are experimented to verify the effectiveness of the proposed approach

variational bayesian inversion of the equivalent current dipole model in eeg meg in magneto and electroencephalography m eeg spatial modelling of sensor data is necessary to make inferences about underlying brain activity most source reconstruction techniques belong to one of two approaches point source models which explain the data with a small number of equivalent current dipoles and distributed source or imaging models which use thousands of dipoles much methodological research has been devoted to developing sophisticated bayesian source imaging inversion schemes while dipoles have received less such attention dipole models have their advantages they are often appropriate summaries of evoked responses or helpful first approximations here we propose a variational bayesian algorithm that enables the fast bayesian inversion of dipole models the approach allows for specification of priors on all the model parameters the posterior distributions can be used to form bayesian confidence intervals for interesting parameters like dipole locations furthermore competing models e g models with different numbers of dipoles can be compared using their evidence or marginal likelihood using synthetic data we found the scheme provides accurate dipole localizations we illustrate the advantage of our bayesian scheme using a multi subject eeg auditory study where we compare competing models for the generation of the n100 component

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

multiple solutions of the periodic boundary value problem for some forced pendulum type equations if f x c 0 and e is a constant t then integrating 0 1 over 0 272 after multiplication of both members of the equation by x shows that the only possible solutions are constant and hence satisfy a sin x c consequently if we exclude the trivial translation by a multiple of 275 0 1 will have no solution if dj a one solution if lp a and two solutions if lc l a in 0th er t erms the intersection of the range of the operator d2 dt2 c d dt f u sin acting on zn periodic functions of class g with the subspace of constant functions in the space c o 2711 of real continuous functions on 0 27r is the closed interval a a whose interior points are images of two distinct solutions and boundary points of one we try to obtain similar results for the case where e is no more constant and

bayesian analysis of a poisson process with a change point summary a bayesian approach to estimation and hypothesis testing for a poisson process with a change point is developed and an example given

a bayesian method for combining results from several binomial experiments abstract the problem of combining information related to i binomial experiments each having a distinct probability of success i is considered instead of using a standard exchangeable prior for 1 i we propose a more flexible distribution that takes into account various degrees of similarity among the i s using ideas developed by malec and sedransk we consider a partition g of the experiments and take the i s belonging to the same partition subset to be exchangeable and the i s belonging to distinct subsets to be independent next we perform bayesian inference on conditional on g of course one is typically uncertain about which partition to use and so a prior distribution is assigned on a set of plausible partitions g the final inference on is obtained by combining the conditional inferences according to the posterior distribution of g the methodology adopted in this article offers a wide flexibility in structuring the dependence among the i s this allows the

efficient posterior exploration of a high dimensional groundwater model from two stage markov chain monte carlo simulation and polynomial chaos expansion 1 this study reports on two strategies for accelerating posterior inference of a highly parameterized and cpu demanding groundwater flow model our method builds on previous stochastic collocation approaches e g marzouk and xiu 2009 and marzouk and najm 2009 and uses generalized polynomial chaos gpc theory and dimensionality reduction to emulate the output of a large scale groundwater flow model the resulting surrogate model is cpu efficient and serves to explore the posterior distribution at a much lower computational cost using two stage mcmc simulation the case study reported in this paper demonstrates a two to five times speed up in sampling efficiency

practical bayesian density estimation using mixtures of normals abstract mixtures of normals provide a flexible model for estimating densities in a bayesian framework there are some difficulties with this model however first standard reference priors yield improper posteriors second the posterior for the number of components in the mixture is not well defined if the reference prior is used third posterior simulation does not provide a direct estimate of the posterior for the number of components we present some practical methods for coping with these problems finally we give some results on the consistency of the method when the maximum number of components is allowed to grow with the sample size

multiplicity of forced oscillations for the spherical pendulum acted on by a retarded periodic force abstract we prove a multiplicity result for forced oscillations of a spherical pendulum that is a massive point moving on a sphere subject to a periodic action with or without friction allowed to depend on the whole past of the motion the approach is based on topological methods in particular when the unperturbed forcing term is the gravity we obtain two harmonic forced oscillations regardless of the presence of friction and of the form of the perturbing force field

forced oscillations on manifolds and multiplicity results for periodically perturbed autonomous systems some qualitative results for forced oscillations on differentiable manifolds are obtained which cannot be deduced via variational or implicit function methods

bayesian generalized kernel mixed models we propose a fully bayesian methodology for generalized kernel mixed models gkmms which are extensions of generalized linear mixed models in the feature space induced by a reproducing kernel we place a mixture of a point mass distribution and silverman s g prior on the regression vector of a generalized kernel model gkm this mixture prior allows a fraction of the components of the regression vector to be zero thus it serves for sparse modeling and is useful for bayesian computation in particular we exploit data augmentation methodology to develop a markov chain monte carlo mcmc algorithm in which the reversible jump method is used for model selection and a bayesian model averaging method is used for posterior prediction when the feature basis expansion in the reproducing kernel hilbert space is treated as a stochastic process this approach can be related to the karhunen loeve expansion of a gaussian process gp thus our sparse modeling framework leads to a flexible approximation method for gps

ill convergence of godard blind equalizers in data communication systems the existence of stable undesirable equilibria for the godard algorithm is demonstrated through a simple autoregressive ar channel model these undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function and thus permit the ill convergence of the godard algorithms which are stochastic gradient descent in nature simulation results confirm predicted misbehavior for channel input of constant modulus it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization a criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached

optimal sample size for multiple testing the case of gene expression microarrays we consider the choice of an optimal sample size for multiple comparison problems the motivating application is the choice of the number of microarray experiments to be carried out when learning about differential gene expression however the approach is valid in any application that involves multiple comparisons in a large number of hypothesis tests we discuss two decision problems in the context of this setup the sample size selection and the decision about the multiple comparisons we adopt a decision theoretic approach using loss functions that combine the competing goals of discovering as many differentially expressed genes as possible while keeping the number of false discoveries manageable for consistency we use the same loss function for both decisions the decision rule that emerges for the multiple comparison problem takes the exact form of the rules proposed in the recent literature to control the posterior expected falsediscovery rate for the sample size selection we combine the expe

spatiotemporal bayesian inference dipole analysis for meg neuroimaging data recently we described a bayesian inference approach to the meg eeg inverse problem that used numerical techniques to estimate the full posterior probability distributions of likely solutions upon which all inferences were based schmidt d m george j s wood c c 1999 bayesian inference applied to the electromagnetic inverse problem human brain mapping 7 195 schmidt d m george j s ranken d m wood c c 2001 spatial temporal bayesian inference for meg eeg in nenonen j ilmoniemi r j katila t eds biomag 2000 12th international conference on biomagnetism espoo norway p 671 schmidt et al 1999 focused on the analysis of data at a single point in time employing an extended region source model they subsequently extended their work to a spatiotemporal bayesian inference analysis of the full spatiotemporal meg eeg data set here we formulate spatiotemporal bayesian inference analysis using a multi dipole model of neural activity this approach is faster than the extended region model does not require use of the subject s anatomical information does not require prior determination of the number of dipoles and yields quantitative probabilistic inferences in addition we have incorporated the ability to handle much more complex and realistic estimates of the background noise which may be represented as a sum of kronecker products of temporal and spatial noise covariance components this reduces the effects of undermodeling noise in order to reduce the rigidity of the multi dipole formulation which commonly causes problems due to multiple local minima we treat the given covariance of the background as uncertain and marginalize over it in the analysis markov chain monte carlo mcmc was used to sample the many possible likely solutions the spatiotemporal bayesian dipole analysis is demonstrated using simulated and empirical whole head meg data

bayesian regression with nonparametric heteroskedasticity abstract this paper studies large sample properties of a semiparametric bayesian approach to inference in a linear regression model the approach is to model the distribution of the regression error term by a normal distribution with the variance that is a flexible function of covariates the main result of the paper is a semiparametric bernstein von mises theorem under misspecification even when the distribution of the regression error term is not normal the posterior distribution of the properly recentered and rescaled regression coefficients converges to a normal distribution with the zero mean and the variance equal to the semiparametric efficiency bound

automatic bayesian curve fitting summary a method of estimating a variety of curves by a sequence of piecewise polynomials is proposed motivated by a bayesian model and an appropriate summary of the resulting posterior distribution a joint distribution is set up over both the number and the position of the knots defining the piecewise polynomials throughout we use reversible jump markov chain monte carlo methods to compute the posteriors the methodology has been successful in giving good estimates for smooth functions i e continuous and differentiable as well as functions which are not differentiable and perhaps not even continuous at a finite number of points the methodology is extended to deal with generalized additive models

model selection and accounting for model uncertainty in graphical models using occam s window abstract we consider the problem of model selection and accounting for model uncertainty in high dimensional contingency tables motivated by expert system applications the approach most used currently is a stepwise strategy guided by tests based on approximate asymptotic p values leading to the selection of a single model inference is then conditional on the selected model the sampling properties of such a strategy are complex and the failure to take account of model uncertainty leads to underestimation of uncertainty about quantities of interest in principle a panacea is provided by the standard bayesian formalism that averages the posterior distributions of the quantity of interest under each of the models weighted by their posterior model probabilities furthermore this approach is optimal in the sense of maximizing predictive ability but this has not been used in practice because computing the posterior model probabilities is hard and the number of models is very large often greater than 1

biclustering models for two mode ordinal data the work in this paper introduces finite mixture models that can be used to simultaneously cluster the rows and columns of two mode ordinal categorical response data such as those resulting from likert scale responses we use the popular proportional odds parameterisation and propose models which provide insights into major patterns in the data model fitting is performed using the em algorithm and a fuzzy allocation of rows and columns to corresponding clusters is obtained the clustering ability of the models is evaluated in a simulation study and demonstrated using two real data sets

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

using closed orbits to bifurcate many periodic solutions for pendulum type equations for pendulum like equations perturbation type arguments and topological tools provide the existence of external forces with many associated periodic solutions

estimating stationary dipoles from meg eeg data contaminated with spatially and temporally correlated background noise the stationary dipole model for the inverse problem of magnetoencephalographic meg and electroencephalographic eeg data is extended by including spatio temporal correlations of the background noise for that purpose the spatio temporal covariances are described as a kronkecker product of a spatial and a temporal covariance matrix the maximum likelihood method is used to estimate this kronecker product from a series of trials of meg eeg data a simulation study shows that the inclusion of the background noise generally improves the dipole estimate substantially when the frequency of the source time functions however coincides with the frequency contents of the covariance function the dipole estimate worsens when the temporal correlations are included the inclusion of spatial correlations always improves the estimates

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

delayed rejection in reversible jump metropolis hastings summary in a metropolis hastings algorithm rejection of proposed moves is an intrinsic part of ensuring that the chain converges to the intended target distribution however persistent rejection perhaps in particular parts of the state space may indicate that locally the proposal distribution is badly calibrated to the target as an alternative to careful off line tuning of state dependent proposals the basic algorithm can be modified so that on rejection a second attempt to move is made a different proposal can be generated from a new distribution that is allowed to depend on the previously rejected proposal we generalise this idea of delaying the rejection and adapting the proposal distribution due to tierney mira 1999 to generate a more flexible class of methods that applies in particular to a variable dimension setting the approach is illustrated by two pedagogical examples and a more realistic application to a changepoints analysis for point processes some key wor ds adaptive changepoint efficiency of markov chain monte carlo estimation integrated autocorrelation time peskun ordering

a fractionally spaced blind equalizer based on linear programming we formulate the blind fractionally spaced equalization fse problem as one that minimizes a piecewise linear convex function subject to some linear constraints on the equalizer parameters we show that this formulation achieves both the interference removal and the carrier phase recovery when the input signal possesses a certain quadrature amplitude modulation qam type symmetry a fast linear programming implementation is presented to solve the convex minimization problem computer simulation results indicate the new linear programming based fse is able to accurately equalize channels that are known to be not equalizable by t spaced or baud rate blind equalizers and yields superior performance to other blind fse methods

bayesian model choice via markov chain monte carlo methods summary markov chain monte carlo mcmc integration methods enable the fitting of models of virtually unlimited complexity and as such have revolutionized the practice of bayesian data analysis however comparison across models may not proceed in a completely analogous fashion owing to violations of the conditions sufficient to ensure convergence of the markov chain in this paper we present a framework for bayesian model choice along with an mcmc algorithm that does not suffer from convergence difficulties our algorithm applies equally well to problems where only one model is contemplated but its proper size is not known at the outset such as problems involving integer valued parameters multiple changepoints or finite mixture distributions we illustrate our approach with two published examples

regularized spectral matching for blind source separation application to fmri imaging the main contribution of this paper is to present a bayesian approach for solving the noisy instantaneous blind source separation problem based on second order statistics of the time varying spectrum the success of the blind estimation relies on the nonstationarity of the second order statistics and their intersource diversity choosing the time frequency domain as the signal representation space and transforming the data by a short time fourier transform stft our method presents a simple em algorithm that can efficiently deal with the time varying spectrum diversity of the sources the estimation variance of the stft is reduced by averaging across time frequency subdomains the algorithm is demonstrated on a standard functional resonance imaging fmri experiment involving visual stimuli in a block design explicitly taking into account the noise in the model the proposed algorithm has the advantage of extracting only relevant task related components and considers the remaining components artifacts to be noise

full diversity blind space time block codes in this paper the systematic design of a space time block code is considered for a wireless communication system with multiple transmitter receiver antennas and flat fading in which channel state information is completely unknown from the viewpoint of blind signal processing a necessary and sufficient condition is given for the unique identification of the multi input multi output flat fading channel and transmitted signal then some novel unique factorizations for a pair of coprime p ary and q ary phase shift keying psk constellations are established with this and currently available coherent space time block code designs a method is developed to systematically construct full diversity blind nonunitary space time block codes as well as unitary codes by just performing the qr decomposition of the nonunitary codes it is proved that under a noise free environment the code design proposed in this paper can guarantee that the transmitted signals and the channel coefficients are uniquely identified and that under a complex gaussian noise environment in which pth order and q th order statistics p and q are co prime of the received signals are available the channel coefficients can be still uniquely identified in addition a closed form solution to determine the channel coefficients is obtained