meaningful design and contrast estimability in fmri optimising the efficiency of an experimental design is known to be of great importance however existing methods for calculating design rank deficiency and contrast estimability an important aspect of experimental design relate to computational precision rather than image noise and are therefore not very meaningful for example a contrast between two experimental conditions may be mathematically estimable while requiring a huge differential bold response for statistical significance to be reached in this paper we formulate standard efficiency equations in terms of required bold effect and use this to generate measures of rank estimability which are meaningful this takes into account the strength and smoothness of the timeseries noise and is applicable to complex contrasts we show how to re express several regressors and an associated contrast vector as a single equivalent regressor so that we can calculate the contrast s effective peak peak height unambiguously we also present some example results on typical designs and characterise noise results from a range of typical fmri acquisitions in order to allow experimenters to apply efficiency estimation in advance of acquiring data

temporal autocorrelation in univariate linear modeling of fmri data in functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them shaping or coloring attempts to negate the effects of not accurately knowing the intrinsic autocorrelations by imposing known autocorrelation via temporal filtering removing the autocorrelation or prewhitening gives the best linear unbiased estimator assuming that the autocorrelation is accurately known for single event designs the efficiency of the estimator is considerably higher for prewhitening compared with coloring however it has been suggested that sufficiently accurate estimates of the autocorrelation are currently not available to give prewhitening acceptable bias to overcome this we consider different ways to estimate the autocorrelation for use in prewhitening after high pass filtering is performed a tukey taper set to smooth the spectral density more than would normally be used in spectral density estimation performs best importantly estimation is further improved by using nonlinear spatial filtering to smooth the estimated autocorrelation but only within tissue type using this approach when prewhitening reduced bias to close to zero at probability levels as low as 1 x 10 5

cortical surface based analysis ii inflation flattening and a surface based coordinate system the surface of the human cerebral cortex is a highly folded sheet with the majority of its surface area buried within folds as such it is a difficult domain for computational as well as visualization purposes we have therefore designed a set of procedures for modifying the representation of the cortical surface to i inflate it so that activity buried inside sulci may be visualized ii cut and flatten an entire hemisphere and iii transform a hemisphere into a simple parameterizable surface such as a sphere for the purpose of establishing a surface based coordinate system r 1999 academic press

periodic solutions for wave equations with variable coefficients with nonlinear localized damping abstract we discuss the existence of periodic solutions to the wave equation with variable coefficients u t t div a x u x u t f x t with dirichlet boundary condition here x v is a function like x v a x g v with g v 0 where a x is nonnegative being positive only in a neighborhood of a part of the domain

global smooth solutions and stabilization of nonlinear elastodynamic systems with locally distributed dissipation we consider the existence of global solutions of the nonlinear elastodynamic system with a locally distributed damping in a bounded domain we assume that the energy function satisfies the strong ellipticity condition at the zero equilibrium the local dissipation is in the form a x u where the nonnegative function a x is only positive on a small portion of the domain we show the existence of global smooth solutions when initial data are small in particular we obtain the exponential decay of the energy which implies the exponential stabilization of the system by internal feedback

energy decay of a variable coefficient wave equation with memory type acoustic boundary conditions abstract we study the energy decay for a variable coefficient wave equation with memory type acoustic boundary conditions boundary memory is described by an integral term applying the riemannian geometry method we obtain the uniform energy decay under some conditions on the memory function and the coefficient matrix

patient specific detection of perfusion abnormalities combining within subject and between subject variances in arterial spin labeling in this paper patient specific perfusion abnormalities in arterial spin labeling asl were identified by comparing a single patient to a group of healthy controls using a mixed effect hierarchical general linear model glm two approaches are currently in use to solve hierarchical glms 1 the homoscedastic approach assumes homogeneous variances across subjects and 2 the heteroscedastic approach is theoretically more efficient in the presence of heterogeneous variances but algorithmically more demanding in practice in functional magnetic resonance imaging studies the superiority of the heteroscedastic approach is still under debate due to the low signal to noise ratio of asl sequences within subject variances have a significant impact on the estimated perfusion maps and the heteroscedastic model might be better suited in this context in this paper we studied how the homoscedastic and heteroscedastic approaches behave in terms of specificity and sensitivity in the detection of patient specific asl perfusion abnormalities validation was undertaken on a dataset of 25 patients diagnosed with brain tumors and 36 healthy volunteers we showed evidence of heterogeneous within subject variances in asl and pointed out an increased false positive rate of the homoscedastic model in the detection of patient specific brain perfusion abnormalities with asl modeling heterogeneous variances increases the sensitivity at the same specificity level

exponential decay for binary time varying covariates in cox models cox models are commonly used in the analysis of time to event data one advantage of cox models is the ability to include time varying covariates often a binary covariate that codes for the occurrence of an event that affects an individual subject a common assumption in this case is that the effect of the event on the outcome of interest is constant and permanent for each subject in this paper we propose a modification to the cox model to allow the influence of an event to exponentially decay over time methods for generating data using the inverse cumulative density function for the proposed model are developed likelihood ratio tests and aic are investigated as methods for comparing the proposed model to the commonly used permanent exposure model a simulation study is performed and 3 different data sets are presented as examples

classical and bayesian inference in neuroimaging theory this paper reviews hierarchical observation models used in functional neuroimaging in a bayesian light it emphasizes the common ground shared by classical and bayesian methods to show that conventional analyses of neuroimaging data can be usefully extended within an empirical bayesian framework in particular we formulate the procedures used in conventional data analysis in terms of hierarchical linear models and establish a connection between classical inference and parametric empirical bayes peb through covariance component estimation this estimation is based on an expectation maximization or em algorithm the key point is that hierarchical models not only provide for appropriate inference at the highest level but that one can revisit lower levels suitably equipped to make bayesian inferences bayesian inferences eschew many of the difficulties encountered with classical inference and characterize brain responses in a way that is more directly predicated on what one is interested in the motivation for bayesian approaches is reviewed and the theoretical background is presented in a way that relates to conventional methods in particular restricted maximum likelihood reml this paper is a technical and theoretical prelude to subsequent papers that deal with applications of the theory to a range of important issues in neuroimaging these issues include i estimating nonsphericity or variance components in fmri time series that can arise from serial correlations within subject or are induced by multisubject i e hierarchical studies ii spatiotemporal bayesian models for imaging data in which voxels specific effects are constrained by responses in other voxels iii bayesian estimation of nonlinear models of hemodynamic responses and iv principled ways of mixing structural and functional priors in eeg source reconstruction although diverse all these estimation problems are accommodated by the peb framework described in this paper

a statistical analysis of brain morphology using wild bootstrapping methods for the analysis of brain morphology including voxel based morphology and surface based morphometries have been used to detect associations between brain structure and covariates of interest such as diagnosis severity of disease age iq and genotype the statistical analysis of morphometric measures usually involves two statistical procedures 1 invoking a statistical model at each voxel or point on the surface of the brain or brain subregion followed by mapping test statistics e g t test or their associated p values at each of those voxels 2 correction for the multiple statistical tests conducted across all voxels on the surface of the brain region under investigation we propose the use of new statistical methods for each of these procedures we first use a heteroscedastic linear model to test the associations between the morphological measures at each voxel on the surface of the specified subregion e g cortical or subcortical surfaces and the covariates of interest moreover we develop a robust test procedure that is based on a resampling method called wild bootstrapping this procedure assesses the statistical significance of the associations between a measure of given brain structure and the covariates of interest the value of this robust test procedure lies in its computationally simplicity and in its applicability to a wide range of imaging data including data from both anatomical and functional magnetic resonance imaging fmri simulation studies demonstrate that this robust test procedure can accurately control the family wise error rate we demonstrate the application of this robust test procedure to the detection of statistically significant differences in the morphology of the hippocampus over time across gender groups in a large sample of healthy subjects

on lagrange interpolations and kramer s sampling theorem associated with self adjoint boundary value problems abstract it is known that kramer s sampling theorem and lagrange type interpolation generalize the celebrated whittaker shannon kotel nikov sampling theorem in two different directions however no direct connection between these two directions seems to be known in this article we show that kramer s sampling theorem gives nothing more than the lagrange type interpolations provided that the kernel function associated with kramer s theorem arises from a self adjoint boundary value problem with sample eigenvalues

on kramer s sampling theorem associated with general strum liouville problems and lagrange interpolation kramer s sampling theorem which is a generalization of shannon s sampling theorem and its relationship with lagrange interpolation is studied kramer s sampling theorem is extended to the case where the interval a b is infinite and it is shown that any function that has a sampling expansion in the scope of kramer s theorem also has a lagrange type interpolation expansion provided that the kernel associated with kramer s theorem arises from a second order sturm liouville boundary value problem whether it is regular or singular this new technique not only reproduces many of the known sampling expansions such as those for the cosine the finite hankel and the continuous legendre transforms but also generates new ones such as those for the continuous jacobi laguerre and hermite transforms

stabilization of the wave equation with variable coefficients and a delay in dissipative boundary feedback we consider the stabilization of the wave equation with variable coefficients and a delay in the dissipative boundary feedback by virtue of the riemannian geometry methods the energy perturbed approach and the multiplier skills we establish the uniform stability of the energy of the closed loop system

tests of homogeneity for generalized linear models abstract we propose two tests for testing homogeneity among clustered data adjusting for the effects of covariates the first is a score test for a generalized linear model with random effect in which the distribution of the response variable given the random effect is entirely defined in contrast to the likelihood ratio test however the score test does not require estimation of the parameters of a mixed effects model nor specification of the mixing distribution the second test is proposed in the framework of the generalized estimating equation gee approach in deriving this test we need only the specification of the marginal expectation and variance of the response variable and the fourth moment for the overdispersion term whereas for deriving the score test for mixed effects models the entire conditional distribution must be specified we demonstrate that the two tests are identical when the covariance matrix assumed in the gee approach is that of the random effects model in both approaches

general multilevel linear modeling for group analysis in fmri this article discusses general modeling of multisubject and or multisession fmri data in particular we show that a two level mixed effects model where parameters of interest at the group level are estimated from parameter and variance estimates from the single session level can be made equivalent to a single complete mixed effects model where parameters of interest at the group level are estimated directly from all of the original single sessions time series data if the co variance at the second level is set equal to the sum of the co variances in the single level form using the blue with known covariances this result has significant implications for group studies in fmri since it shows that the group analysis requires only values of the parameter estimates and their co variance from the first level generalizing the well established summary statistics approach in fmri the simple and generalized framework allows different prewhitening and different first level regressors to be used for each subject the framework incorporates multiple levels and cases such as repeated measures paired or unpaired t tests and f tests at the group level explicit examples of such models are given in the article using numerical simulations based on typical first level covariance structures from real fmri data we demonstrate that by taking into account lower level covariances and heterogeneity a substantial increase in higher level z score is possible

existence and energy decay rates of solutions to the variable coefficient euler bernoulli plate with a delay in localized nonlinear internal feedback abstract this paper is concerned with the existence and energy decay estimates of solutions to the variable coefficient euler bernoulli plate with a delay in localized nonlinear internal feedback the existence of solutions to the nonlinear system is obtained by using galerkin method combined with some energy estimates furthermore applying riemannian geometry method we establish uniform decay rates of the plate equation with variable coefficients and a nonlinear delay term

using variance information in magnetoencephalography measures of functional connectivity the use of magnetoencephalography meg to assess long range functional connectivity across large scale distributed brain networks is gaining popularity recent work has shown that electrodynamic networks can be assessed using both seed based correlation or independent component analysis ica applied to meg data and further that such metrics agree with fmri studies to date techniques for meg connectivity assessment have typically used a variance normalised approach either through the use of pearson correlation coefficients or via variance normalisation of envelope timecourses prior to ica here we show that the use of variance information i e data that have not been variance normalised in source space projected hilbert envelope time series yields important spatial information and is of significant functional relevance further we show that employing this information in functional connectivity analyses improves the spatial delineation of network nodes using both seed based and ica approaches the use of variance is particularly important in meg since the non independence of source space voxels brought about by the ill posed meg inverse problem means that spurious signals can exist in areas of low signal variance we therefore suggest that this approach be incorporated into future studies

multi subject analyses with dynamic causal modeling currently most studies that employ dynamic causal modeling dcm use random effects rfx analysis to make group inferences applying a second level frequentist test to subjects parameter estimates in some instances however fixed effects ffx analysis can be more appropriate such analyses can be implemented by combining the subjects posterior densities according to bayes theorem either on a multivariate bayesian parameter averaging or bpa or univariate basis posterior variance weighted averaging or pvwa or by applying dcm to time series averaged across subjects beforehand temporal averaging or ta while all these ffx approaches have the advantage of allowing for bayesian inferences on parameters a systematic comparison of their statistical properties has been lacking so far based on simulated data generated from a two region network we examined the effects of signal to noise ratio snr and population heterogeneity on group level parameter estimates data sets were simulated assuming either a homogeneous large population n 60 with constant connectivities across subjects or a heterogeneous population with varying parameters ta showed advantages at lower snr but is limited in its applicability because bpa and pvwa take into account posterior co variance structure they can yield non intuitive results when only considering posterior means this problem is relevant for high snr data pronounced parameter interdependencies and when ffx assumptions are violated i e inhomogeneous groups it diminishes with decreasing snr and is absent for models with independent parameters or when ffx assumptions are appropriate group results obtained with these ffx approaches should therefore be interpreted carefully by considering estimates of dependencies among model parameters

a comprehensive review of group level model performance in the presence of heteroscedasticity can a single model control type i errors in the presence of outliers even after thorough preprocessing and a careful time series analysis of functional magnetic resonance imaging fmri data artifact and other issues can lead to violations of the assumption that the variance is constant across subjects in the group level model this is especially concerning when modeling a continuous covariate at the group level as the slope is easily biased by outliers various models have been proposed to deal with outliers including models that use the first level variance or that use the group level residual magnitude to differentially weight subjects the most typically used robust regression implementing a robust estimator of the regression slope has been previously studied in the context of fmri studies and was found to perform well in some scenarios but a loss of type i error control can occur for some outlier settings a second type of robust regression using a heteroscedastic autocorrelation consistent hac estimator which produces robust slope and variance estimates has been shown to perform well with better type i error control but with large sample sizes 500 1000 subjects the type i error control with smaller sample sizes has not been studied in this model and has not been compared to other modeling approaches that handle outliers such as fsl s flame 1 and fsl s outlier de weighting focusing on group level inference with a continuous covariate over a range of sample sizes and degree of heteroscedasticity which can be driven either by the within or between subject variability both styles of robust regression are compared to ordinary least squares ols fsl s flame 1 flame 1 with outlier de weighting algorithm and kendall s tau additionally subject omission using the cook s distance measure with ols and nonparametric inference with the ols statistic are studied pros and cons of these models as well as general strategies for detecting outliers in data and taking precaution to avoid inflated type i error rates are discussed

permutation inference for canonical correlation analysis canonical correlation analysis cca has become a key tool for population neuroimaging allowing investigation of associations between many imaging and non imaging measurements as age sex and other variables are often a source of variability not of direct interest previous work has used cca on residuals from a model that removes these effects then proceeded directly to permutation inference we show that a simple permutation test as typically used to identify significant modes of shared variation on such data adjusted for nuisance variables produces inflated error rates the reason is that residualisation introduces dependencies among the observations that violate the exchangeability assumption even in the absence of nuisance variables however a simple permutation test for cca also leads to excess error rates for all canonical correlations other than the first the reason is that a simple permutation scheme does not ignore the variability already explained by previous canonical variables here we propose solutions for both problems in the case of nuisance variables we show that transforming the residuals to a lower dimensional basis where exchangeability holds results in a valid permutation test for more general cases with or without nuisance variables we propose estimating the canonical correlations in a stepwise manner removing at each iteration the variance already explained while dealing with different number of variables in both sides we also discuss how to address the multiplicity of tests proposing an admissible test that is not conservative and provide a complete algorithm for permutation inference for cca

robust group analysis using outlier inference neuroimaging group studies are typically performed with the assumption that subjects used are randomly drawn from a population of subjects the population of subjects is assumed to have a distribution of effect sizes associated with it that are gaussian distributed however in practice group studies can include outlier subjects whose effect sizes are completely at odds with the general population for reasons that are not of experimental interest if ignored these outliers can dramatically affect the inference results to solve this problem we propose a group inference approach which includes inference of outliers using a robust general linear model glm approach this approach models the errors as being a mixture of two gaussian distributions one for the normal population and one for the outliers crucially the robust glm is part of a traditional hierarchical group model which uses glms at each level of the hierarchy this combines the benefits of outlier inference with the benefits of using variance information from lower levels in the hierarchy a bayesian inference framework is used to infer on the robust glm while using the lower level variance information the performance of the method is demonstrated on simulated and fmri data and is compared with iterative reweighted least squares and permutation testing

posterior probability maps and spms this technical note describes the construction of posterior probability maps that enable conditional or bayesian inferences about regionally specific effects in neuroimaging posterior probability maps are images of the probability or confidence that an activation exceeds some specified threshold given the data posterior probability maps ppms represent a complementary alternative to statistical parametric maps spms that are used to make classical inferences however a key problem in bayesian inference is the specification of appropriate priors this problem can be finessed using empirical bayes in which prior variances are estimated from the data under some simple assumptions about their form empirical bayes requires a hierarchical observation model in which higher levels can be regarded as providing prior constraints on lower levels in neuroimaging observations of the same effect over voxels provide a natural two level hierarchy that enables an empirical bayesian approach in this note we present a brief motivation and the operational details of a simple empirical bayesian method for computing posterior probability maps we then compare bayesian and classical inference through the equivalent ppms and spms testing for the same effect in the same data

variational inference a review for statisticians abstractone of the core problems of modern statistics is to approximate difficult to compute probability densities this problem is especially important in bayesian statistics which frames all inference about unknown quantities as a calculation involving the posterior density in this article we review variational inference vi a method from machine learning that approximates probability densities through optimization vi has been used in many applications and tends to be faster than classical methods such as markov chain monte carlo sampling the idea behind vi is to first posit a family of densities and then to find a member of that family which is close to the target density closeness is measured by kullback leibler divergence we review the ideas behind mean field variational inference discuss the special case of vi applied to exponential family models present a full example with a bayesian mixture of gaussians and derive a variant that uses stochastic optimization to scale up to massive data

sampling of vector valued transforms associated with green s matrix of dirac systems recently a sampling theorem associated with regular one dimensional dirac systems has been developed integral transforms whose kernels are solutions of the systems have been reconstructed from their values at the eigenvalues in the present article the situation is considered where the kernels are replaced by green s matrix of the problem thus a vector valued sampling theorem is established for vector valued transforms a family of examples where the systems have variable coefficients and a vector valued kramer type sampling lemma are given at the end of the paper

analysis of fmri time series revisited again friston et al 1995 neuroimage 2 45 53 presented a method for detecting activations in fmr1 time series based on the general linear model and a heuristic analysis of the effective degrees of freedom in this communication we present corrected results that replace those of the previous paper and solve the same problem without recourse to heuristic arguments specifically we introduce a proper and unbiased estimator for the error terms and provide a more generally correct expression for the effective degrees of freedom the previous estimates of error variance were biased and in some instances could have led to a 10 20 overestimate of z values although the previous results are almost correct for the random regressors chosen for validation the present theoretical results are exact for any covariate or waveform we comment on some aspects of experimental design and data analysis in the light of the theoretical framework discussed here

variational bayesian mixed effects inference for classification studies multivariate classification algorithms are powerful tools for predicting cognitive or pathophysiological states from neuroimaging data assessing the utility of a classifier in application domains such as cognitive neuroscience brain computer interfaces or clinical diagnostics necessitates inference on classification performance at more than one level i e both in individual subjects and in the population from which these subjects were sampled such inference requires models that explicitly account for both fixed effects within subjects and random effects between subjects variance components while models of this sort are standard in mass univariate analyses of fmri data they have not yet received much attention in multivariate classification studies of neuroimaging data presumably because of the high computational costs they entail this paper extends a recently developed hierarchical model for mixed effects inference in multivariate classification studies and introduces an efficient variational bayes approach to inference using both synthetic and empirical fmri data we show that this approach is equally simple to use as yet more powerful than a conventional t test on subject specific sample accuracies and computationally much more efficient than previous sampling algorithms and permutation tests our approach is independent of the type of underlying classifier and thus widely applicable the present framework may help establish mixed effects inference as a future standard for classification group analyses

linear mixed effects modeling approach to fmri group analysis conventional group analysis is usually performed with student type t test regression or standard an c ova in which the variance covariance matrix is presumed to have a simple structure some correction approaches are adopted when assumptions about the covariance structure is violated however as experiments are designed with different degrees of sophistication these traditional methods can become cumbersome or even be unable to handle the situation at hand for example most current fmri software packages have difficulty analyzing the following scenarios at group level 1 taking within subject variability into account when there are effect estimates from multiple runs or sessions 2 continuous explanatory variables covariates modeling in the presence of a within subject repeated measures factor multiple subject grouping between subjects factors or the mixture of both 3 subject specific adjustments in covariate modeling 4 group analysis with estimation of hemodynamic response hdr function by multiple basis functions 5 various cases of missing data in longitudinal studies and 6 group studies involving family members or twins here we present a linear mixed effects modeling lme methodology that extends the conventional group analysis approach to analyze many complicated cases including the six prototypes delineated above whose analyses would be otherwise either difficult or unfeasible under traditional frameworks such as an c ova and general linear model glm in addition the strength of the lme framework lies in its flexibility to model and estimate the variance covariance structures for both random effects and residuals the intraclass correlation icc values can be easily obtained with an lme model with crossed random effects even at the presence of confounding fixed effects the simulations of one prototypical scenario indicate that the lme modeling keeps a balance between the control for false positives and the sensitivity for activation detection the importance of hypothesis formulation is also illustrated in the simulations comparisons with alternative group analysis approaches and the limitations of lme are discussed in details

bayesian estimation of dynamical systems an application to fmri this paper presents a method for estimating the conditional or posterior distribution of the parameters of deterministic dynamical systems the procedure conforms to an em implementation of a gauss newton search for the maximum of the conditional or posterior density the inclusion of priors in the estimation procedure ensures robust and rapid convergence and the resulting conditional densities enable bayesian inference about the model parameters the method is demonstrated using an input state output model of the hemodynamic coupling between experimentally designed causes or factors in fmri studies and the ensuing bold response this example represents a generalization of current fmri analysis models that accommodates nonlinearities and in which the parameters have an explicit physical interpretation second the approach extends classical inference based on the likelihood of the data given a null hypothesis about the parameters to more plausible inferences about the parameters of the model given the data this inference provides for confidence intervals based on the conditional density 2002 elsevier science usa

repeated measures in clinical trials analysis using mean summary statistics and its implications for design this paper explores the use of simple summary statistics for analysing repeated measurements in randomized clinical trials with two treatments quite often the data for each patient may be effectively summarized by a pre treatment mean and a post treatment mean analysis of covariance is the method of choice and its superiority over analysis of post treatment means or analysis of mean changes is quantified as regards both reduced variance and avoidance of bias using a simple model for the covariance structure between time points quantitative consideration is also given to practical issues in the design of repeated measures studies the merits of having more than one pre treatment measurement are demonstrated and methods for determining sample sizes in repeated measures designs are provided several examples from clinical trials are presented and broad practical recommendations are made the examples support the value of the compound symmetry assumption as a realistic simplification in quantitative planning of repeated measures trials the analysis using summary statistics makes no such assumption however allowance in design for alternative non equal correlation structures can and should be made when necessary

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

on lagrange interpolation and kramer type sampling theorems associated with sturm liouville problems this article is devoted to a connection between kramer s sampling theorem and sampling expansions generated by lagrange interpolation it is shown that any function that has a sampling expansion in the scope of kramer s theorem also has a lagrange type interpolation expansion provided that the kernel associated with kramer s theorem arises from a second order sturm liouville boundary value problem this new approach which for a variety of regular and singular sturm liouville problems leads to associated sampling theorems recovers not only many known sampling expansions but also gives new ways to calculate the corresponding sampling functions new sampling series are included

global smooth solutions of the quasi linear wave equation with internal velocity feedback we study the existence of global smooth solutions for the quasi linear wave equation by an internal local damping when initial data are close to a given equilibrium our interest is in studying the structure of the damping region which guarantees the existence of global solutions our results show that the structure of the damping region depends on the geometric properties of a riemannian metric based on the coefficients and the equilibrium of the system some geometrical conditions are presented to obtain the damping region

open capture recapture models with heterogeneity ii jolly seber model summary estimation of abundance is important in both open and closed population capture recapture analysis but unmodeled heterogeneity of capture probability leads to negative bias in abundance estimates this article defines and develops a suite of open population capture recapture models using finite mixtures to model heterogeneity of capture and survival probabilities model comparisons and parameter estimation use likelihood based methods a real example is analyzed and simulations are used to check the main features of the heterogeneous models especially the quality of estimation of abundance survival recruitment and turnover the two major advances in this article are the provision of realistic abundance estimates that take account of heterogenetiy of capture and an appraisal of the amount of overestimation of survival arising from conditioning on the first capture when heterogeneity of survival is present

sampling expansions associated with kamke problems the present paper is devoted to the derivation of sampling expansions for entire functions which are represented as integral transforms where a differential operator is acting on the kernels the situation generalizes the results obtained in sampling theory associated with boundary value problems to the case when the differential equation has the form n y lambda p y where n and p are two differential expressions of orders n and p respectively n p and lambda is the eigenvalue parameter both self adjoint and non self adjoint cases will be considered with examples in which the boundary conditions are strongly regular

multi level block permutation under weak and reasonable assumptions mainly that data are exchangeable under the null hypothesis permutation tests can provide exact control of false positives and allow the use of various non standard statistics there are however various common examples in which global exchangeability can be violated including paired tests tests that involve repeated measurements tests in which subjects are relatives members of pedigrees any dataset with known dependence among observations in these cases some permutations if performed would create data that would not possess the original dependence structure and thus should not be used to construct the reference null distribution to allow permutation inference in such cases we test the null hypothesis using only a subset of all otherwise possible permutations i e using only the rearrangements of the data that respect exchangeability thus retaining the original joint distribution unaltered in a previous study we defined exchangeability for blocks of data as opposed to each datum individually then allowing permutations to happen within block or the blocks as a whole to be permuted here we extend that notion to allow blocks to be nested in a hierarchical multi level definition we do not explicitly model the degree of dependence between observations only the lack of independence the dependence is implicitly accounted for by the hierarchy and by the permutation scheme the strategy is compatible with heteroscedasticity and variance groups and can be used with permutations sign flippings or both combined we evaluate the method for various dependence structures apply it to real data from the human connectome project hcp as an example application show that false positives can be avoided in such cases and provide a software implementation of the proposed approach

multilevel linear modelling for fmri group analysis using bayesian inference functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and or multiple subjects a hierarchical approach can be taken to modelling such data with a general linear model glm at each level of the hierarchy introducing different random effects variance components inferring on these models is nontrivial with frequentist solutions being unavailable a solution is to use a bayesian framework one important ingredient in this is the choice of prior on the variance components and top level regression parameters due to the typically small numbers of sessions or subjects in neuroimaging the choice of prior is critical to alleviate this problem we introduce to neuroimage modelling the approach of reference priors which drives the choice of prior such that it is noninformative in an information theoretic sense we propose two inference techniques at the top level for multilevel hierarchies a fast approach and a slower more accurate approach we also demonstrate that we can infer on the top level of multilevel hierarchies by inferring on the levels of the hierarchy separately and passing summary statistics of a noncentral multivariate t distribution between them

uniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditions abstract a variable coefficient wave equation with nonlinear damped acoustic boundary conditions is considered the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients the uniform decay of the energy is achieved without any geometrical conditions on the shape of the dissipative portion of the boundary

to smooth or not to smooth bias and efficiency in fmri time series analysis this paper concerns temporal filtering in fmri time series analysis whitening serially correlated data is the most efficient approach to parameter estimation however if there is a discrepancy between the assumed and the actual correlations whitening can render the analysis exquisitely sensitive to bias when estimating the standard error of the ensuing parameter estimates this bias although not expressed in terms of the estimated responses has profound effects on any statistic used for inference the special constraints of fmri analysis ensure that there will always be a misspecification of the assumed serial correlations one resolution of this problem is to filter the data to minimize bias while maintaining a reasonable degree of efficiency in this paper we present expressions for efficiency of parameter estimation and bias in estimating standard error in terms of assumed and actual correlation structures in the context of the general linear model we show that i whitening strategies can result in profound bias and are therefore probably precluded in parametric fmri data analyses ii band pass filtering and implicitly smoothing has an important role in protecting against inferential bias

combining spatial extent and peak intensity to test for activations in functional imaging within the framework of statistical mapping there are up to now only two tests used to assess the regional significance in functional images one is based on the magnitude of the foci and tends to detect high intensity signals while the second is based on the spatial extent of regions defined by a simple thresholding of the statistical map a test that is more sensitive to extended signals the aim of this paper is to combine the two tests into a single test that is more sensitive to a wider range of signals this combined test is based on an analytical approximation of the distribution of these two parameters size and height and is applied in the context of statistical maps the risk of error in noise only 2d or 3d volumes is assessed under a wide range of experimental conditions obtained by varying both the resolution of the map and the threshold at which clusters are defined in addition we have investigated this new test on simulated signals and applied it to an experimental pet dataset the experimental risk of error is close to the predicted one and the overall sensitivity increases when analyzing a volume containing different types of signals

estimating and testing variance components in a multi level glm most analysis of multi subject fmri data is concerned with determining whether there exists a significant population wide activation in a comparison between two or more conditions this is typically assessed by testing the average value of a contrast of parameter estimates cope against zero in a general linear model glm analysis however important information can also be obtained by testing whether there exist significant individual differences in effect magnitude between subjects i e whether the variance of a cope is significantly different from zero intuitively such a test amounts to testing whether inter individual differences are larger than would be expected given the within subject error variance we compare several methods for estimating variance components including a a naive estimate using ordinary least squares ols b linear mixed effects in r lmer c a novel matlab implementation of iterative generalized least squares igls and its restricted maximum likelihood variant rigls all methods produced reasonable estimates of within and between subject variance components with igls providing an attractive balance between sensitivity and appropriate control of false positives finally we use the igls method to estimate inter subject variance in a perfusion fmri study n 18 of social evaluative threat and show evidence for significant inter individual differences in ventromedial prefrontal cortex vmpfc amygdala hippocampus and medial temporal lobes insula and brainstem with predicted inverse coupling between vmpfc and the midbrain periaqueductal gray only when high inter individual variance was used to define the seed for functional connectivity analyses in sum tests of variance provides a way of selecting regions that show significant inter individual variability for subsequent analyses that attempt to explain those individual differences

sampling theorem associated with a dirac operator and the hartley transform abstract kramer s sampling theorem indicates that under certain conditions sampling theorems associated with boundary value problems involving n th order self adjoint differential operators can be obtained in this paper we extend this result and derive a sampling theorem associated with boundary value problems involving a one dimensional system of dirac operators as a special case we obtain a sampling theorem for the hartley transform of a bandlimited function

improved optimization for the robust and accurate linear registration and motion correction of brain images linear registration and motion correction are important components of structural and functional brain image analysis most modern methods optimize some intensity based cost function to determine the best registration to date little attention has been focused on the optimization method itself even though the success of most registration methods hinges on the quality of this optimization this paper examines the optimization process in detail and demonstrates that the commonly used multiresolution local optimization methods can and do get trapped in local minima to address this problem two approaches are taken 1 to apodize the cost function and 2 to employ a novel hybrid global local optimization method this new optimization method is specifically designed for registering whole brain images it substantially reduces the likelihood of producing misregistrations due to being trapped by local minima the increased robustness of the method compared to other commonly used methods is demonstrated by a consistency test in addition the accuracy of the registration is demonstrated by a series of experiments with motion correction these motion correction experiments also investigate how the results are affected by different cost functions and interpolation methods

robust nonparametric tests of general linear model coefficients a comparison of permutation methods and test statistics statistical inference in neuroimaging research often involves testing the significance of regression coefficients in a general linear model in many applications the researcher assumes a model of the form y x z e where y is the observed brain signal and x and z contain explanatory variables that are thought to be related to the brain signal the goal is to test the null hypothesis h0 0 with the nuisance parameters included in the model several nonparametric permutation methods have been proposed for this problem and each method uses some variant of the f ratio as the test statistic however recent research suggests that the f ratio can produce invalid permutation tests of h0 0 when the e terms are heteroscedastic i e have non constant variance which can occur for a variety of reasons this study compares the classic f test statistic to the robust w wald test statistic using eight different permutation methods the results reveal that permutation tests using the f ratio can produce accurate results when the errors are homoscedastic but high false positive rates when the errors are heteroscedastic in contrast permutation tests using the w test statistic produced valid results when the errors were homoscedastic and asymptotically valid results when the errors were heteroscedastic in the situation with homoscedastic errors permutation tests using the w statistic showed slightly reduced power compared to the f statistic but the difference disappeared as the sample size n increased consequently the w test statistic is recommended for robust nonparametric hypothesis tests of regression coefficients in neuroimaging research

multigrid priors for a bayesian approach to fmri we introduce multigrid priors to construct a bayesian inspired method to asses brain activity in functional magnetic resonance imaging fmri a sequence of different scale grids is constructed over the image starting from the finest scale coarse grain data variables are sequentially defined for each scale then we move back to finer scales determining for each coarse scale a set of posterior probabilities the posterior on a coarse scale is used as the prior for activity at the next finer scale to test the method we use a linear model with a given hemodynamic response function to construct the likelihood we apply the method both to real and simulated data of a boxcar experiment to measure the number of errors we impose a decision to determine activity by setting a threshold on the posterior receiver operating characteristic roc curves are used to study the dependence on threshold and on a few hyperparameters in the relation between specificity and sensitivity we also study the deterioration of the results for real data under information loss this is done by decreasing the number of images in each period and also by decreasing the signal to noise ratio and compare the robustness to other methods

asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints summary the analysis of moment structural models has become an important tool of investigation in behavioural educational and economic studies the chi squared largesample test is routinely employed to assess the goodness of fit of the model considered however in order to invoke the standard asymptotic distribution theory certain regularity conditions have to be met here we consider the case where the population value of the parameter vector is a boundary point of the feasible region we show that in this case the asymptotic distribution of test statistic is a mixture of chi squared distributions the problem of finding the corresponding weights is discussed

mixed effect statistics for group analysis in fmri a nonparametric maximum likelihood approach this technical note describes a collection of test statistics accounting for estimation uncertainties at the within subject level that can be used as alternatives to the standard t statistic in one sample random effect analyses i e when testing the mean effect of a population we build such test statistics by estimating the across subject distribution of the effects using maximum likelihood under a nonparametric mixed effect model for inference purposes the statistics are calibrated using permutation tests to achieve exact false positive control under a symmetry assumption regarding the across subject distribution the new tests are implemented in a freely available toolbox for spm called distance

a general statistical analysis for fmri data we propose a method for the statistical analysis of fmri data that seeks a compromise between efficiency generality validity simplicity and execution speed the main differences between this analysis and previous ones are a simple bias reduction and regularization for voxel wise autoregressive model parameters the combination of effects and their estimated standard deviations across different runs sessions subjects via a hierarchical random effects analysis using the em algorithm overcoming the problem of a small number of runs session subjects using a regularized variance ratio to increase the degrees of freedom

oversampling and aliasing in de branges spaces arising from bessel operators abstract we show that a class of de branges spaces generated by means of generalized fourier transforms associated with perturbed bessel differential equations has the properties of oversampling and aliasing

sampling in paley wiener spaces associated with fractional integro differential operators this paper employs the theory of kramer analytic kernels established by everitt et al results in math 34 1998 310 to derive sampling expansions the kernels of the recovered transforms are mittag leffler functions of two parameters these kernels are solutions of certain classes of fractional integro differential equations the technique used here is different from the analytic approach by djrbashian harmonic analysis and boundary value problems in the complex domain birkhauser basel 1993

stabilization of the euler bernoulli plate with variable coefficients by nonlinear internal feedback we consider the energy decay for solutions of the euler bernoulli plate equation with variable coefficients where a nonlinear internal feedback acts in a suitable subregion of the domain the riemannian geometric method is used to deal with variable coefficient problems when the feedback region has a structure similar to that for the wave equation with constant coefficients we establish the stabilization of the system in the case of fixed boundary conditions several energy decay rates are established according to various growth restrictions on the nonlinear feedback near the origin and at infinity we further show that unlike for the case of constant coefficients choices of such feedback regions depend not only on the type of boundary conditions but also on the curvature of a riemannian metric based on the coefficients of the system

probabilistic model based functional parcellation reveals a robust fine grained subdivision of the striatum the striatum is involved in many different aspects of behaviour reflected by the variety of cortical areas that provide input to this structure this input is topographically organized and is likely to result in functionally specific signals such specificity can be examined using functional clustering approaches here we propose a bayesian model based functional clustering approach applied solely to resting state striatal functional mri timecourses to identify intrinsic striatal functional modules data from two sets of ten participants were used to obtain parcellations and examine their robustness this stable clustering was used to initialize a more constrained model in order to obtain individualized parcellations in 57 additional participants resulting cluster time courses were used to examine functional connectivity between clusters and related to the rest of the brain in a glm analysis we find six distinct clusters in each hemisphere with clear inter hemispheric correspondence and functional relevance these clusters exhibit functional connectivity profiles that further underscore their homologous nature and are consistent with existing notions on segregation and integration in parallel cortico basal ganglia loops our findings suggest that multiple territories within both the affective and motor regions can be distinguished solely using resting state functional mri from these regions

latent change classes in dichotomous data changes in dichotomous data caused by treatments can be analyzed by means of the so called linear logistic model with relaxed assumptions llra the llra does not require observable criteria representing a single underlying latent trait but it postulates the generalizability of the treatment effects over criteria and subjects to test this latter crucial assumption the mixture llra was proposed that allows directly unobservable types of subjects to have different treatment effects as the earlier methods for estimating the parameters of the mixture llra have specific drawbacks a further method based on the conditional maximum likelihood principle will be presented here in contrast to the earlier conditional methods it uses all of the dichotomous change data while having fewer parameters further its goodness of fit tests become more sensitive to a falsely specified number of change types even though the treatment effects are biased for typically occurring small to moderate sample sizes however parametric bootstrapping of the distributions of the fit statistics is recommended for performing hypotheses tests finally three applications of the new method to empirical data are described first about the effect of the so called trager psychophysical integration second about the effect of autogenic therapy on patients with psychosomatic symptoms and third about the effect of religious education on the attitude towards sects

sampling theorems associated with fourth and higher order self adjoint eigenvalue problems abstract consider a regular self adjoint eigenvalue problem of n th order and the associated whittaker shannon kramer sampling series the samples being taken at the eigenvalues and the sinc function being replaced by the generalized fourier coefficients of the kernel arising from the eigenvalue problem with respect to the complete set of orthogonal eigenfunctions the major aim of this paper is to show that each such sampling expansion can be written as a lagrange interpolation series provided the kernel satisfies suitable conditions two concrete fourth order eigenvalue problems are examined a regular one as an application of the general result and a singular one the problem whether the two resulting sampling series are really new or can be reduced to already known results is in part open