incorporating spatial dependence into bayesian multiple testing of statistical parametric maps in functional neuroimaging abstract the analysis of functional neuroimaging data often involves the simultaneous testing for activation at thousands of voxels leading to a massive multiple testing problem this is true whether the data analyzed are time courses observed at each voxel or a collection of summary statistics such as statistical parametric maps spms it is known that classical multiplicity corrections become strongly conservative in the presence of a massive number of tests some more popular approaches for thresholding imaging data such as the benjamini hochberg step up procedure for false discovery rate control tend to lose precision or power when the assumption of independence of the data does not hold bayesian approaches to large scale simultaneous inference also often rely on the assumption of independence we introduce a spatial dependence structure into a bayesian testing model for the analysis of spms by using spms rather than the voxel time courses much of the computational burden of bayesian analysis is mitigated increased power is demonstrated by using the dependence model to draw inference on a real dataset collected in a fmri study of cognitive control the model also is shown to lead to improved identification of neural activation patterns known to be associated with eye movement tasks

bayesian fmri time series analysis with spatial priors we describe a bayesian estimation and inference procedure for fmri time series based on the use of general linear models glms importantly we use a spatial prior on regression coefficients which embodies our prior knowledge that evoked responses are spatially contiguous and locally homogeneous further using a computationally efficient variational bayes framework we are able to let the data determine the optimal amount of smoothing we assume an arbitrary order auto regressive ar model for the errors our model generalizes earlier work on voxel wise estimation of glm ar models and inference in glms using posterior probability maps ppms results are shown on simulated data and on data from an event related fmri experiment

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

option pricing formulas based on a non gaussian stock price model options are financial instruments that depend on the underlying stock we explain their non gaussian fluctuations using the nonextensive thermodynamics parameter q a generalized form of the black scholes bs partial differential equation and some closed form solutions are obtained the standard bs equation q 1 which is used by economists to calculate option prices requires multiple values of the stock volatility known as the volatility smile using q 1 5 which well models the empirical distribution of returns we get a good description of option prices using a single volatility

graph partitioned spatial priors for functional magnetic resonance images abstract spatial models of functional magnetic resonance imaging fmri data allow one to estimate the spatial smoothness of general linear model glm parameters and eschew pre process smoothing of data entailed by conventional mass univariate analyses recently diffusion based spatial priors harrison l m penny w daunizeau j and friston k j 2008 diffusion based spatial priors for functional magnetic resonance images neuroimage were proposed which provide a way to formulate an adaptive spatial basis where the diffusion kernel of a weighted graph laplacian wgl is used as the prior covariance matrix over glm parameters an advantage of these is that they can be used to relax the assumption of isotropy and stationarity implicit in smoothing data with a fixed gaussian kernel the limitation of diffusion based models is purely computational due to the large number of voxels in a brain volume one solution is to partition a brain volume into slices using a spatial model for each slice this reduces computational burden by approximating the full wgl with a block diagonal form where each block can be analysed separately while fmri data are collected in slices the functional structures exhibiting spatial coherence and continuity are generally three dimensional calling for a more informed partition we address this using the graph laplacian to divide a brain volume into sub graphs whose shape can be arbitrary their shape depends crucially on edge weights of the graph which can be based on the euclidean distance between voxels isotropic or on glm parameters anisotropic encoding functional responses the result is an approximation the full wgl that retains its 3d form and also has potential for parallelism we applied the method to high resolution 1 mm3 fmri data and compared models where a volume was divided into either slices or graph partitions models were optimized using expectation maximization and the approximate log evidence computed to compare these different ways to partition a spatial prior the high resolution fmri data presented here had greatest evidence for the graph partitioned anisotropic model which was best able to preserve fine functional detail

comparing methods of analyzing fmri statistical parametric maps approaches for the analysis of statistical parametric maps spms can be crudely grouped into three main categories in which different philosophies are applied to delineate activated regions these being type i error control thresholding false discovery rate fdr control thresholding and posterior probability thresholding to better understand the properties of these main approaches we carried out a simulation study to compare the approaches as they would be used on real data sets using default settings we find that posterior probability thresholding is the most powerful approach and type i error control thresholding provides the lowest levels of type i error false discovery rate control thresholding performs in between the other approaches for both these criteria although for some parameter settings this approach can approximate the performance of posterior probability thresholding based on these results we discuss the relative merits of the three approaches in an attempt to decide upon an optimal approach we conclude that viewing the problem of delineating areas of activation as a classification problem provides a highly interpretable framework for comparing the methods within this framework we highlight the role of the loss function which explicitly penalizes the types of errors that may occur in a given analysis

a switching multi scale dynamical network model of eeg meg we introduce a new generative model of the encephalography eeg meg data the inversion of which allows for inferring the locations and temporal evolution of the underlying sources as well as their dynamical interactions the proposed switching mesostate space model smsm builds on the multi scale generative model for eeg meg by daunizeau and friston 2007 smsm inherits the assumptions that 1 bioelectromagnetic activity is generated by a set of distributed sources 2 the dynamics of these sources can be modelled as random fluctuations about a small number of mesostates and 3 the number of mesostates engaged by a cognitive task is small additionally four generalising assumptions are now included 4 the mesostates interact according to a full dynamical causal network dcn that can be estimated 5 the dynamics of the mesostates can switch between multiple approximately linear operating regimes 6 each operating regime remains stable over finite periods of time temporal clusters and 7 the total number of times the mesostates dynamics can switch is small the proposed model adds therefore a level of flexibility by accommodating complex brain processes that cannot be characterised by purely linear and stationary gaussian dynamics importantly the smsm furnishes a new interpretation of the eeg meg data in which the source activity may have multiple discrete modes of behaviour each with approximately linear dynamics this is modelled by assuming that the connection strengths of the underlying mesoscopic dcn are time dependent but piecewise constant i e they can undergo discrete changes over time a variational bayes inversion scheme is derived to estimate all the parameters of the model by maximising a negative free energy lower bound on the model evidence this bound is used to select among different model choices that are defined by the number of mesostates as well as by the number of stationary linear regimes the full model is compared to a simplified version that uses no dynamical assumptions as well as to a standard eeg inversion technique the comparison is carried out using an extensive set of simulations and the application of smsm to a real data set is also demonstrated our results show that for experimental situations in which we have some a priori belief that there are multiple approximately linear dynamical regimes the proposed smsm provides a natural modelling tool

portfolio selection problem with value at risk constraints under non extensive statistical mechanics the optimal portfolio selection problem is a major issue in the financial field in which the process of asset prices is usually modeled by a wiener process that is the return distribution of the asset is normal however several empirical results have shown that the return distribution of the asset has the characteristics of fat tails and aiguilles and is not normal in this work we propose an optimal portfolio selection model with a value at risk var constraint in which the process of asset prices is modeled by the non extensive statistical mechanics instead of the classical wiener process the model can describe the characteristics of fat tails and aiguilles of returns using the dynamic programming principle we derive a hamilton jacobi bellman hjb equation then employing the lagrange multiplier method we obtain closed form solutions for the case of logarithmic utility moreover the empirical results show that the price process can more accurately fit the empirical distribution of returns than the familiar wiener process in addition as the time increases the constraint becomes binding that is to control the risk the agent reduces the proportion of the wealth invested in the risky asset furthermore at the same confidence level the agent reduces the proportion of the wealth invested in the risky asset more quickly under our model than under the model based on the wiener process this can give investors a good decision making reference

hybrid dirichlet mixture models for functional data summary in functional data analysis curves or surfaces are observed up to measurement error at a finite set of locations for say a sample of n individuals often the curves are homogeneous except perhaps for individual specific regions that provide heterogeneous behaviour e g damaged areas of irregular shape on an otherwise smooth surface motivated by applications with functional data of this nature we propose a bayesian mixture model with the aim of dimension reduction by representing the sample of n curves through a smaller set of canonical curves we propose a novel prior on the space of probability measures for a random curve which extends the popular dirichlet priors by allowing local clustering non homogeneous portions of a curve can be allocated to different clusters and the n individual curves can be represented as recombinations hybrids of a few canonical curves more precisely the prior proposed envisions a conceptual hidden factor with k levels that acts locally on each curve we discuss several models incorporating this prior and illustrate its performance with simulated and real data sets we examine theoretical properties of the proposed finite hybrid dirichlet mixtures specifically their behaviour as the number of the mixture components goes to 1 and their connection with dirichlet process mixtures

a new look at q exponential distributions via excess statistics q exponential distributions play an important role in nonextensive statistics they appear as the canonical distributions i e the maximum generalized q entropy distributions under mean constraint their relevance is also independently justified by their appearance in the theory of superstatistics introduced by beck and cohen in this paper we provide a third and independent rationale for these distributions we indicate that q exponentials are stable by a statistical normalization operation and that pickands extreme values theorem plays the role of a clt like theorem in this context this suggests that q exponentials can arise in many contexts if the system at hand or the measurement device introduces some threshold moreover we give an asymptotic connection between excess distributions and maximum q entropy we also highlight the role of generalized pareto distributions in many applications and present several methods for the practical estimation of q exponential parameters

multi period semi variance portfolio selection model and numerical solution variance is substituted by semi variance in markowitz s portfolio selection model moreover one period portfolio selection is extended to multi period in this paper a class of multi period semi variance model is formulated originally besides a hybrid genetic algorithm ga which makes use of the position displacement strategy of the particle swarm optimizer pso as a mutation operation is applied to solve the multi period semi variance model for this class of portfolio model numerical results show that the hybrid ga with pso is effective and feasible

a bayesian discovery procedure we discuss a bayesian discovery procedure for multiple comparison problems we show that under a coherent decision theoretic framework a loss function combining true positive and false positive counts leads to a decision rule based on a threshold of the posterior probability of the alternative under a semi parametric model for the data we show that the bayes rule can be approximated by the optimal discovery procedure odp recently introduced by storey 2007a improving the approximation leads us to a bayesian discovery procedure bdp which exploits the multiple shrinkage in clusters implied by the assumed nonparametric model we compare the bdp and the odp estimates in a simple simulation study and in an assessment of differential gene expression based on microarray data from tumor samples we extend the setting of the odp by discussing modifications of the loss function that lead to different single thresholding statistics finally we provide an application of the previous arguments to dependent spatial data

impact of foreign exchange rate on oil companies risk in stock market during the recent years the importance of effective risk management has become extremely crucial value at risk var is a standard downside measure to explain the behavior of financial series as the garch models have been successfully applied in modeling the volatility structure of securities and other financial assets the var of garch models has turned into an important quantity to study in addition to garch family models the markov regime switching garch mrs garch models are a widely used approach to model financial volatility with potential structural breaks in this paper we evaluated the performance of the mrs garch models with the traditional arma garch family models for estimating var of the stock return of operating companies in the oil industry srocoi in irans stock market under the normal student t and ged distributions our findings showed that the mrs garch models outperform the arma garch family models to capture the characteristics of the srocois volatility additionally we evaluated impact of the foreign exchange rate fluctuations on the var of srocois that were calculated from the optimal models under two regimes usingardl model the results further demonstrated that foreign exchange rate fluctuations have significant and different impacts on the var of srocois across regimes we modeled srocois in irans stock market using mrs garch and arma garch family models mrs garch models under student t and ged distributions have better performance to capture srocois we estimated in sample and out of sample var of srocois from optima models we evaluated impact of the foreign exchange rate fluctuations on the var of srocois foreign exchange rate significantly effect on the var of srocois in different regimes

portfolio selection based on a benchmark process with dynamic value at risk constraints abstract portfolio selection is an essential issue in finance it studies how to allocate one s wealth in a basket of securities to maximize the return and minimize the risk and dynamic portfolio selection based on a benchmark process is one of the most important types different from the existing literature we impose a dynamic risk control on it as a matter of fact performing an optimal portfolio strategy in the light of a dynamic portfolio formulation does not eliminate the possibility of an investor going to bankruptcy or even more serious situations in a volatile financial market before the terminal time so it is reasonable and necessary to impose a dynamic risk control on the instantaneous wealth throughout the investment horizon to ensure that the investment behavior can proceed and we intend to address this interesting issue in this paper more specifically we investigate the dynamic portfolio selection problem based on a benchmark process coupled with a dynamic value at risk constraint by stochastic dynamic programming techniques we derive the corresponding hamilton jacobi bellman equation moreover the optimal portfolio strategies are obtained by lagrange multiplier method to verify the model two numerical examples are illustrated the results show the difference of optimal portfolio strategies with and without the dynamic var constraint the composition of the risky assets is constant but the investment proportion is reduced as the var constraint becomes binding this research can provide a good decision making reference for risk averse investors

a mesostate space model for eeg and meg abstract we present a multi scale generative model for eeg that entails a minimum number of assumptions about evoked brain responses namely 1 bioelectric activity is generated by a set of distributed sources 2 the dynamics of these sources can be modelled as random fluctuations about a small number of mesostates 3 mesostates evolve in a temporal structured way and are functionally connected i e influence each other and 4 the number of mesostates engaged by a cognitive task is small e g between one and a few a variational bayesian learning scheme is described that furnishes the posterior density on the models parameters and its evidence since the number of meso sources specifies the model the model evidence can be used to compare models and find the optimum number of meso sources in addition to estimating the dynamics at each cortical dipole the mesostate space model and its inversion provide a description of brain activity at the level of the mesostates i e in terms of the dynamics of meso sources that are distributed over dipoles the inclusion of a mesostate level allows one to compute posterior probability maps of each dipole being active i e belonging to an active mesostate critically this model accommodates constraints on the number of meso sources while retaining the flexibility of distributed source models in explaining data in short it bridges the gap between standard distributed and equivalent current dipole models furthermore because it is explicitly spatiotemporal the model can embed any stochastic dynamical causal model e g a neural mass model as a markov process prior on the mesostate dynamics the approach is evaluated and compared to standard inverse eeg techniques using synthetic data and real data the results demonstrate the added value of the mesostate space model and its variational inversion

empirical regularities of opening call auction in chinese stock market abstract we study the statistical regularities of an opening call auction using the ultra high frequency data of 22 liquid stocks traded on the shenzhen stock exchange in 2003 the distribution of the relative price defined as the relative difference between the order price in the opening call auction and the closing price on the last trading day is asymmetric and that the distribution displays a sharp peak at the zero relative price and a relatively wide peak at the negative relative price the detrended fluctuation analysis dfa method is adopted to investigate the long term memory of relative order prices we further study the statistical regularities of order sizes in the opening call auction and observe a phenomenon of number preference known as order size clustering the probability density function pdf of order sizes could be well fitted by a q gamma function and the long term memory also exists in order sizes in addition both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit order book lob established immediately after the opening call auction and a price clustering phenomenon is observed

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

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

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

monotonically equivalent entropies and solution of additivity equation generalized entropies are studied as lyapunov functions for the master equation markov chains three basic properties of these lyapunov functions are taken into consideration universality independence of the kinetic coefficients trace form the form of sum over the states and additivity for composition of independent subsystems all the entropies which have all three properties simultaneously and are defined for positive probabilities are found they form a one parametric family we consider also pairs of entropies s1 s2 which are connected by the monotonous transformation s2 f s1 equivalent entropies all classes of pairs of universal equivalent entropies one of which has a trace form and another is additive these entropies can be different one from another were found these classes consist of two one parametric families the family of entropies which are equivalent to the additive trace form entropies and the family of renyi tsallis entropies

bayesian spatiotemporal model of fmri data this research describes a new bayesian spatiotemporal model to analyse block design bold fmri studies in the temporal dimension we parameterise the hemodynamic response function s hrf shape with a potential increase of signal and a subsequent exponential decay in the spatial dimension we use gaussian markov random fields gmrf priors on activation characteristics parameters location and magnitude that embody our prior knowledge that evoked responses are spatially contiguous and locally homogeneous the result is a spatiotemporal model with a small number of parameters all of them interpretable simulations from the model are performed in order to ascertain the performance of the sampling scheme and the ability of the posterior to estimate model parameters as well as to check the model sensitivity to signal to noise ratio results are shown on synthetic data and on real data from a block design fmri experiment

diffusion based spatial priors for functional magnetic resonance images we recently outlined a bayesian scheme for analyzing fmri data using diffusion based spatial priors harrison l m penny w ashburner j trujillo barreto n friston k j 2007 diffusion based spatial priors for imaging neuroimage 38 677 695 the current paper continues this theme applying it to a single subject functional magnetic resonance imaging fmri study of the auditory system we show that spatial priors on functional activations based on diffusion can be formulated in terms of the eigenmodes of a graph laplacian this allows one to discard eigenmodes with small eigenvalues to provide a computationally efficient scheme furthermore this formulation shows that diffusion based priors are a generalization of conventional laplacian priors penny w d trujillo barreto n j friston k j 2005 bayesian fmri time series analysis with spatial priors neuroimage 24 350 362 finally we show how diffusion based priors are a special case of gaussian process models that can be inverted using classical covariance component estimation techniques like restricted maximum likelihood patterson h d thompson r 1974 maximum likelihood estimation of components of variance paper presented at 8th international biometrics conference constanta romania the convention in spm is to smooth data with a fixed isotropic gaussian kernel before inverting a mass univariate statistical model this entails the strong assumption that data are generated smoothly throughout the brain however there is no way to determine if this assumption is supported by the data because data are smoothed before statistical modeling in contrast if a spatial prior is used smoothness is estimated given non smoothed data explicit spatial priors enable formal model comparison of different prior assumptions e g that data are generated from a stationary i e fixed throughout the brain or non stationary spatial process indeed for the auditory data we provide strong evidence for a non stationary process which concurs with a qualitative comparison of predicted activations at the boundary of functionally selective regions

fractal surfaces from simple arithmetic operations fractal surfaces patchwork quilts are shown to arise under most general circumstances involving simple bitwise operations between real numbers a theory is presented for all deterministic bitwise operations on a finite alphabet it is shown that these models give rise to a roughness exponent h that shapes the resulting spatial patterns larger values of the exponent leading to coarser surfaces

generalized kolmogorov entropy in the dynamics of multifractal generation abstract we point out that applying a maximization principle on a tsallis like generalized form of the kolmogorov entropy for iterated function systems naturally provides a canonical statistical frame for the description of the multifractal measures generated by such dynamical processes multifractal spectra can then be characterized by usual statistical parameters in particular the temperature we show that in the limit of zero temperature the multifractal measure collapses to a homogeneous distribution over a fractal support for finite temperatures multifractal spectra are studied numerically in an illustrative example

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

optimal investment problem under non extensive statistical mechanics abstract the optimal investment problem in which the asset price process is modeled by the non extensive statistical mechanics is studied in this paper by the methods of deterministic control and the dynamic programming we obtain the optimal strategy with logarithmic utility function power utility function and quadratic utility function respectively moreover the numerical results indicate that the optimal investment strategy is affected by the non extensive parameter the proportion invested in the risky asset decreases as the wealth increases under quadratic utility function but it remains unchanged under power utility and logarithmic utility function

differential equations connecting var and cvar abstract the value at risk var is a very important risk measure for practitioners supervisors and researchers many practitioners draw on var as a critical instrument in risk management and other actuarial financial problems while supervisors and regulators must deal with var due to the basel accords and solvency ii among other reasons from a theoretical point of view var presents some drawbacks overcome by other risk measures such as the conditional value at risk cvar var is neither differentiable nor sub additive because it is neither continuous nor convex on the contrary cvar satisfies all of these properties and this simplifies many analytical studies if var is replaced by cvar in this paper several differential equations connecting both var and cvar will be given they will allow us to address several important issues involving var with the help of the cvar properties this new methodology seems to be very efficient in particular a new var representation theorem may be found and optimization problems involving var or probabilistic constraints always have an equivalent differentiable optimization problem applications in var marginal var cvar and marginal cvar estimates will be addressed as well illustrative actuarial and financial examples will be likewise presented

variational free energy and the laplace approximation this note derives the variational free energy under the laplace approximation with a focus on accounting for additional model complexity induced by increasing the number of model parameters this is relevant when using the free energy as an approximation to the log evidence in bayesian model averaging and selection by setting restricted maximum likelihood reml in the larger context of variational learning and expectation maximisation em we show how the reml objective function can be adjusted to provide an approximation to the log evidence for a particular model this means reml can be used for model selection specifically to select or compare models with different covariance components this is useful in the context of hierarchical models because it enables a principled selection of priors that under simple hyperpriors can be used for automatic model selection and relevance determination ard deriving the reml objective function from basic variational principles discloses the simple relationships among variational bayes em and reml furthermore we show that em is formally identical to a full variational treatment when the precisions are linear in the hyperparameters finally we also consider briefly dynamic models and how these inform the regularisation of free energy ascent schemes like em and reml

disequilibrium complexity the schottky effect and q entropies in paramagnetism abstract we investigate connections between statistical quantifiers and paramagnetism more concretely we apply the notions of i disequilibrium and ii statistical complexity to a paramagnetic system of non coupled dipoles interesting insights are thereby obtained in particular we encounter a kind of criticality not associated to the temperature but to the disequilibrium

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

indices for testing neural codes one of the most critical challenges in systems neuroscience is determining the neural code a principled framework for addressing this can be found in information theory with this approach one can determine whether a proposed code can account for the stimulus response relationship specifically one can compare the transmitted information between the stimulus and the hypothesized neural code with the transmitted information between the stimulus and the behavioral response if the former is smaller than the latter i e if the code cannot account for the behavior the code can be ruled out the information theoretic index most widely used in this context is shannon s mutual information the shannon test however is not ideal for this purpose while the codes it will rule out are truly nonviable there will be some nonviable codes that it will fail to rule out here we describe a wide range of alternative indices that can be used for ruling codes out the range includes a continuum from shannon information to measures of the performance of a bayesian decoder we analyze the relationship of these indices to each other and their complementary strengths and weaknesses for addressing this problem

a meshless discrete galerkin mdg method for the numerical solution of integral equations with logarithmic kernels abstract this paper describes a computational method for solving fredholm integral equations of the second kind with logarithmic kernels the method is based on the discrete galerkin method with the shape functions of the moving least squares mls approximation constructed on scattered points as basis the mls methodology is an effective technique for the approximation of an unknown function that involves a locally weighted least square polynomial fitting the numerical scheme developed in the current paper utilizes the non uniform gauss legendre quadrature rule for approximating logarithm like singular integrals and so reduces the solution of the logarithmic integral equation to the solution of a linear system of algebraic equations the proposed method is meshless since it does not require any background mesh or domain elements the error analysis of the method is provided the scheme is also applied to a boundary integral equation which is a reformulation of a boundary value problem of laplace s equation with linear robin boundary conditions finally numerical examples are included to show the validity and efficiency of the new technique

some properties of q logarithm and q exponential functions in tsallis statistics we present some formulae which q logarithmic and q exponential functions introduced in tsallis statistics satisfy exact expression of the mellin transform of q exponential function is given moreover the q generalization of the digamma function is presented

convergence in reaction diffusion systems an information theory approach abstract we have applied an information theory approach in order to study the problem of convergence to point like or extended attractors in reaction diffusion systems a distance between two states based on the kullback leibler relative information was defined different forms of the probability distribution some of them based on the knowledge of the nonequilibrium potential when accesible give the possibility to look for a faster and or more accurate convergence this approach offers the chance to estimate the attraction basins of the different attractors as well as detecting limit circles together with an easy evaluation of their periods

path integral approach to the nonextensive canonical density matrix abstract feynman s path integral is herein generalized to the nonextensive canonical density matrix based on tsallis entropy this generalization is done in two ways by using unnormalized and normalized constraints firstly we consider the path integral formulation with unnormalized constraints and this generalization is worked out through two different ways which are shown to be equivalent these formulations with unnormalized constraints are solutions to the two generalized bloch equations proposed in this work the first form of the generalized bloch equation is linear but with a temperature dependent effective hamiltonian the second form is nonlinear and resembles the anomalous correlated diffusion equation porous medium equation furthermore we can extend these results to the prescription of field theory using integral representations the second development is dedicated to analyzing the path integral formulation with normalized constraints to illustrate the methods introduced here we analyze the free particle case and a non interacting scalar field the results herein obtained are expected to be useful in the discussion of generic nonextensive contexts

student s t and r distributions unified derivation from an entropic variational principle abstract the optimization of the recently generalized entropy of the form s q 1 dx p x q q 1 with the constraints dx p x 1 and x 2 q dx x 2 p x q 1 yields the student s t distribution for q 1 and the r distribution for q

var as the cvar sensitivity var minimization is a complex problem playing a critical role in many actuarial and financial applications of mathematical programming the usual methods of convex programming do not apply due to the lack of sub additivity the usual methods of differentiable programming do not apply either due to the lack of continuity taking into account that the cvar may be given as an integral of var one has that var becomes a first order mathematical derivative of cvar this property will enable us to give accurate approximations in var optimization since the optimization var and cvar will become quite closely related topics applications in both finance and insurance will be given

numerical solution of integral equations with a logarithmic kernel by the method of arbitrary collocation points an integral equation whose kernel presents logarithmic singularity is numerically solved by the method of arbitrary collocation points acp as a first step a gaussian quadrature of order n hence of polynomial accuracy 2n 1 is employed for the numerical approximation of the integral until now the collocation which follows was performed on special points xk determined as roots of appropriate transcedental functions in order to retain the 2n 1 degree of polynomial accuracy of the gaussian quadrature in this paper an appropriate interpolatory technique is proposed so that xk may be arbitrary and yet the high 2n 1 accuracy of the gaussian quadrature is retained

zeroth law compatibility of nonadditive thermodynamics nonextensive thermodynamics is criticized by the statement that the zeroth law cannot be satisfied with nonadditive composition rules corrected in this paper we determine the general functional form of those nonadditive composition rules that are compatible with the zeroth law of thermodynamics we find that this general form is additive for the formal logarithms of the original quantities and the familiar relations of thermodynamics apply to these our result offers a possible solution to the long standing questions about equilibrium between extensive and nonextensive systems or systems with different nonextensivity parameters

fractal structure with a typical scale in order to understand the characteristics common to distributions which have both fractal and non fractal scale regions in a unified framework we introduce the concept of a typical scale we employ a model of 2d gravity modified by the r2 term as a tool to understand such distributions through the typical scale this model is obtained by adding an interaction term with a typical scale to a scale invariant system a distribution derived in the model provides power law one in the large scale region but weibull like one in the small scale region as examples of distributions which have both fractal and non fractal regions we take those of personal income and citation number of scientific papers we show that these distributions are fitted fairly well by the distribution curves derived analytically in the r2 2d gravity model as a result we consider that the typical scale is a useful concept to understand various distributions observed in the real world in a unified way we also point out that the r2 2d gravity model provides us with an effective tool to read the typical scales of various distributions in a systematic way

multiwavelet packet entropy and its application in transmission line fault recognition and classification multiwavelets possess better properties than traditional wavelets multiwavelet packet transformation has more high frequency information spectral entropy can be applied as an analysis index to the complexity or uncertainty of a signal this paper tries to define four multiwavelet packet entropies to extract the features of different transmission line faults and uses a radial basis function rbf neural network to recognize and classify 10 fault types of power transmission lines first the preprocessing and postprocessing problems of multiwavelets are presented shannon entropy and tsallis entropy are introduced and their difference is discussed second multiwavelet packet energy entropy time entropy shannon singular entropy and tsallis singular entropy are defined as the feature extraction methods of transmission line fault signals third the plan of transmission line fault recognition using multiwavelet packet entropies and an rbf neural network is proposed finally the experimental results show that the plan with the four multiwavelet packet energy entropies defined in this paper achieves better performance in fault recognition the performance with sa4 symmetric antisymmetric multiwavelet packet tsallis singular entropy is the best among the combinations of different multiwavelet packets and the four multiwavelet packet entropies

simultaneous control of error rates in fmri data analysis the key idea of statistical hypothesis testing is to fix and thereby control the type i error false positive rate across samples of any size multiple comparisons inflate the global family wise type i error rate and the traditional solution to maintaining control of the error rate is to increase the local comparison wise type ii error false negative rates however in the analysis of human brain imaging data the number of comparisons is so large that this solution breaks down the local type ii error rate ends up being so large that scientifically meaningful analysis is precluded here we propose a novel solution to this problem allow the type i error rate to converge to zero along with the type ii error rate it works because when the type i error rate per comparison is very small the accumulation or global type i error rate is also small this solution is achieved by employing the likelihood paradigm which uses likelihood ratios to measure the strength of evidence on a voxel by voxel basis in this paper we provide theoretical and empirical justification for a likelihood approach to the analysis of human brain imaging data in addition we present extensive simulations that show the likelihood approach is viable leading to cleaner looking brain maps and operational superiority lower average error rate finally we include a case study on cognitive control related activation in the prefrontal cortex of the human brain

population level inferences for distributed meg source localization under multiple constraints application to face evoked fields we address some key issues entailed by population inference about responses evoked in distributed brain systems using magnetoencephalography meg in particular we look at model selection issues at the within subject level and feature selection issues at the between subject level using responses evoked by intact and scrambled faces around 170 ms m170 we compared the face validity of subject specific forward models and their summary statistics in terms of how estimated responses reproduced over subjects at the within subject level we focused on the use of multiple constraints or priors for inverting distributed source models we used restricted maximum likelihood reml estimates of prior covariance components in both sensor and source space and show that their relative importance is conserved over subjects at the between subject level we used standard anatomical normalization methods to create posterior probability maps that furnish inference about regionally specific population responses we used these to compare different summary statistics namely i whether to test for differences between condition specific source estimates or whether to test the source estimate of differences between conditions and ii whether to accommodate differences in source orientation by using signed or unsigned absolute estimates of source activity

numerical solution of an integral equation with logarithmic singularity abstract two numerical methods based on gaussian quadrature formulae are proposed for solving integral equations of the first kind with a logarithmic singularity while the first method requires the evaluation of derivatives of the input functions the second method avoids them

portfolio selection under different attitudes in fuzzy environment abstract this paper studies stock portfolio selection problem based on varying conservative neutral aggressive attitudes the return rates of stocks are characterized by fuzzy variables the pareto optimal solutions are obtained by maximizing the return and minimizing the risk subject to constraints of transaction cost and value at risk since investors with different attitudes may have different understanding of the likelihoods of occurrence measure me with the ability of reflecting varying conservative neutral aggressive attitudes is adopted based on me the expected value of fuzzy return and the lower absolute deviation are used to quantify the return and risk levels of a portfolio respectively then the constraint method is employed to obtain the efficient frontier finally an empirical study is carried out using the data of 10 stocks in chinese stock market sensitivity comparisons are conducted to demonstrate the effectiveness of the proposed model the results show that different frontiers can be obtained under different attitudes confidence levels and values at risk

portfolio selection problem with nonlinear wealth equations under non extensive statistical mechanics for time varying sde abstract this paper is dedicated to the study of continuous time mean variance optimal portfolio selection problem with non linear wealth equations under non extensive statistical mechanics for the time varying stochastic differential equation model firstly we allow the returns and variance of risky assets are time varying functions which can fit the financial data better secondly we consider an investor with the non linear wealth equation in fact the wealth equations are not linear in many cases the investor has to pay some taxes which leads to a non linear wealth equation moreover since the return of the stocks price may be affected by a large investors portfolio selection the wealth equation is non linear in this case thirdly the non linear wealth equation driven by tsallis distribution is constructed under non extensive statistical mechanics which can capture the characteristics of fat tails and aiguilles of the risky asset s return the viscosity solution of the hjb equation for the portfolio problem is proposed by the optimal stochastic control theory and lagrange multiplier method finally the efficient portfolio strategy and efficient frontier under non extensive statistical mechanics are obtained furthermore numerical analysis and real data study are discussed to show our results

diffusion based spatial priors for imaging we describe a bayesian scheme to analyze images which uses spatial priors encoded by a diffusion kernel based on a weighted graph laplacian this provides a general framework to formulate a spatial model whose parameters can be optimized the application we have in mind is a spatiotemporal model for imaging data we illustrate the method on a random effects analysis of fmri contrast images from multiple subjects this simplifies exposition of the model and enables a clear description of its salient features typically imaging data are smoothed using a fixed gaussian kernel as a pre processing step before applying a mass univariate statistical model e g a general linear model to provide images of parameter estimates an alternative is to include smoothness in a multivariate statistical model penny w d trujillo barreto n j friston k j 2005 bayesian fmri time series analysis with spatial priors neuroimage 24 350 362 the advantage of the latter is that each parameter field is smoothed automatically according to a measure of uncertainty given the data in this work we investigate the use of diffusion kernels to encode spatial correlations among parameter estimates nonlinear diffusion has a long history in image processing in particular flows that depend on local image geometry romeny b m t 1994 geometry driven diffusion in computer vision kluwer academic publishers can be used as adaptive filters this can furnish a non stationary smoothing process that preserves features which would otherwise be lost with a fixed gaussian kernel we describe a bayesian framework that incorporates non stationary adaptive smoothing into a generative model to extract spatial features in parameter estimates critically this means adaptive smoothing becomes an integral part of estimation and inference we illustrate the method using synthetic and real fmri data

extracting features of gaussian self similar stochastic processes via the bandt pompe approach by recourse to appropriate information theory quantifiers normalized shannon entropy and martin plastino rosso intensive statistical complexity measure we revisit the characterization of gaussian self similar stochastic processes from a bandt pompe viewpoint we show that the ensuing approach exhibits considerable advantages with respect to other treatments in particular clear quantifiers gaps are found in the transition between the continuous processes and their associated noises

on the derivation of power law distributions within classical statistical mechanics far from the thermodynamic limit we show that within classical statistical mechanics without taking the thermodynamic limit the most general boltzmann factor for the canonical ensemble is a q exponential function the only assumption here is that microcanonical distributions have to be separated from the total system energy which is the prerequisite for any sensible measurement we derive that all separable distributions are parametrized by a mathematical separation constant q which can be related to the non extensivity q parameter in tsallis distributions we further demonstrate that nature fixes the separation constant q to 1 for large dimensionality of gibbs phase space our results will be relevant for systems with a low dimensional space for example nanosystems comprised of a small number of particles or for systems with a dimensionally collapsed phase space which might be the case for a large class of complex systems

improving reliability of subject level resting state fmri parcellation with shrinkage estimators abstract a recent interest in resting state functional magnetic resonance imaging rsfmri lies in subdividing the human brain into anatomically and functionally distinct regions of interest for example brain parcellation is often a necessary step for defining the network nodes used in connectivity studies while inference has traditionally been performed on group level data there is a growing interest in parcellating single subject data however this is difficult due to the inherent low signal to noise ratio of rsfmri data combined with typically short scan lengths a large number of brain parcellation approaches employ clustering which begins with a measure of similarity or distance between voxels the goal of this work is to improve the reproducibility of single subject parcellation using shrinkage based estimators of such measures allowing the noisy subject specific estimator to borrow strength in a principled manner from a larger population of subjects we present several empirical bayes shrinkage estimators and outline methods for shrinkage when multiple scans are not available for each subject we perform shrinkage on raw inter voxel correlation estimates and use both raw and shrinkage estimates to produce parcellations by performing clustering on the voxels while we employ a standard spectral clustering approach our proposed method is agnostic to the choice of clustering method and can be used as a pre processing step for any clustering algorithm using two datasets a simulated dataset where the true parcellation is known and is subject specific and a test retest dataset consisting of two 7 minute resting state fmri scans from 20 subjects we show that parcellations produced from shrinkage correlation estimates have higher reliability and validity than those produced from raw correlation estimates application to test retest data shows that using shrinkage estimators increases the reproducibility of subject specific parcellations of the motor cortex by up to 30