estimating a state space model from point process observations a widely used signal processing paradigm is the state space model the state space model is defined by two equations an observation equation that describes how the hidden state or latent process is observed and a state equation that defines the evolution of the process through time inspired by neurophysiology experiments in which neural spiking activity is induced by an implicit latent stimulus we develop an algorithm to estimate a state space model observed through point process measurements we represent the latent process modulating the neural spiking activity as a gaussian autoregressive model driven by an external stimulus given the latent process neural spiking activity is characterized as a general point process defined by its conditional intensity function we develop an approximate expectation maximization em algorithm to estimate the unobservable state space process its parameters and the parameters of the point process the em algorithm combines a point process recursive nonlinear filter algorithm the fixed interval smoothing algorithm and the state space covariance algorithm to compute the complete data log likelihood efficiently we use a kolmogorov smirnov test based on the time rescaling theorem to evaluate agreement between the model and point process data we illustrate the model with two simulated data examples an ensemble of poisson neurons driven by a common stimulus and a single neuron whose conditional intensity function is approximated as a local bernoulli process

on a spectral flow formula for the homological index abstract consider a selfadjoint unbounded operator d on a hilbert space h and a one parameter norm continuous family of selfadjoint bounded operators a t t r that converges in norm to asymptotes a at then under certain conditions 22 that include the assumption that the operators d t d a t t r all have discrete spectrum the spectral flow along the path d t can be shown to be equal to the index of t d t when the latter is an unbounded fredholm operator on l 2 r h in 16 an investigation of the index spectral flow question when the operators in the path may have some essential spectrum was started but under restrictive assumptions that rule out differential operators in general in 11 the question of what happens when the fredholm condition is dropped altogether was investigated in these circumstances the fredholm index is replaced by the witten index in this paper we take the investigation begun in 11 much further we show how to generalize a formula known from the setting of the l 2 index theorem to the non fredholm setting restricting back to the case of selfadjoint fredholm operators our formula extends the result of 22 in the sense of relaxing the discrete spectrum condition it also generalizes some other fredholm operator results of 21 16 11 that permit essential spectrum for the operators in the path our result may also apply however when the operators d t have essential spectrum equal to the whole real line our main theorem gives a trace formula relating the homological index of 7 to an integral formula that is known for a path of selfadjoint fredholms with compact resolvent and with unitarily equivalent endpoints to compute spectral flow our formula however applies to paths of selfadjoint non fredholm operators we interpret this as indicating there is a generalization of spectral flow to the non fredholm setting

determinant bundles manifolds with boundary and surgery we define determinant bundles associated to the following data i a family of generalized dirac operators on even dimensional manifolds with boundary ii the choice of a spectral section for the family of dirac operators induced on the boundary under the assumption that the operators of the boundary family have null spaces of constant dimension we define through the notion ofb zeta function a quillen metric we also introduce the analogue of the bismut freed connection we prove that the curvature of a natural perturbation of the bismut freed connection equals the 2 form piece in the right hand side of the family index formula thus extending to manifolds with boundary results of quillen bismut and freed given a closed fibration we investigate the behaviour of the quillen metric and of the bismut freed connection under the operation of surgery along a fibering hypersurface we prove in particular additivity formulae for the curvature and for the logarithm of the holonomy

transitional regression models with application to environmental time series abstract environmental epidemiologists often encounter time series data in the form of discrete or other nonnormal outcomes for example in modeling the relationship between air pollution and hospital admissions or mortality rates we present a case study examining the association between pollen counts and meteorologic covariates although such time series data are inadequately described by standard methods for gaussian time series they are often autocorrelated and warrant an analysis beyond those provided by ordinary generalized linear models glms transitional regression models trms signifying nonlinear regression models expressed in terms of conditional means and variances given past observations provide a unifying framework for two mainstream approaches to extending the glm for autocorrelated data the first approach models current outcomes with a glm that incorporates past outcomes as covariates whereas the second models individual outcomes with marginal glms and then couples the error term

on the gluing problem for the eta invariant we solve the gluing problem for the invariant consider a generalized dirac operator d over a compact riemannian manifold m that is partitioned by a compact hypersurface n such that m m un m2 we assume that the riemannian metric of m and d have a product structure near n i e d i d d dn with some dirac operator dn on n using boundary conditions of atiyah patodi singer type parametrized by lagrangian subspaces l of kerd we define selfadjoint extensions d i 1 2 over m we express the invariant of d in terms of the invariants of di an invariant m l l2 of the pair of the lagrangian subspaces l l2 which is related to the maslov index and an integer valued term j in the adiabatic limit i e if a tubular neighborhood of n is long enough the vanishing of j is shown under certain regularity conditions we apply this result in order to prove cutting and pasting formulas for the invariant a wall nonadditivity result for the index of atiyah patodi singer boundary value problems and a splitting formula for the spectral flow 1 the gluing problem and applications 1 1 introduction we solve the gluing problem for the invariant of generalized dirac operators consider a closed compact riemannian manifold carrying a dirac bundle with a generalized dirac operator assume that this manifold is separated into two pieces by a compact hypersurface the gluing problem for the invariant consists in expressing the invariant of the original dirac operator in terms of the invariants of the dirac operators living on the pieces the selfadjoint operators on the two components with boundary depend on a boundary condition given by lagrangian subspaces lx l2 of a certain symplectic vector space the gluing formula also contains an additional real valued term m l l2 which is nicely related to the symplectic geometry and the maslov index

dynamic stochastic models for time dependent ordered paired comparison systems abstract when paired comparisons are made sequentially over time as for example in chess competitions it is natural to assume that the underlying abilities do change with time previous approaches are based on fixed updating schemes where the increments and decrements are fixed functions of the underlying abilities the parameters that determine the functions have to be specified a priori and are based on rational reasoning we suggest an alternative scheme for keeping track with the underlying abilities our approach is based on two components a response model that specifies the connection between the observations and the underlying abilities and a transition model that specifies the variation of abilities over time the response model is a very general paired comparison model allowing for ties and ordered responses the transition model incorporates random walk models and local linear trend models taken together these two components form a non gaussian state space model based on recent results rec

likelihood analysis of non gaussian measurement time series summary in this paper we provide methods for estimating non gaussian time series models these techniques rely on markov chain monte carlo to carry out simulation smoothing and bayesian posterior analysis of parameters and on importance sampling to estimate the likelihood function for classical inference the time series structure of the models is used to ensure that our simulation algorithms are efficient

a monte carlo em approach for partially observable diffusion processes theory and applications to neural networks we present a monte carlo approach for training partially observable diffusion processes we apply the approach to diffusion networks a stochastic version of continuous recurrent neural networks the approach is aimed at learning probability distributions of continuous paths not just expected values interestingly the relevant activation statistics used by the learning rule presented here are inner products in the hilbert space of square integrable functions these inner products can be computed using hebbian operations and do not require backpropagation of error signals moreover standard kernel methods could potentially be applied to compute such inner products we propose that the main reason that recurrent neural networks have not worked well in engineering applications e g speech recognition is that they implicitly rely on a very simplistic likelihood model the diffusion network approach proposed here is much richer and may open new avenues for applications of recurrent neural networks we present some analysis and simulations to support this view very encouraging results were obtained on a visual speech recognition task in which neural networks outperformed hidden markov models

the scan sampler for time series models summary an algorithm called the scan sampler is developed and discussed the scan sampler has a variety of uses for time series analysis based on the state space model with nongaussian observations the algorithm is based on the kalman filter smoothing algorithm it can be used for bayesian inference using markov chain monte carlo and to find posterior modes

anomalous thresholds and edge singularities in electrical impedance tomography studies of models of current flow behaviour in electrical impedance tomography eit have shown that the current density distribution varies extremely rapidly near the edge of the electrodes used in the technique this behaviour imposes severe restrictions on the numerical techniques used in image reconstruction algorithms in this paper we have considered a simple two dimensional case and we have shown how the theory of end point pinch singularities which was developed for studying the anomalous thresholds encountered in elementary particle physics can be used to give a complete description of the analytic structure of the current density near to the edge of the electrodes as a byproduct of this study it was possible to give a complete description of the riemann sheet manifold of the eigenfunctions of the logarithmic kernel these methods can be readily extended to other weakly singular kernels

effects of measurement precision and finite numbers of electrodes on linear impedance imaging algorithms impedance imaging systems reconstruct approximations to the conductivity inside a body from electrical measurements made on the boundary the linearized problem was studied by calderon who showed that if the conductivity differs little from a constant then it can be reconstructed approximately in his work calderon assumed that arbitrary current densities can be applied anywhere on the body s surface and the resulting voltages perfectly measured in practice however imaging systems apply currents through a finite number of electrodes on the surface and measure the resulting voltages with a limited precision in this paper linear algorithms are described for approximating the electrical conductivity in a disk from finitely many limited precision measurements the effects of finite precision and electrode number on a two dimensional version of calderon s method are studied it is shown that as the measurement errors go to zero and the electrodes proliferate in a space filling manner the finite electro

spinq twistor and spinc spinq structures induce spinq style twistor spaces which possess canonical spinc structures such structures produce dirac operators their indices for the even dimensional case and the adiabatic limit of their reduced invariants for the odd dimensional case are discussed

the ζ determinant and the additivity of the η invariant on the smooth self adjoint grassmannian in this paper we discuss the existence of the determinant of a dirac operator on a compact manifold with boundary we show that the determinant is well defined in the case of the operator with a domain determined by a boundary condition from the smooth self adjoint grassmannian discussed in the papers 5 13 29 we prove a generalization of a pasting formula for the invariant see 34 the results of the paper are used in the recent proof of the projective equality of the determinant and quillen determinant on see 30 31

bayesian forecasting of multinomial time series through conditionally gaussian dynamic models abstract we consider inference in the class of conditionally gaussian dynamic models for nonnormal multivariate time series in such models data are represented as drawn from nonnormal sampling distributions whose parameters are related both through time and hierarchically across several multivariate series a key example the main focus here is time series of multinomial observations a common occurrence in sociological and demographic studies involving categorical count data however we present this development in a more general setting as the resulting methods apply beyond the multinomial context we discuss inference in the proposed model class via a posterior simulation scheme based on appropriate modifications of existing markov chain monte carlo algorithms for normal dynamic linear models and including metropolis hastings components we develop an analysis of time series of flows of students in the italian secondary education system as an illustration of the models and methods

adiabatic limits of the η invariants the odd dimensional atiyah patodi singer problem we study the invariant of boundary value problems of atiyah patodi singer type we prove the formula for the spectral flow of the families overs1 assuming a product structure in a collar neighbourhood of the boundary we show that the invariant behaves the same way as on a closed manifold we also study the adiabatic limit of the spectral invariants in nice cases we are able to split them into a contribution from the interior one from the cylinder and an error term then we show that the error term disappears with the increasing length of the cylinder

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

the additivity of the η invariant the case of a singular tangential operator we prove the decomposition formula for the invariant of the compatible dirac operator on a closed manifoldm which is a sum of two submanifolds with common boundary

auxiliary mixture sampling for parameter driven models of time series of counts with applications to state space modelling we consider parameter driven models of time series of counts where the observations are assumed to arise from a poisson distribution with a mean changing over time according to a latent process estimation of these models is carried out within a bayesian framework using data augmentation and markov chain monte carlo methods we suggest a new auxiliary mixture sampler which possesses a gibbsian transition kernel where we draw from full conditional distributions belonging to standard distribution families only emphasis lies on application to state space modelling of time series of counts but we show that auxiliary mixture sampling may be applied to a wider range of parameter driven models including random effects models and panel data models based on the poisson distribution

the hessian method highly efficient simulation smoothing in a nutshell abstract i introduce the hessian highly efficient simulation smoothing in a nutshell method for numerically efficient simulation smoothing in state space models with univariate states given a vector of parameters the vector of states 1 n is gaussian and the observed vector y y 1 y n need not be i describe a procedure to construct a close approximation q y to the target density p y it requires code to compute five derivatives of log p y t t with respect to t t 1 n and is not otherwise model specific since q y is proper fully normalised and simulable it can be used as an importance density for importance sampling is or as a proposal density for markov chain monte carlo mcmc hessian is an acronym but it also refers to the sparse hessian matrix of log p y with respect to the hessian method is based on sparse matrix operations rather than the kalman filter i construct q y and a related approximation q y of p y for two stochastic volatility models two stochastic count models and a stochastic duration model i illustrate their use for numerical approximation of likelihood function values and marginal likelihoods using is and for posterior inference using is and mcmc compared with other simulation smoothing methods the hessian method is highly numerically efficient in an is application featuring a student s t stochastic volatility model and n 8851 daily log returns the efficiency of is for numerical approximation of the elements of the posterior mean e y is between 80 and 100

on cobordism of manifolds with corners this work sets up a cobordism theory for manifolds with corners and gives an identication with the homotopy of a certain limit of thom spectra it thereby creates a geometrical interpretation of adams novikov resolutions and lays the foundation for investigating the chromatic status of the elements so realized as an application lie groups together with their left invariant framings are calculated by regarding them as corners of manifolds with interesting chern numbers the work also shows how elliptic cohomology can provide useful invariants for manifolds of codimension 2

non gaussian state space modeling of nonstationary time series abstract a non gaussian state space approach to the modeling of nonstationary time series is shown the model is expressed in state space form where the system noise and the observational noise are not necessarily gaussian recursive formulas of prediction filtering and smoothing for the state estimation and identification of the non gaussian state space model are given also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas significant merits of non gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples a typical application of this non gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes simple gaussian state space modeling is not adequate for this situation here the model with small system noise variance cannot detect jump whereas the one with large system noise variance yields unfavorable wiggle to work

z k manifolds and families of dirac operators the index of a family of a family of dirac operators is ak theory element in the parameter space sullivan s k manifolds are used to detect this index completely for the first chern class this gives a topological interpretation of witten s global anomaly the relationship with the geometry of the index bundle is considered

corners in m theory m theory can be defined on closed manifolds as well as on manifolds with boundary as an extension we show that manifolds with corners appear naturally in m theory we illustrate this with four situations the lift to bounding 12 dimensions of m theory on anti de sitter spaces ten dimensional heterotic string theory in relation to 12 dimensions and the two m branes within m theory in the presence of a boundary the m2 brane is taken with or as a boundary and the worldvolume of the m5 brane is viewed as a tubular neighborhood we then concentrate on the variant of the heterotic theory as a corner and explore analytical and geometric consequences in particular we formulate and study the phase of the partition function in this setting and identify the corrections due to the corner s the analysis involves considering m theory on disconnected manifolds and makes use of the extension of the atiyah patodi singer index theorem to manifolds with corners and the b calculus of melrose

monte carlo maximum likelihood estimation for non gaussian state space models state space models are considered for observations which have non gaussian distributions we obtain accurate approximations to the loglikelihood for such models by monte carlo simulation devices are introduced which improve the accuracy of the approximations and which increase computational efficiency the loglikelihood function is maximised numerically to obtain estimates of the unknown hyperparameters standard errors of the estimates due to simulation are calculated details are given for the important special cases where the observations come from an exponential family distribution and where the observation equation is linear but the observation errors are non gaussian the techniques are illustrated with a series for which the observations have a poisson distribution and a series for which the observation errors have a t distribution

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

separable laplace equation magic toeplitz matrix and generalized ohm s law we say that a laplace equation on an inhomogeneous medium is separable if the medium can be represented as the product of the argument functions it is shown that the conductivity equation on a 2 d disk is reduced to a couple of ordinary differential equations if the conductivity of the medium is the product of the angle and radius functions several important cases are discussed such as circular and a noncircular blob like medium conductivity we derive a closed form of the neumann to dirichlet map that gives rise to a new family of symmetric matrices we call it the magic toeplitz matrix a symmetric toeplitz matrix with the rows and columns summing to the same value the generalized ohm s law on the disk is derived which relates the vector of the current density to the vector of voltages through the resistance matrix we demonstrate how a separable laplace pde can be applied to electrical impedance tomography and breast cancer detection

the hierarchical logistic regression model for multilevel analysis abstract a hierarchical logistic regression model is proposed for studying data with group structure and a binary response variable the group structure is defined by the presence of micro observations embedded within contexts macro observations and the specification is at both of these levels at the first micro level the usual logistic regression model is defined for each context the same regressors are used in each context but the micro regression coefficients are free to vary over contexts at the second level the micro coefficients are treated as functions of macro regressors an empirical bayes estimation procedure is proposed for estimating the micro and macro coefficients explicit formulas are provided that are computationally feasible for large scale data analyses these include an algorithm for finding the maximum likelihood estimates of the covariance components representing within and between macro equation error variability the methodology is applied to world fertility survey data

rapid estimation of high parameter auditory filter shapes a bayesian adaptive procedure the quick auditory filter qaf procedure was used to estimate auditory filter shapes that were asymmetric about their peaks in three experiments listeners who were naive to psychoacoustic experiments detected a fixed level pure tone target presented with a spectrally notched noise masker the qaf procedure adaptively manipulated the masker spectrum level and the position of the masker notch which was optimized for the efficient estimation of the five parameters of an auditory filter model experiment i demonstrated that the qaf procedure provided a convergent estimate of the auditory filter shape at 2 khz within 150 to 200 trials approximately 15 min to complete and for a majority of listeners excellent test retest reliability in experiment ii asymmetric auditory filters were estimated for target frequencies of 1 and 4 khz and target levels of 30 and 50 db sound pressure level the estimated filter shapes were generally consistent with published norms especially at the low target level it is known that the auditory filter estimates are narrower for forward masking than simultaneous masking due to peripheral suppression a result replicated in experiment iii using fewer than 200 qaf trials

markov chain monte carlo for dynamic generalised linear models summary this paper presents a new methodological approach for carrying out bayesian inference about dynamic models for exponential family observations the approach is simulationbased and involves the use of markov chain monte carlo techniques a metropolishastings algorithm is combined with the gibbs sampler in repeated use of an adjusted version of normal dynamic linear models different alternative schemes based on sampling from the system disturbances and state parameters separately and in a block are derived and compared the approach is fully bayesian in obtaining posterior samples with state parameters and unknown hyperparameters illustrations with real datasets with sparse counts and missing values are presented extensions to accommodate more general evolution forms and distributions for observations and disturbances are outlined

aps boundary conditions eta invariants and adiabatic limits we prove an adiabatic limit formula for the eta invariant of a manifold with boundary the eta invariant is defined using the atiyah patodisinger boundary condition and the underlying manifold is fibered over a manifold with boundary our result extends the work of bismut cheeger to manifolds with boundary

twistor spaces and the general adiabatic expansions abstract we investigate the behavior of derivatives of the fundamental solution of a parabolic equation for the square of dirac operator on a twistor space when the metric is blown up in the base space direction such a blowing up operation is expected to be an effective method for extracting some intrinsic values from various geometric invariants most of whose cores consist of some derivatives of the fundamental solution

bar partial torsion for complex manifolds and the adiabatic limit torsion for complex manifolds and the adiabatic limit we consider a complex fibration f m l b and pull back bundles e 1 and e 2 over m using the adiabatic limit idea we compute the metric invariant tp e1 tp e2 where tp e denotes the complex ray singer torsion

posterior mode estimation by extended kalman filtering for multivariate dynamic generalized linear models abstract a family of multivariate dynamic generalized linear models is introduced as a general framework for the analysis of time series with observations from the exponential family besides common conditionally gaussian models this article deals with univariate models for counted and binary data and as the most interesting multivariate case models for nonstationary multicategorical time series for univariate responses a related yet different class of models has been introduced in a bayesian setting by west harrison and migon assuming conjugate prior posterior distributions for the natural parameter of the exponential family they derive an approximate filter for estimation of time varying states or parameters however their method raises some problems in particular in extending it to the multivariate case a different approach to filtering and smoothing is chosen in this article to avoid a full bayesian analysis based on numerical integration which becomes computationally critical for higher

covariance matrix and transfer function of dynamic generalized linear models statistical inference for dynamic generalized linear models dglms is challenging due to the time varying nature of the unknown parameters in these models in this paper we focus on the covariance matrix and the transfer function the two key components in dglms we first establish some convergence results for the covariance matrix estimation we then provide an in depth study of the transfer function on its stability and fourier transformation which is necessary for parameter estimation in dglms implications of our results on estimation in dglms are illustrated in the paper through a simulation study and a real data example our understanding on dglms has substantially improved though this study

dynamic generalized linear models and bayesian forecasting abstract dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters this leads to the calculation of closed standard form predictive distributions for forecasting and model criticism the structure of the models depends on the time evolution of underlying state variables and the feedback of observational information to these variables is achieved using linear bayesian prediction methods data analytic aspects of the models concerning scale parameters and outliers are discussed and some applications are provided dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and

alternative algorithms for the estimation of dynamic factor mimic and varying coefficient regression models this paper provides a general approach to the formulation and estimation of dynamic unobserved component models after introducing the general model two methods for estimating the unknown parameters are presented both are algorithms for maximizing the likelihood function the first is based on the method of scoring the second is the em algorithm a derivative free method each iteration of em requires a kalman filter and smoother followed by straightforward regression calculations the paper suggests using the em methods to quickly locate a neighborhood of the maximum scoring can then be used to pinpoint the maximum and calculate the information matrix

smoothing hazard functions and time varying effects in discrete duration and competing risks models abstract state space or dynamic approaches to discrete or grouped duration data with competing risks or multiple terminating events allow simultaneous modeling and smooth estimation of hazard functions and time varying effects in a flexible way full bayesian or posterior mean estimation using numerical integration techniques or monte carlo methods can become computationally rather demanding or even infeasible for higher dimensions and larger datasets therefore based on previous work on filtering and smoothing for multicategorical time series and longitudinal data our approach uses posterior mode estimation thus we have to maximize posterior densities or equivalently a penalized likelihood which enforces smoothness of hazard functions and time varying effects by a roughness penalty dropping the bayesian smoothness prior and adopting a nonparametric viewpoint one might also start directly from maximizing this penalized likelihood we show how fisher scoring smoothing iterations can be carried ou

regression models for nonstationary categorical time series asymptotic estimation theory for the analysis of nonstationary categorical time series a parsimonious and flexible class of models is proposed these models are generalizations of regression models for stochastically independent categorical observations consistency asymptotic normality and efficiency of the maximum likelihood estimator are shown under weak and easily verifiable requirements some models for binary time series are discussed in detail to demonstrate asymptotic properties a theorem is given addressing maximum likelihood estimation for general stochastic processes then it is shown that the assumptions of this theorem are consequences of the requirements for categorical time series for this proof some lemmas are used which may be of interest in similar cases

statistical estimation of resistance conductance by electrical impedance tomography measurements this paper is built upon the assumption that in electrical impedance tomography vectors of voltages and currents are linearly dependent through a resistance matrix this linear relationship was confirmed experimentally and may be derived analytically under certain assumptions regarding electrodes isaacson 1991 given measurement data consisting of voltages and currents we treat this relationship as a linear statistical model thus our goal is not to reconstruct the image but directly estimate its electromagnetic properties reflected in the resistance and or conductance matrix using electrical impedance tomography eit measurements of voltages and currents on the periphery of the body since no inverse problem is involved the algorithm for estimation merely reduces to one matrix inversion we estimate the impedance resistance matrix using well established statistical inference techniques for linear regression models we provide a comprehensive treatment for a two dimensional homogeneous body of a circular shape by which many concepts of electrical impedance tomography such as width of electrodes the difference between voltage current and current voltage systems are illustrated our theory may be applied to various tests including eit hardware calibration and whether the medium is homogeneous these tests are illustrated on phantom agar data

a generalization of the kalman filter for models with state dependent observation variance abstract the kalman filter is generalized to cover state space models in which the variance of the observation error depends on the state vector derivations of the filter yielding minimum mean squared error linear estimators and associated error covariance matrices are obtained from two differing viewpoints linear bayes theory and gauss markov theory the results are applied to a model for which y t t 1 2 n follow a poisson distribution with corresponding intensities t t 1 2 n that are assumed to follow an autoregressive process of order 1 namely the steady state generalized kalman filter algorithm in the case for which 1 gives a generalization of exponential smoothing for a poisson process with time varying intensity

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

consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models generalized linear models are used for regression analysis in a number of cases including categorical responses where the classical assumptions are violated the statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator we present mild general conditions which respectively assure weak or strong consistency or asymptotic normality most of the previous work has been concerned with natural link functions in this case our normality condition though obtained by a different approach is closely related to a condition of haberman 1977a examples show how the general conditions reduce to weak requirements for special exponential families further for regressors with a compact range sufficient conditions are given which do not involve the unknown parameter and are therefore easy to check in practice responses with a bounded range e g categorical responses and stochastic regressors also are treated

global uniqueness for a two dimensional inverse boundary value problem we show that the coefficient y x of the elliptic equation vie qyvu 0 in a two dimensional domain is uniquely determined by the corresponding dirichlet to neumann map on the boundary and give a reconstruction pro

framed m branes corners and topological invariants we uncover and highlight relations between the m branes in m theory and various topological invariants the hopf invariant over q z and z2 the kervaire invariant the f invariant and the invariant this requires either a framing or a corner structure the canonical framing provides a minimum for the classical action and the change of framing encodes the structure of the action and possible anomalies we characterize the flux quantization condition on the c field and the topological action of the m5 brane via the hopf invariant and the dual of the c field as a refinement of an element of hopf invariant two in the signature formulation the contribution to the m brane effective action is given by the maslov index of the corner the kervaire invariant implies that the effective action of the m5 brane is quadratic our study leads to viewing the self dual string which is the boundary of the m2 brane on the m5 brane worldvolume as a string theory in the sense of cobordism of manifolds with corners we show that the dynamics of the c field and its dual are encoded in a unified way in the 4 sphere which suggests the corresponding spectrum as the generalized cohomology theory describing the fields the effective action of the corner is captured by the f invariant which is an invariant at chromatic level two finally considering m theory on manifolds with g2 holonomy we show that the canonical g2 structure minimizes the topological part of the m5 brane action this is done via the invariant and a variant that we introduce related to the one loop polynomial we uncover and highlight relations between the m branes in m theory and various topological invariants the hopf invariant over q z and z2 the kervaire invariant the f invariant and the invariant this requires either a framing or a corner structure the canonical framing provides a minimum for the classical action and the change of framing encodes the structure of the action and possible anomalies we characterize the flux quantization condition on the c field and the topological action of the m5 brane via the hopf invariant and the dual of the c field as a refinement of an element of hopf invariant two in the signature formulation the contribution to the m brane effective action is given by the maslov index of the corner the kervaire invariant implies that the effective action of the m5 brane is quadratic our study leads to viewing the self dual string which is the boundary of the m2 brane on the m5 brane worldvolume as a string theory in the sense of cobordism of manifolds with corners

collapsing riemannian manifolds while keeping their curvature bounded i soit y n une variete de riemann connexe complete et p y n le rayon d injectivite i p de l application exponentielle en p est defini comme etant le plus petit r tel que exp p b r p n est pas un diffeomorphisme sur son image on etudie la situation dans laquelle la taille du rayon d injectivite est petite relativement a la courbure

setting the quantum integrand of m theory in anomaly free quantum field theories the integrand in the bosonic functional integral the exponential of the effective action after integrating out fermions is often defined only up to a phase without an additional choice we term this choice setting the quantum integrand in the low energy approximation to m theory the e8 model for the c field allows us to set the quantum integrand using geometric index theory we derive mathematical results of independent interest about pfaffians of dirac operators in 8k 3 dimensions both on closed manifolds and manifolds with boundary these theorems are used to set the quantum integrand of m theory for closed manifolds and for compact manifolds with either temporal global or spatial local boundary conditions in particular we show that m theory makes sense on arbitrary 11 manifolds with spatial boundary generalizing the construction of heterotic m theory on cylinders

filtering and smoothing via estimating functions abstract we consider the problem of filtering and smoothing in state space models which include nonlinear and non gaussian models we do not make any distributional assumptions about the processes involved our approach to these problems is based on the theory of estimating functions filter and smoother are obtained as solutions of estimating equations that are optimal in appropriate classes we illustrate our procedures by simulation studies of a model where the observational variance depends on the state and a binomial logit model with a covariate in non gaussian cases procedures based on estimating equations often perform considerably better than the existing semiparametric procedures

existence and uniqueness for electrode models for electric current computed tomography the following experiment is considered to a body of given conductivity a number of electrodes are attached through which current is sent on the same electrodes the resulting voltages are measured this experiment can be described by a number of mathematical models k s cheng et al ieee transactions on biomedical engineering 36 1989 pp 918 924 these models are discussed and their predictions compared with experiment in particular a model is exhibited that is capable of predicting the experimentally measured voltages to within 0 1 percent for this model existence and uniqueness of the associated electrical potential is proved

dynamic modelling and penalized likelihood estimation for discrete time survival data summmary this paper describes a dynamic or state space approach for analyzing discrete time or grouped survival data simultaneous estimation of baseline hazard functions and of timevarying covariate effects is based on maximization of posterior densities or equivalently a penalized likelihood leading to kalman type smoothing algorithms data driven choice of unknown smoothing parameters is possible via an em type procedure the methods are illustrated by applications to real data