multiple window parallel adaptive boundary finding in computer vision the problem considered in this paper is the estimation of highly variable object boundaries in noisy images boundaries may be those of a tank in an ir image a spinal canal in a cat scan a cloud in a visible light image etc or they may be internal to an object such as the boundary between a spherical surface and a cylindrical surface in a manufactured object the focus of the paper is on parallel multiple window boundary estimation algorithms here the image field is parti tioned into an array of rectangular windows and boundary finders are run simultaneously within the windows the boundary segments found within the windows are then seamed together to obtain meaningful global boundaries the entire procedure is treated within a maximum likelihood estimation framework that we have developed for boundary finding although our multiple window estimation approach can be used with a number of local boundary finding algorithms we concen trate on one which is based on dynamic programming and will produce the true maximum likelihood boundary some theoretical considera tions for boundary model design and boundary finding runtime are covered included is the use of a low computational cost f test for test ing whether a window contains a boundary and an analytical treatment which shows that use of coarse pixels with a chi square test or an f test improves the probability of correctly recognizing whether a boundary is present in a window

compatible conditional distributions abstract consider two families of candidate conditional densities or probability mass functions f x y y s y and f y x x s x this article investigates necessary and sufficient conditions for the existence of a joint density or joint probability mass function f x y with the given families as its associated conditional densities this supplements previous work that has addressed the question of uniqueness of f x y assuming its existence

model choice versus model criticism ratmann et al 1 radically modifies the perception of the approximate bayesian computation abc error into a genuine parameter whereas the unification of abc representations in section 2 is immensely valuable however it requires that the data are informative about e which is not necessarily true for instance when then e e x0 e e

a binless correlation measure reduces the variability of memory reactivation estimates summary the standard procedure for measuring correlations between pairs of spike trains is to count the numbers of spikes occurring within a specified set of time intervals partitioning the continuous time line into discrete bins of width w seconds one then computes the pearson correlation between pairs of the bin occupancy vectors this method introduces a form of quantization noise similar to that in analog to digital signal processing devices due to the arbitrary positioning of bin boundaries relative to pairs of spikes small changes in bin width and small uniform shifts in bin boundaries typically produce large variations in the apparent correlation an alternative method of determining a correlation between pairs of spike trains was recently introduced rather than discretize the data in time the original spike trains are convolved with a gaussian kernel with parameter chosen to give an effective width matching the bin width w 12 calculating the pearson correlation of the resulting smooth functions gives an estimate of the correlation between the spike trains matching that given by the bin based procedure without introducing the significant variability of the bin based estimate measures of memory reactivation based on the partial correlations between ensembles of pairwise spike train correlations are biased downwards by the quantization noise present in the pairwise correlation estimates using a binless method to measure pairwise correlation we find that the partial correlation or explained variance of rat hippocampal maze activity and post maze sleep taking into account pre maze sleep correlations increases significantly over estimates made with the standard bin based procedure copyright 2007 john wiley sons ltd

on the φ0 stability of comparison differential systems for many years now the variety of problems of the qualitative properties of differential equations in the context of lyaponov second method has been successfully investigated in a unified way using the comparison principle s in this method the qualitative properties of the system of differential equations are inferred from the corresponding properties of the solutions of the system of comparison equations in order to successfully employ this method it is generally required that the comparison systems possess some special properties the conditions under which the scalar comparison equations possess positivity and stability behaviour have been investigated using scalar lyapunov function method by brauer l siljak and grujic 9 and others ladde 3 gave suficient conditions for nonnegativity and stability of solutions of systems of comparison equations in his investigation of stability of comparison differential systems ladde 3 considered the asymptotic stability and exponential asymptotic stability of the comparison differential system using the method of vector lyapunov functions however imbedded in the method of vector lyapunov function is the requirement of quasimonotone nondecreasing property of the comparison system but quasimonotonicity of the comparison system is not a necessary condition for the system to be stable thus the limitation of the application potential of this general and effective method is due to the fact that

inference for stereological extremes in the production of clean steels the occurrence of imperfections so called inclusions is unavoidable the strength of a clean steel block is largely dependent on the size of the largest imperfection that it contains so inference on extreme inclusion size forms an important part of quality control sampling is generally done by measuring imperfections on planar slices leading to an extreme value version of a standard stereological problem how to make inference on large inclusions using only the sliced observations under the assumption that inclusions are spherical this problem has been tackled previously using a combination of extreme value models stereological calculations a bayesian hierarchical model and standard markov chain monte carlo mcmc techniques our objectives in this article are twofold 1 to assess the robustness of such inferences with respect to the assumption of spherical inclusions and 2 to develop an inference procedure that is valid for nonspherical inclusions we inv

boosting bayesian parameter inference of nonlinear stochastic differential equation models by hamiltonian scale separation parameter inference is a fundamental problem in data driven modeling given observed data that is believed to be a realization of some parameterized model the aim is to find parameter values that are able to explain the observed data in many situations the dominant sources of uncertainty must be included into the model for making reliable predictions this naturally leads to stochastic models stochastic models render parameter inference much harder as the aim then is to find a distribution of likely parameter values in bayesian statistics which is a consistent framework for data driven learning this so called posterior distribution can be used to make probabilistic predictions we propose a novel exact and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series the algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer where the measurements are mapped on heavier beads compared to those of the simulated data to arrive at distribution samples we employ a hamiltonian monte carlo approach combined with a multiple time scale integration a separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large furthermore at least for one dimensional problems we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically our approach is applicable to a wide range of inference problems and is highly parallelizable

a comparison of descriptive models of a single spike train by information geometric measure in examining spike trains different models are used to describe their structure the different models often seem quite similar but because they are cast in different formalisms it is often difficult to compare their predictions here we use the information geometric measure an orthogonal coordinate representation of point processes to express different models of stochastic point processes in a common coordinate system within such a framework it becomes straightforward to visualize higher order correlations of different models and thereby assess the differences between models we apply the information geometric measure to compare two similar but not identical models of neuronal spike trains the inhomogeneous markov and the mixture of poisson models it is shown that they differ in the second and higher order interaction terms in the mixture of poisson model the second and higher order interactions are of comparable magnitude within each order whereas in the inhomogeneous markov model they have alternating signs over different orders this provides guidance about what measurements would effectively separate the two models as newer models are proposed they also can be compared to these models using information geometry

unitary events in multiple single neuron spiking activity ii nonstationary data in order to detect members of a functional group cell assembly in simultaneously recorded neuronal spiking activity we adopted the widely used operational definition that membership in a common assembly is expressed in near simultaneous spike activity unitary event analysis a statistical method to detect the significant occurrence of coincident spiking activity in stationary data was recently developed see the companion article in this issue the technique for the detection of unitary events is based on the assumption that the underlying processes are stationary in time this requirement however is usually not fulfilled in neuronal data here we describe a method that properly normalizes for changes of rate the unitary events by moving window analysis uemwa analysis for unitary events is performed separately in overlapping time segments by sliding a window of constant width along the data in each window stationarity is assumed performance and sensitivity are demonstrated by use of simulated spike trains of independently firing neurons into which coincident events are inserted if cortical neurons organize dynamically into functional groups the occurrence of near simultaneous spike activity should be time varying and related to behavior and stimuli uemwa also accounts for these potentially interesting nonstationarities and allows locating them in time the potential of the new method is illustrated by results from multiple single unit recordings from frontal and motor cortical areas in awake behaving monkey

an interpretation of partial least squares abstract univariate partial least squares pls is a method of modeling relationships between a y variable and other explanatory variables it may be used with any number of explanatory variables even far more than the number of observations a simple interpretation is given that shows the method to be a straightforward and reasonable way of forming prediction equations its relationship to multivariate pls in which there are two or more y variables is examined and an example is given in which it is compared by simulation with other methods of forming prediction equations with univariate pls linear combinations of the explanatory variables are formed sequentially and related to y by ordinary least squares regression it is shown that these linear combinations here called components may be viewed as weighted averages of predictors where each predictor holds the residual information in an explanatory variable that is not contained in earlier components and the quantity to be predicted is the vecto

estimation of parameters for macroparasite population evolution using approximate bayesian computation we estimate the parameters of a stochastic process model for a macroparasite population within a host using approximate bayesian computation abc the immunity of the host is an unobserved model variable and only mature macroparasites at sacrifice of the host are counted with very limited data process rates are inferred reasonably precisely modeling involves a three variable markov process for which the observed data likelihood is computationally intractable abc methods are particularly useful when the likelihood is analytically or computationally intractable the abc algorithm we present is based on sequential monte carlo is adaptive in nature and overcomes some drawbacks of previous approaches to abc the algorithm is validated on a test example involving simulated data from an autologistic model before being used to infer parameters of the markov process model for experimental data the fitted model explains the observed extra binomial variation in terms of a zero one immunity variable which has a short lived presence in the host

relevant statistics for bayesian model choice the choice of the summary statistics that are used in bayesian inference and in particular in approximate bayesian computation algorithms has bearings on the validation of the resulting inference those statistics are nonetheless customarily used in approximate bayesian computation algorithms without consistency checks we derive necessary and sufficient conditions on summary statistics for the corresponding bayes factor to be convergent namely to select the true model asymptotically those conditions which amount to the expectations of the summary statistics differing asymptotically under the two models are quite natural and can be exploited in approximate bayesian computation settings to infer whether or not a choice of summary statistics is appropriate via a monte carlo validation

ϕ0 stability of hybrid impulsive dynamic systems on time scales abstract in this paper we shall employ the method of cone valued lyapunov functions and comparison principle to investigate the 0 stability of impulsive hybrid systems on time scales

convergence of regression adjusted approximate bayesian computation we present asymptotic results for the regression adjusted version of approximate bayesian computation introduced by beaumont et al 2002 we show that for an appropriate choice of the bandwidth regression adjustment will lead to a posterior that asymptotically correctly quantifies uncertainty furthermore for such a choice of bandwidth we can implement an importance sampling algorithm to sample from the posterior whose acceptance probability tends to unity as the data sample size increases this compares favourably to results for standard approximate bayesian computation where the only way to obtain a posterior that correctly quantifies uncertainty is to choose a much smaller bandwidth one for which the acceptance probability tends to zero and hence for which monte carlo error will dominate

expectation propagation for likelihood free inference many models of interest in the natural and social sciences have no closed form likelihood function which means that they cannot be treated using the usual techniques of statistical inference in the case where such models can be efficiently simulated bayesian inference is still possible thanks to the approximate bayesian computation abc algorithm although many refinements have been suggested abc inference is still far from routine abc is often excruciatingly slow due to very low acceptance rates in addition abc requires introducing a vector of summary statistics s y the choice of which is relatively arbitrary and often require some trial and error making the whole process laborious for the user we introduce in this work the ep abc algorithm which is an adaptation to the likelihood free context of the variational approximation algorithm known as expectation propagation the main advantage of ep abc is that it is faster by a few orders of magnitude than standard algorithms while producing

triplet markov fields for the classification of complex structure data we address the issue of classifying complex data we focus on three main sources of complexity namely the high dimensionality of the observed data the dependencies between these observations and the general nature of the noise model underlying their distribution we investigate the recent triplet markov fields and propose new models in this class designed for such data and in particular allowing very general noise models in addition our models can handle the inclusion of a learning step in a consistent way so that they can be used in a supervised framework one advantage of our models is that whatever the initial complexity of the noise model parameter estimation can be carried out using state of the art bayesian clustering techniques under the usual simplifying assumptions as generative models they can be seen as an alternative in the supervised case to discriminative conditional random fields identifiability issues underlying the models in the nonsupervised case are discussed while the models performance is illustrated on simulated and real data exhibiting the mentioned various sources of complexity

comparison of asymptotic variances of inhomogeneous markov chains with application to markov chain monte carlo methods in this paper we study the asymptotic variance of sample path averages for inhomogeneous markov chains that evolve alternatingly according to two different 7 reversible markov transition kernels p and q more specifically our main result allows us to compare directly the asymptotic variances of two inhomogeneous markov chains associated with different kernels pi and q i i is an element of 0 1 as soon as the kernels of each pair p 0 p 1 and q 0 q 1 can be ordered in the sense of lag one autocovariance as an important application we use this result for comparing different data augmentation type metropolis hastings algorithms in particular we compare some pseudo marginal algorithms and propose a novel exact algorithm referred to as the random refreshment algorithm which is more efficient in terms of asymptotic variance than the grouped independence metropolis hastings algorithm and has a computational complexity that does not exceed that of the monte carlo within metropolis algorithm

outperforming the gibbs sampler empirical estimator for nearest neighbor random fields given a markov chain sampling scheme does the standard empirical estimator make best use of the data we show that this is not so and construct better estimators we restrict attention to nearest neighbor random fields and to gibbs samplers with deterministic sweep but our approach applies to any sampler that uses reversible variable at a time updating with deterministic sweep the structure of the transition distribution of the sampler is exploited to construct further empirical estimators that are combined with the standard empirical estimator to reduce asymptotic variance the extra computational cost is negligible when the random field is spatially homogeneous symmetrizations of our estimator lead to further variance reduction the performance of the estimators is evaluated in a simulation study of the ising model

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

particle markov chain monte carlo methods summary markov chain monte carlo and sequential monte carlo methods have emerged as the two main tools to sample from high dimensional probability distributions although asymptotic convergence of markov chain monte carlo algorithms is ensured under weak assumptions the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and or if highly correlated variables are updated independently we show here how it is possible to build efficient high dimensional proposal distributions by using sequential monte carlo methods this allows us not only to improve over standard markov chain monte carlo schemes but also to make bayesian inference feasible for a large class of statistical models where this was not previously so we demonstrate these algorithms on a non linear state space model and a levy driven stochastic volatility model

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

analysis of spike statistics in neuronal systems with continuous attractors or multiple discrete attractor states attractor networks are likely to underlie working memory and integrator circuits in the brain it is unknown whether continuous quantities are stored in an analog manner or discretized and stored in a set of discrete attractors in order to investigate the important issue of how to differentiate the two systems here we compare the neuronal spiking activity that arises from a continuous line attractor with that from a series of discrete attractors stochastic fluctuations cause the position of the system along its continuous attractor to vary as a random walk whereas in a discrete attractor noise causes spontaneous transitions to occur between discrete states at random intervals we calculate the statistics of spike trains of neurons firing as a poisson process with rates that vary according to the underlying attractor network since individual neurons fire spikes probabilistically and since the state of the network as a whole drifts randomly the spike trains of individual neurons follow a doubly stochastic poisson point process we compare the series of spike trains from the two systems using the autocorrelation function fano factor and interspike interval isi distribution although the variation in rate can be dramatically different especially for short time intervals surprisingly both the autocorrelation functions and fano factors are identical given appropriate scaling of the noise terms since the range of firing rates is limited in neurons we also investigate systems for which the variation in rate is bounded by either rigid limits or because of leak to a single attractor state such as the ornstein uhlenbeck process in these cases the time dependence of the variance in rate can be different between discrete and continuous systems so that in principle these processes can be distinguished using second order spike statistics

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

approximate bayesian computation with the wasserstein distance a growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions approximate bayesian computation has become a popular approach to overcome this issue in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values we propose to avoid the use of summaries and the ensuing loss of information by instead using the wasserstein distance between the empirical distributions of the observed and synthetic data this generalizes the well known approach of using order statistics within approximate bayesian computation to arbitrary dimensions we describe how recently developed approximations of the wasserstein distance allow the method to scale to realistic data sizes and we propose a new distance based on the hilbert space filling curve we provide a theoretical study of the method proposed describing consistency as the threshold goes to 0 while the observations are kept fixed and concentration properties as the number of observations grows various extensions to time series data are discussed the approach is illustrated on various examples including univariate and multivariate g and k distributions a toggle switch model from systems biology a queuing model and a levy driven stochastic volatility model

digital image restoration using spatial interaction models this paper is concerned with developing fast nonrecursive algorithms for the minimum mean squared error restoration of degraded images the degradation is assumed to be due to a space invariant periodic nonseparable known point spread function and additive white noise our basic approach is to represent the images by a class of spatial interaction models namely the simultaneous autoregressve models and the conditional markov models defined on toroidal lattices and develop minimum mean squared error restoration algorithms using these models the restoration algorithms are optimal if the parameters characterizing the interaction models are exactly known however in practice the parameters are estimated from the images by using spatial interaction models we develop restoration algorithms that do not require the availability of the original image or its prototype the specific structure of the underlying lattice enables the implementation of the filters using fast fourier transform fft computations several restoration examples are given

messages of oscillatory correlograms a spike train model oscillatory correlograms are widely used to study neuronal activity that shows a joint periodic rhythm in most cases the statistical analysis of cross correlation histograms cch features is based on the null model of independent processes and the resulting conclusions about the underlying processes remain qualitative therefore we propose a spike train model for synchronous oscillatory firing activity that directly links characteristics of the cch to parameters of the underlying processes the model focuses particularly on asymmetric central peaks which differ in slope and width on the two sides asymmetric peaks can be associated with phase offsets in the sub millisecond range these spatiotemporal firing patterns can be highly consistent across units yet invisible in the underlying processes the proposed model includes a single temporal parameter that accounts for this peak asymmetry the model provides approaches for the analysis of oscillatory correlograms taking into account dependencies and nonstationarities in the underlying processes in particular the auto and the cross correlogram can be investigated in a joint analysis because they depend on the same spike train parameters particular temporal interactions such as the degree to which different units synchronize in a common oscillatory rhythm can also be investigated the analysis is demonstrated by application to a simulated data set

approximate bayesian computation a nonparametric perspective approximate bayesian computation is a family of likelihood free inference techniques that are well suited to models defined in terms of a stochastic generating mechanism in a nutshell approximate bayesian computation proceeds by computing summary statistics sobs from the data and simulating summary statistics for different values of the parameter the posterior distribution is then approximated by an estimator of the conditional density g sobs in this paper we derive the asymptotic bias and variance of the standard estimators of the posterior distribution which are based on rejection sampling and linear adjustment additionally we introduce an original estimator of the posterior distribution based on quadratic adjustment and we show that its bias contains a fewer number of terms than the estimator with linear adjustment although we find that the estimators with adjustment are not universally superior to the estimator based on rejection sampling we find that they can achieve better performance

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

estimating ocean circulation an mcmc approach with approximated likelihoods via the bernoulli factory we provide a bayesian analysis of ocean circulation based on data collected in the south atlantic ocean the analysis incorporates a reaction diffusion partial differential equation that is not solvable in closed form this leads to an intractable likelihood function we describe a novel markov chain monte carlo approach that does not require a likelihood evaluation rather we use unbiased estimates of the likelihood and a bernoulli factory to decide whether or not proposed states are accepted the variates required to estimate the likelihood function are obtained via a feynman kac representation this lifts the common restriction of selecting a regular grid for the physical model and eliminates the need for data preprocessing we implement our approach using the parallel graphic processing unit gpu computing environment

theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback a network of leaky integrate and fire neurons with global inhibitory feedback and under the influence of spatially correlated noise is studied we calculate the spectral statistics of the network power spectrum of the population activity cross spectrum between spike trains of different neurons as well as of a single neuron power spectrum of spike train cross spectrum between external noise and spike train within the network as shown by comparison with numerical simulations our theory works well for arbitrary network size if the feedback is weak and the amount of external noise does not exceed that of the internal noise by means of our analytical results we discuss the quality of the correlation induced oscillation in a large network as a function of the transmission delay and the internal noise intensity it is shown that the strongest oscillation is obtained in a system with zero internal noise and adiabatically long delay i e the delay period is longer than any other time scale in the system for a neuron with a strong intrinsic frequency the oscillation becomes strongly anharmonic in the case of a long delay time we also discuss briefly the kind of synchrony introduced by the feedback induced oscillation

analyzing functional connectivity using a network likelihood model of ensemble neural spiking activity analyzing the dependencies between spike trains is an important step in understanding how neurons work in concert to represent biological signals usually this is done for pairs of neurons at a time using correlation based techniques chornoboy schramm and karr 1988 proposed maximum likelihood methods for the simultaneous analysis of multiple pair wise interactions among an ensemble of neurons one of these methods is an iterative continuous time estimation algorithm for a network likelihood model formulated in terms of multiplicative conditional intensity functions we devised a discrete time version of this algorithm that includes a new efficient computational strategy a principled method to compute starting values and a principled stopping criterion in an analysis of simulated neural spike trains from ensembles of interacting neurons the algorithm recovered the correct connectivity matrices and interaction parameters in the analysis of spike trains from an ensemble of rat hippocampal place cells the algorithm identified a connectivity matrix and interaction parameters consistent with the pattern of conjoined firing predicted by the overlap of the neurons spatial receptive fields these results suggest that the network likelihood model can be an efficient tool for the analysis of ensemble spiking activity

variance bounding and geometric ergodicity of markov chain monte carlo kernels for approximate bayesian computation approximate bayesian computation has emerged as a standard computational tool when dealing with intractable likelihood functions in bayesian inference we show that many common markov chain monte carlo kernels used to facilitate inference in this setting can fail to be variance bounding and hence geometrically ergodic which can have consequences for the reliability of estimates in practice this phenomenon is typically independent of the choice of tolerance in the approximation we prove that a recently introduced markov kernel can inherit the properties of variance bounding and geometric ergodicity from its intractable metropolis hastings counterpart under reasonably weak conditions we show that the computational cost of this alternative kernel is bounded whenever the prior is proper and present indicative results for an example where spectral gaps and asymptotic variances can be computed as well as an example involving inference for a partially and discretely observed time homogeneous pure jump markov process we also supply two general theorems one providing a simple sufficient condition for lack of variance bounding for reversible kernels and the other providing a positive result concerning inheritance of variance bounding and geometric ergodicity for mixtures of reversible kernels

segmentation given partial grouping constraints we consider data clustering problems where partial grouping is known a priori we formulate such biased grouping problems as a constrained optimization problem where structural properties of the data define the goodness of a grouping and partial grouping cues define the feasibility of a grouping we enforce grouping smoothness and fairness on labeled data points so that sparse partial grouping information can be effectively propagated to the unlabeled data considering the normalized cuts criterion in particular our formulation leads to a constrained eigenvalue problem by generalizing the rayleigh ritz theorem to projected matrices we find the global optimum in the relaxed continuous domain by eigendecomposition from which a near global optimum to the discrete labeling problem can be obtained effectively we apply our method to real image segmentation problems where partial grouping priors can often be derived based on a crude spatial attentional map that binds places with common salient features or focuses on expected object locations we demonstrate not only that it is possible to integrate both image structures and priors in a single grouping process but also that objects can be segregated from the background without specific object knowledge

on lipschitz stability for comparison systems of differential equations via limiting equation lipschitz f 0 stability notion was introduced in this paper we will discuss the notion of lipschitz f 0 stability of comparison systems of differential equations our technique depends on limiting equation method

asymptotic properties of approximate bayesian computation approximate bayesian computation abc is becoming an accepted tool for statistical analysis in models with intractable likelihoods with the initial focus being primarily on the practical import of abc exploration of its formal statistical properties has begun to attract more attention in this paper we consider the asymptotic behavior of the posterior obtained from abc and the ensuing posterior mean we give general results on i the rate of concentration of the abc posterior on sets containing the true parameter vector ii the limiting shape of the posterior and iii the asymptotic distribution of the abc posterior mean these results hold under given rates for the tolerance used within abc mild regularity conditions on the summary statistics and a condition linked to identification of the true parameters using simple illustrative examples that have featured in the literature we demonstrate that the required identification condition is far from guaranteed the implications of the theoretical results for practitioners of abc are also highlighted

genetic algorithms for ambiguous labelling problems abstract consistent labelling problems frequently have more than one solution most work in the field has aimed at disambiguating early in the interpretation process using only local evidence this paper starts with a review of the literature on labelling problems and ambiguity based on this review we propose a strategy for simultaneously extracting multiple related solutions to the consistent labelling problem in a preliminary experimental study we show that an appropriately modified genetic algorithm is a robust tool for finding multiple solutions to the consistent labelling problem these solutions are related by common labellings of the most strongly constrained junctions we have proposed three run time measures of algorithm performance the maximum fitness of the genetic algorithm s population its shannon entropy and the total hamming distance between its distinct members the results to date indicate that when the shannon entropy falls below a certain threshold new solutions are unlikely to emerge and that most of the diversity in the population disappears within the first few generations

an efficient markov chain monte carlo method for distributions with intractable normalising constants maximum likelihood parameter estimation and sampling from bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter in this paper an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value the proposal distribution is constructed so that the normalising constant cancels from the metropolis hastings ratio the method is illustrated by producing posterior samples for parameters of the ising model given a particular lattice realisation

markov random field texture models we consider a texture to be a stochastic possibly periodic two dimensional image field a texture model is a mathematical procedure capable of producing and describing a textured image we explore the use of markov random fields as texture models the binomial model where each point in the texture has a binomial distribution with parameter controlled by its neighbors and number of tries equal to the number of gray levels was taken to be the basic model for the analysis a method of generating samples from the binomial model is given followed by a theoretical and practical analysis of the method s convergence examples show how the parameters of the markov random field control the strength and direction of the clustering in the image the power of the binomial model to produce blurry sharp line like and blob like textures is demonstrated natural texture samples were digitized and their parameters were estimated under the markov random field model a hypothesis test was used for an objective assessment of goodness of fit under the markov random field model overall microtextures fit the model well the estimated parameters of the natural textures were used as input to the generation procedure the synthetic microtextures closely resembled their real counterparts while the regular and inhomogeneous textures did not

sequential monte carlo samplers summary we propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space each distribution being known up to a normalizing constant these probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential monte carlo methods this methodology allows us to derive simple algorithms to make parallel markov chain monte carlo algorithms interact to perform global optimization and sequential bayesian estimation and to compute ratios of normalizing constants we illustrate these algorithms for various integration tasks arising in the context of bayesian inference

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

estimation and accuracy after model selection classical statistical theory ignores model selection in assessing estimation accuracy here we consider bootstrap methods for computing standard errors and confidence intervals that take model selection into account the methodology involves bagging also known as bootstrap smoothing to tame the erratic discontinuities of selection based estimators a useful new formula for the accuracy of bagging then provides standard errors for the smoothed estimators two examples nonparametric and parametric are carried through in detail a regression model where the choice of degree linear quadratic cubic is determined by the cp criterion and a lasso based estimation problem

correlations without synchrony peaks in spike train correlograms are usually taken as indicative of spike timing synchronization between neurons strictly speaking however a peak merely indicates that the two spike trains were not independent two biologically plausible ways of departing from independence that are capable of generating peaks very similar to spike timing peaks are described here covariations over trials in response latency and covariations over trials in neuronal excitability since peaks due to these interactions can be similar to spike timing peaks interpreting a correlogram may be a problem with ambiguous solutions what peak shapes do latency or excitability interactions generate when are they similar to spike timing peaks when can they be ruled out from having caused an observed correlogram peak these are the questions addressed here the previous article in this issue proposes quantitative methods to tell cases apart when latency or excitability covariations cannot be ruled out

on the asymptotic efficiency of approximate bayesian computation estimators many statistical applications involve models for which it is difficult to evaluate the likelihood but from which it is relatively easy to sample approximate bayesian computation is a likelihood free method for implementing bayesian inference in such cases we present results on the asymptotic variance of estimators obtained using approximate bayesian computation in a large data limit our key assumption is that the data is summarized by a fixed dimensional summary statistic that obeys a central limit theorem we prove asymptotic normality of the mean of the approximate bayesian computation posterior this result also shows that in terms of asymptotic variance we should use a summary statistic that is the same dimension as the parameter vector p and that any summary statistic of higher dimension can be reduced through a linear transformation to dimension p in a way that can only reduce the asymptotic variance of the posterior mean we look at how the monte carlo error of an importance sampling algorithm that samples from the approximate bayesian computation posterior affects the accuracy of estimators we give conditions on the importance sampling proposal distribution such that the variance of the estimator will be the same order as that of the maximum likelihood estimator based on the summary statistics used this suggests an iterative importance sampling algorithm which we evaluate empirically on a stochastic volatility model

monte carlo methods of inference for implicit statistical models a prescribed statistical model is a parametric specification of the distribution of a random vector whilst an implicit statistical model is one defined at a more fundamental level in terms of a generating stochastic mechanism this paper develops methods of inference which can be used for implicit statistical models whose distribution theory is intractable the kernel method of probability density estimation is advocated for estimating a log likelihood from simulations of such a model the development and testing of an algorithm for maximizing this estimated log likelihood function is described an illustrative example involving a stochastic model for quantal response assays is given possible applications of the maximization algorithm to ad hoc methods of parameter estimation are noted briefly and illustrated by an example involving a model for the spatial pattern of displaced amacrine cells in the retina of a rabbit

a note on multiple imputation under complex sampling summary multiple imputation is popular for handling item nonresponse in survey sampling current multiple imputation techniques with complex survey data assume that the sampling design is ignorable in this paper we propose a new multiple imputation procedure for parametric inference without this assumption instead of using the sample data likelihood we use the sampling distribution of the pseudo maximum likelihood estimator to derive the posterior distribution of the parameters the asymptotic properties of the proposed method are investigated a simulation study confirms that the new procedure provides unbiased point estimation and valid confidence intervals with correct coverage properties whether or not the sampling design is ignorable

approximate bayesian computation by subset simulation a new approximate bayesian computation abc algorithm for bayesian updating of model parameters is proposed in this paper which combines the abc principles with the technique of subset simulation for efficient rare event simulation first developed in s k au and j l beck probabilistic engrg mech 16 2001 pp 263 277 it has been named abc subsim the idea is to choose the nested decreasing sequence of regions in subset simulation as the regions that correspond to increasingly closer approximations of the actual data vector in observation space the efficiency of the algorithm is demonstrated in two examples that illustrate some of the challenges faced in real world applications of abc we show that the proposed algorithm outperforms other recent sequential abc algorithms in terms of computational efficiency while achieving the same or better measure of accuracy in the posterior distribution we also show that abc subsim readily provides an estimate of the evidence marginal likelihood for posterior model class assessment as a by product

frequentist accuracy of bayesian estimates in the absence of relevant prior experience popular bayesian estimation techniques usually begin with some form of uninformative prior distribution intended to have minimal inferential influence bayes rule will still produce nice looking estimates and credible intervals but these lack the logical force attached to experience based priors and require further justification this paper concerns the frequentist assessment of bayes estimates a simple formula is shown to give the frequentist standard deviation of a bayesian point estimate the same simulations required for the point estimate also produce the standard deviation exponential family models make the calculations particularly simple and bring in a connection to the parametric bootstrap

bayesian analysis of accumulated damage models in lumber reliability abstractwood products that are subjected to sustained stress over a period of long duration may weaken and this effect must be considered in models for the long term reliability of lumber the dam

adaptive approximate bayesian computation sequential techniques can be adapted to the abc algorithm to enhance its efficiency for instance when sisson et al 2007 introduced the abc prc algorithm the goal was to improve upon existing abc mcmc algorithms marjoram et al 2003 while the abc prc method is based upon the theoretical developments of del moral et al 2006 the application to the setting of approximate bayesian computation induces a bias in the approximation to the posterior distribution of interest as we demonstrate in this paper via both theoretical reasoning and experimental results it is however possible to devise an alternative version based on genuine importance sampling arguments that we call abc pmc in connection with the population monte carlo method introduced in cappe et al 2004 furthermore the abc pmc algorithm is simpler than the abc prc algorithm in that it does not require any backward transition kernel and proposes an automatic scaling of the forward kernel in this paper we demonstrate the applicability of abc pmc and compare its performances with abc prc

surrogate data methods based on a shuffling of the trials for synchrony detection the centering issue we investigate several distribution free dependence detection procedures all based on a shuffling of the trials from a statistical point of view the mathematical justification of such procedures lies in the bootstrap principle and its approximation properties in particular we show that such a shuffling has mainly to be done on centered quantities that is quantities with zero mean under independence to construct correct p values meaning that the corresponding tests control their false positive fp rate thanks to this study we introduce a method named permutation ue which consists of a multiple testing procedure based on permutation of experimental trials and delayed coincidence count each involved single test of this procedure achieves the prescribed level so that the corresponding multiple testing procedure controls the false discovery rate fdr and this with as few assumptions as possible on the underneath distribution except independence and identical distribution across trials the mathematical meaning of this assumption is discussed and it is in particular argued that it does not mean what is commonly referred in neuroscience to as cross trials stationarity some simulations show moreover that permutation ue outperforms the trial shuffling of pipa and grun 2003 and the mtgaue method of tuleau malot eti al 2014 in terms of single levels and fdr for a comparable amount of false negatives application to real data is also provided

can spike coordination be differentiated from rate covariation there has been a long and lively debate on whether rate covariance and temporal coordination of spikes regarded as potential origins for correlations in cortical spike signals fulfill different roles in the cortical code in this context studies that report spike coordination have often been criticized for ignoring fast nonstationarities which would result in wrongly assigned spike coordination the underlying hypothesis of this critique is that spike coordination is essentially identical to rate covariation only on a shorter timescale this study investigates the validity of this critique we provide a decomposition for the cross correlation function of doubly stochastic point processes where each of the components corresponds precisely to the concepts of dependence under investigation this allows us to correct the correlation function for rate effects which implies that spike coordination and rate covariation are statistically separable concepts of dependence furthermore we present direct and intuitive model implementations of the discussed concepts and illustrate that their difference is not a matter of timescale analysis of data generated by our models and analytical description of the relevant estimators reveals however that spike coordination dramatically influences the accuracy of rate covariance estimation as a consequence extreme parameter combinations can lead to situations where the concept of dependence cannot be identified empirically however for a wide range of parameters the concept of dependence underlying a given data set can be identified regardless of its timescale

constructing summary statistics for approximate bayesian computation semi automatic approximate bayesian computation summary many modern statistical applications involve inference for complex stochastic models where it is easy to simulate from the models but impossible to calculate likelihoods approximate bayesian computation abc is a method of inference for such models it replaces calculation of the likelihood by a step which involves simulating artificial data for different parameter values and comparing summary statistics of the simulated data with summary statistics of the observed data here we show how to construct appropriate summary statistics for abc in a semi automatic manner we aim for summary statistics which will enable inference about certain parameters of interest to be as accurate as possible theoretical results show that optimal summary statistics are the posterior means of the parameters although these cannot be calculated analytically we use an extra stage of simulation to estimate how the posterior means vary as a function of the data and we then use these estimates of our summary statistics within abc empirical results show that our approach is a robust method for choosing summary statistics that can result in substantially more accurate abc analyses than the ad hoc choices of summary statistics that have been proposed in the literature we also demonstrate advantages over two alternative methods of simulation based inference

estimating functions in indirect inference summary there are models for which the evaluation of the likelihood is infeasible in practice for these models the metropolis hastings acceptance probability cannot be easily computed this is the case for instance when only departure times from a g g 1 queue are observed and inference on the arrival and service distributions are required indirect inference is a method to estimate a parameter in models whose likelihood function does not have an analytical closed form but from which random samples can be drawn for fixed values of first an auxiliary model is chosen whose parameter can be directly estimated next the parameters in the auxiliary model are estimated for the original data leading to an estimate the parameter is also estimated by using several sampled data sets simulated from the original model for different values of the original parameter finally the parameter which leads to the best match to is chosen as the indirect inference estimate we analyse which properties an auxiliary model should have to give satisfactory indirect inference we look at the situation where the data are summarized in a vector statistic t and the auxiliary model is chosen so that inference on is drawn from t only under appropriate assumptions the asymptotic covariance matrix of the indirect estimators is proportional to the asymptotic covariance matrix of t and componentwise inversely proportional to the square of the derivative with respect to of the expected value of t we discuss how these results can be used in selecting good estimating functions we apply our findings to the queuing problem

segmentation based on fusion of range and intensity images using robust trimmed methods abstract this paper proposes a segmentation algorithm based on fusion of range and intensity images using robust trimmed methods based on the bayesian theory a priori knowledge is represented using the markov random field mrf a maximum a posteriori map estimator is constructed using the edge features extracted from both range and intensity images objects are represented by a number of local planar surfaces in range images and the parametric space for surface representation is constructed with the surface parameters estimated pixel by pixel based on the least trimmed squares lts method whereas in intensity images the trimmed variance is adopted as the feature for edge extraction a final edge map is obtained by the map estimator that is constructed using the likelihood functions based on the edge information obtained from range and intensity images finally an image is segmented using the fused edge map computer simulation results show that our new segmentation algorithm effectively segments test images independent of shadow noise and lighting environment

unitary events in multiple single neuron spiking activity i detection and significance it has been proposed that cortical neurons organize dynamically into functional groups cell assemblies by the temporal structure of their joint spiking activity here we describe a novel method to detect conspicuous patterns of coincident joint spike activity among simultaneously recorded single neurons the statistical significance of these unitary events of coincident joint spike activity is evaluated by the joint surprise the method is tested and calibrated on the basis of simulated stationary spike trains of independently firing neurons into which coincident joint spike events were inserted under controlled conditions the sensitivity and specificity of the method are investigated for their dependence on physiological parameters firing rate coincidence precision coincidence pattern complexity and temporal resolution of the analysis in the companion article in this issue we describe an extension of the method designed to deal with nonstationary firing rates

on stability of nonlinear systems of functional differential equations the aim of this paper is to extend some results of f 0 stability for systems of functional differential equations f d e and to give results via razumikhin s method

revealing pairwise coupling in linear nonlinear networks through an asymptotic analysis of a simple network we derive an estimate of the coupling between a pair of units when all other units are unobservable the analysis is based on a model where the response of each unit is a linear nonlinear function of a white noise stimulus the results accurately determine the coupling when all unmeasured units respond to the stimulus differently than the measured pair to account for the possibility of unmeasured units similar to the measured pair we cast our results in the framework of subpopulations which are defined as a group of units who respond to the stimulus similarly we demonstrate that we can determine when correlations between two units are caused by a connection between their subpopulations although the precise identity of the units involved in the connection may remain ambiguous the result is rigorously valid only when the coupling is sufficiently weak to justify a second order approximation in the coupling strength we demonstrate through simulations that the results are still valid even with stronger coupling and in the presence of some deviations from the linear nonlinear model the analysis is presented in terms of neuronal networks although the general framework is more widely applicable

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

rigid body segmentation and shape description from dense optical flow under weak perspective we present an algorithm for identifying and tracking independently moving rigid objects from optical flow some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field while discontinuities do indicate a change in scene depth they do not in general signal a boundary between two separate objects the proposed method uses the fact that each independently moving object has a unique epipolar constraint associated with its motion thus motion discontinuities based on self occlusion can be distinguished from those due to separate objects the use of epipolar geometry allows for the determination of individual motion parameters for each object as well as the recovery of relative depth for each point on the object the algorithm assumes an affine camera where perspective effects are limited to changes in overall scale no camera calibration parameters are required a kalman filter based approach is used for tracking motion parameters with time

bayesian computation via empirical likelihood approximate bayesian computation has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable however the well established statistical method of empirical likelihood provides another route to such settings that bypasses simulations from the model and the choices of the approximate bayesian computation parameters summary statistics distance tolerance while being convergent in the number of observations furthermore bypassing model simulations may lead to significant time savings in complex models for instance those found in population genetics the bayesian computation with empirical likelihood algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size the method is illustrated using several examples including estimation of standard distributions time series and population genetics models

the effect of source amplitude and phase in matched field source localization traditional matched field processing is typically employed for localization of a source with unknown amplitude and phase at transmission the spectral information of the source is estimated via maximum likelihood and is used for localization with the bartlett processor maximum a posteriori estimation of the spectrum of the source is here proposed along with the estimation of source location and noise variance where the joint posterior probability distribution of all parameters is computed with gibbs sampling it is shown that the proposed method has a higher probability of correct localization than the traditional approach

a new pod based approximate bayesian computation method to identify parameters for formed ahss abstract forming has significant influence on the material properties which are critical for the accuracy of simulations however at present most of the existing works took the uniform raw mechanical properties of plate as the one after forming which inevitably resulted in the inaccuracy simulation in this study in order to figure out the material properties of formed dp590 comprehensive experiments based on micro indentation tests and digital image correlation dic are presented the versatile approximate bayesian computation abc inverse method is utilized to identify material parameters due to its difficulty of selection of summary statistics a new flexible and feasible proper orthogonal decomposition pod based abc framework is proposed the pod can project the high dimensional observations into a much lower dimensional coefficient vector thus we can make use of comparisons between simulated and observed coefficient vector of pod to determine the material parameters with the pod the abc can circumvent the complex selection of summary statistics in the computational process the neural network nn is used to construct the nonlinear connection between material properties and its pod coefficient vector thus the coefficient vector with given material properties can be determined efficiently with the well constructed nn instead of time consuming finite element fe simulations

component wise approximate bayesian computation via gibbs like steps approximate bayesian computation methods are useful for generative models with intractable likelihoods these methods are however sensitive to the dimension of the parameter space requiring exponentially increasing resources as this dimension grows to tackle this difficulty we explore a gibbs version of the abc approach that runs component wise approximate bayesian computation steps aimed at the corresponding conditional posterior distributions and based on summary statistics of reduced dimensions while lacking the standard justifications for the gibbs sampler the resulting markov chain is shown to converge in distribution under some partial independence conditions the associated stationary distribution can further be shown to be close to the true posterior distribution and some hierarchical versions of the proposed mechanism enjoy a closed form limiting distribution experiments also demonstrate the gain in efficiency brought by the gibbs version over the standard solution

functional structure of cortical neuronal networks grown in vitro we apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown in vitro we infer connectivity between two neurons via the measurement of the mutual information between their spike trains in addition we measure higher point multi information between any two spike trains conditional on the activity of a third cell as a means to identify and distinguish classes of functional connectivity among three neurons the use of a conditional three cell measure removes some interpretational shortcomings of the pairwise mutual information and sheds light on the functional connectivity arrangements of any three cells we analyze the resultant connectivity graphs in light of other complex networks and demonstrate that despite their ex vivo development the connectivity maps derived from cultured neural assemblies are similar to other biological networks and display nontrivial structure in clustering coefficient network diameter and assortative mixing specifically we show that these networks are weakly disassortative small world graphs which differ significantly in their structure from randomized graphs with the same degree we expect our analysis to be useful in identifying the computational motifs of a wide variety of complex networks derived from time series data