spatially dependent polya tree modeling for survival data with the proliferation of spatially oriented time to event data spatial modeling in the survival context has received increased recent attention a traditional way to capture a spatial pattern is to introduce frailty terms in the linear predictor of a semiparametric model such as proportional hazards or accelerated failure time we propose a new methodology to capture the spatial pattern by assuming a prior based on a mixture of spatially dependent polya trees for the baseline survival in the proportional hazards model thanks to modern markov chain monte carlo mcmc methods this approach remains computationally feasible in a fully hierarchical bayesian framework we compare the spatially dependent mixture of polya trees mpt approach to the traditional spatial frailty approach and illustrate the usefulness of this method with an analysis of iowan breast cancer survival data from the surveillance epidemiology and end results seer program of the national cancer institute our method provides better goodness of fit over the traditional alternatives as measured by log pseudo marginal likelihood lpml the deviance information criterion dic and full sample score fss statistics

edge effects and efficient parameter estimation for stationary random fields summary we consider the estimation of the parameters of a stationary random field on d dimensional lattice by minimizing the classical whittle approximation to the gaussian log likelihood if the usual biased sample covariances are used the estimate is efficient only in one dimension to remove this edge effect we introduce data tapers and show that the resulting modified estimate is efficient also in two and three dimensions this avoids the use of the unbiased sample covariances which are in general not positive definite

on conditional and intrinsic autoregressions summary gaussian conditional autoregressions have been widely used in spatial statistics and bayesian image analysis where they are intended to describe interactions between random variables at fixed sites in euclidean space the main appeal of these distributions is in the markovian interpretation of their full conditionals intrinsic autoregressions are limiting forms that retain the markov property despite being improper they can have advantages over the standard autoregressions both conceptually and in practice for example they often avoid difficulties in parameter estimation without apparent loss or exhibit appealing invariances as in texture analysis however on small arrays and in nonlattice applications both forms of autoregression can lead to undesirable second order characteristics either in the variables themselves or in contrasts among them this paper discusses standard and intrinsic autoregressions and describes how the problems that arise can be alleviated using dempster s 1972 algorithm or an appropriate modification the approach represents a partial synthesis of standard geostatistical and gaussian markov random field formulations some nonspatial applications are also mentioned

direct evaluation of large deviation functions we introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities such as current or density that are local in time the large deviation functions are given in terms of the typical properties of a modified dynamics and since they no longer involve rare events can be evaluated efficiently and over a wider ranges of values we illustrate the method with the current fluctuations of the totally asymmetric exclusion process and with the work distribution of a driven lorentz gas

finite size scaling of current fluctuations in the totally asymmetric exclusion process we study the fluctuations of the current j t of the totally asymmetric exclusion process with open boundaries using a density matrix renormalization group approach we calculate the cumulant generating function of the current this function can be interpreted as a free energy for an ensemble in which histories are weighted by exp sj t we show that in this ensemble the model has a first order spacetime phase transition at s 0 we numerically determine the finite size scaling of the cumulant generating function near this phase transition both in the non equilibrium steady state and for large times

adaptive estimation of stationary gaussian fields we study the nonparametric covariance estimation of a stationary gaussian field x observed on a regular lattice in the time series setting some procedures like aic are proved to achieve optimal model selection among autoregressive models however there exists no such equivalent results of adaptivity in a spatial setting by considering collections of gaussian markov random fields gmrf as approximation sets for the distribution of x we introduce a novel model selection procedure for spatial fields for all neighborhoods m in a given collection mathcal m this procedure first amounts to computing a covariance estimator of x within the gmrfs of neighborhood m then it selects a neighborhood m by applying a penalization strategy the so defined method satisfies a nonasymptotic oracle type inequality if x is a gmrf the procedure is also minimax adaptive to the sparsity of its neighborhood more generally the procedure is adaptive to the rate of approximation of the true distribution by gmrfs with growing neighborhoods

on the precision of the conditionally autoregressive prior in spatial models summary bayesian analyses of spatial data often use a conditionally autoregressive car prior which can be written as the kernel of an improper density that depends on a precision parameter that is typically unknown to include in the bayesian analysis the kernel must be multiplied by k for some k this article rigorously derives k n i 2 for the l2 norm car prior also called a gaussian markov random field model and k n i for the l1 norm car prior where n is the number of regions and i the number of islands disconnected groups of regions in the spatial map since i 1 for a spatial structure defining a connected graph this supports knorr held s 2002 in highly structured stochastic systems 260 264 suggestion that k n 1 2 in the l2 norm case instead of the more common k n 2 we illustrate the practical significance of our results using a periodontal example

statistical analysis of field experiments using neighbouring plots the paper describes and provides examples of four different applications of the use of neighbouring plot values in the analysis of agricultural field experiments the topics include the use of check plots to control environmental variation in large unreplicated variety trials spatial models based on first differences to accommodate fertility effects in trials that have some degree of replication adjustment for interplot competition using a simultaneous equations formulation and the analysis of trials in which plot values are affected by the particular treatments on neighbouring plots

parameter estimation for a stationary process on a d dimensional lattice summary we study asymptotic properties of various estimation procedures for a general stationary regular process on a d dimensional lattice differences between d 1 time series and d 2 spatial processes are pointed out we suppose that the process is observed on a set pn with cn points which tends to infinity with the same speed in all directions the relative edge effect is of order cn lid increasing with d this effect is without statistical importance if d 1 but is important if d 2 we give a lcn consistent asymptotically normal estimator of the underlying parameter the procedure being constructed by a modification of whittle s approximation to the log likelihood in the gaussian case this procedure is asymptotically efficient

a quadratic identity for the number of perfect matchings of plane graphs we present a quadratic identity on the number of perfect matchings of plane graphs by the method of graphical condensation which generalizes the results found by propp j propp generalized domino shuffling theoret comput sci 303 2003 267 301 kuo e h kuo applications of graphical condensation for enumerating matchings and tilings theoret comput sci 319 2004 29 57 and yan yeh and zhang w g yan y n yeh f j zhang graphical condensation of plane graphs a combinatorial approach theoret comput sci 349 2005 452 461

a bayesian spatiotemporal model for very large data sets functional mri provides a unique perspective of neuronal organization however these data include many complex sources of spatiotemporal variability which require spatial preprocessing and statistical analysis for the latter bayesian models provide a promising alternative to classical inference which uses results from gaussian random field theory to assess the significance of spatially correlated statistic images a bayesian approach generalizes the application of these ideas in that 1 random fields are used to model all spatial parameters not solely observation error 2 their smoothness is optimized and 3 a broader class of models can be compared the main problem however is computational due to the large number of voxels in a brain volume sampling methods are time consuming however approximate inference using variational bayes vb offers a principled and transparent way to specify assumptions necessary for computational tractability penny et al 2005b described such a scheme using a joint spatial prior and approximated the joint posterior density with one that factorized over voxels however a further computational bottleneck is encountered when evaluating the log model evidence used to compare models this has lead to dividing a brain volume into slices and treating each independently this amounts to approximating the spatial prior over a full volume with stacked 2d priors that is smoothness along the z axis is not included in the model here we describe a vb scheme that approximates the zero mean joint spatial prior with a non zero mean empirical prior that factors over voxels thereby overcoming this problem we do this by modifying the original vb algorithm of penny et al using the conditional form of a so called conditional autoregressive car prior to update a marginal prior over voxels we refer to this as a spatially informed voxel wise prior svp and use them to spatially regularise general linear model glm and autoregressive ar coefficients over time to model serial correlations this algorithm scales more favourably with the number of voxels providing a truly 3d spatiotemporal model over volumes containing tens of thousands of voxels we compare the scaling of compute times with the number of voxels and performance with a joint prior applied to synthetic and single subject data

empirical bayes estimates of age standardized relative risks for use in disease mapping there have been many attempts in recent years to map incidence and mortality from diseases such as cancer such maps usually display either relative rates in each district as measured by a standardized mortality ratio smr or some similar index or the statistical significance level for a test of the difference between the rates in that district and elsewhere neither of these approaches is fully satisfactory and we propose a new approach using empirical bayes estimation the resulting estimators represent a weighted compromise between the smr the overall mean relative rate and a local mean of the relative rate in nearby areas the compromise solution depends on the reliability of each individual smr and on estimates of the overall amount of dispersion of relative rates over different districts

universal cumulants of the current in diffusive systems on a ring we calculate exactly the first cumulants of the integrated current and of the activity which is the total number of changes of configurations of the symmetric simple exclusion process on a ring with periodic boundary conditions our results indicate that for large system sizes the large deviation functions of the current and of the activity take a universal scaling form with the same scaling function for both quantities this scaling function can be understood either by an analysis of bethe ansatz equations or in terms of a theory based on fluctuating hydrodynamics or on the macroscopic fluctuation theory of bertini de sole gabrielli jona lasinio and landim

classification of rotated and scaled textured images using gaussian markov random field models consideration is given to the problem of classifying a test textured image that is obtained from one of c possible parent texture classes after possibly applying unknown rotation and scale changes to the parent texture the training texture images parent classes are modeled by gaussian markov random fields gmrfs to classify a rotated and scaled test texture the rotation and scale changes are incorporated in the texture model through an appropriate transformation of the power spectral density of the gmrf for the rotated and scaled image a bona fide likelihood function that shows the explicit dependence of the likelihood function on the gmrf parameters as well as on the rotation and scale parameters is derived although in general the scaled and or rotated texture does not correspond to a finite order gmrf it is possible nonetheless to write down a likelihood function for the image data the likelihood function of the discrete fourier transform of the image data corresponds to that of a white nonstationary gaussian random field with the variance at each pixel i j being a known function of the rotation the scale the gmrf model parameters and i j the variance is an explicit function of the appropriately sampled power spectral density of the gmrf the estimation of the rotation and scale parameters is performed in the frequency domain by maximizing the likelihood function associated with the discrete fourier transform of the image data cramer rao error bounds on the scale and rotation estimates are easily computed a modified bayes decision rule is used to classify a given test image into one of c possible texture classes the classification power of the method is demonstrated through experimental results on natural textures from the brodatz album

empirical bayes estimates of cancer mortality rates using spatial models we give results of empirical bayes eb estimation of mortality rates designed to smooth observed smr when random fluctuation of the observed deaths is important we have specially studied the case where the prior distributions of the eb method have a spatial structure the need for spatial modelling of cancer mortality rates in france is first shown with testing autocorrelation and fitting autoregressive spatial models conditional car or simultaneous sar a positive autocorrelation of the rates is shown for most cancer sites studied as expected eb estimates of mortality rates for common tumours are similar to smrs for rare tumours the eb method identifies the extreme rates more clearly than smrs by smoothing the smrs with large variances car or sar models are adequate prior distributions for autocorrelated rates and produce quite similar rate estimates

intrinsic autoregressions and related models on the two dimensional lattice summary stationary autoregressions on a two dimensional lattice are generalized to intrinsic models where only increments are assumed to be stationary prediction formulae and the asymptotic behaviour of the semivariogram are derived for parameter estimation we propose an approximate maximum likelihood estimator a generalization of whittle s estimator it is derived also for general intrinsic models

bayesian identification selection and estimation of semiparametric functions in high dimensional additive models in this paper we propose an approach to both estimate and select unknown smooth functions in an additive model with potentially many functions each function is written as a linear combination of basis terms with coefficients regularized by a proper linearly constrained gaussian prior given any potentially rank deficient prior precision matrix we show how to derive linear constraints so that the corresponding effect is identified in the additive model this allows for the use of a wide range of bases and precision matrices in priors for regularization by introducing indicator variables each constrained gaussian prior is augmented with a point mass at zero thus allowing for function selection posterior inference is calculated using markov chain monte carlo and the smoothness in the functions is both the result of shrinkage through the constrained gaussian prior and model averaging we show how using non degenerate priors on the shrinkage parameters enables the application of substantially more computationally efficient sampling schemes than would otherwise be the case we show the favourable performance of our approach when compared to two contemporary alternative bayesian methods to highlight the potential of our approach in high dimensional settings we apply it to estimate two large seemingly unrelated regression models for intra day electricity load both models feature a variety of different univariate and bivariate functions which require different levels of smoothing and where component selection is meaningful priors for the error disturbance covariances are selected carefully and the empirical results provide a substantive contribution to the electricity load modelling literature in their own right

computation of current cumulants for small nonequilibrium systems we analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems recently discussed in the framework of full counting statistics for mesoscopic systems this method is based on identifying the current cumulants from a rayleigh schrodinger perturbation expansion for the generating function here it is derived from a simple path distribution identity and extended to the joint statistics of multiple currents for a possible thermodynamical interpretation we compare this approach to a generalized onsager machlup formalism we present calculations for a boundary driven kawasaki dynamics on a one dimensional chain both for attractive and repulsive particle interactions

variational bayes group sparse time adaptive parameter estimation with either known or unknown sparsity pattern in this paper we study the problem of time adaptive group sparse signal estimation from a bayesian viewpoint we propose two online variational bayes schemes that are specifically designed to estimate and track group sparse signals in time the proposed schemes address both the cases where the grouping information of the signal is either known or not for the case of known group sparsity pattern the proposed scheme builds on a novel hierarchical model for the bayesian adaptive group lasso utilizing the variational bayes framework update equations for all model parameters are given for both the batch and time adaptive estimation scenarios to address the case where the group sparsity pattern is unknown the hierarchical bayesian model of the former scheme is extended by organizing the penalty parameters of the bayesian lasso in a conditional autoregressive model intrinsic conditional autoregression is exploited to penalize the signal coefficients in a structured manner and thus obtain group sparse solutions automatically again a robust and computationally efficient online variational bayes estimator is developed capitalizing on the conjugacy of the proposed hierarchical bayesian formulation experimental results are reported that corroborate the superior estimation performance of the proposed online schemes when compared with state of the art methods

simple parallel hierarchical and relaxation algorithms for segmenting noncausal markovian random fields the modeling and segmentation of images by mrf s markov random fields is treated these are two dimensional noncausal markovian stochastic processes two conceptually new algorithms are presented for segmenting textured images into regions in each of which the data are modeled as one of c mrf s the algorithms are designed to operate in real time when implemented on new parallel computer architectures that can be built with present technology a doubly stochastic representation is used in image modeling here a gaussian mrf is used to model textures in visible light and infrared images and an autobinary or autoternary etc mrf to model a priori information about the local geometry of textured image regions for image segmentation the true texture class regions are treated either as a priori completely unknown or as a realization of a binary or ternary etc mrf in the former case image segmentation is realized as true maximum likelihood estimation in the latter case it is realized as true maximum a posteriori likelihood segmentation in addition to providing a mathematically correct means for introducing geometric structure the autobinary or ternary etc mrf can be used in a generative mode to generate image geometries and artificial images and such simulations constitute a very powerful tool for studying the effects of these models and the appropriate choice of model parameters the first segmentation algorithm is hierarchical and uses a pyramid like structure in new ways that exploit the mutual dependencies among disjoint pieces of a textured region

dynamical fluctuations for semi markov processes wedevelopanonsager machlup typetheoryfornonequilibriumsemi markov processes our main result is an exact large time asymptotics for the joint probability of the occupation times and the currents in the system establishing some generic large deviation structures we discuss in detail how the nonequilibrium driving and the non exponential waiting time distribution influence the occupation current statistics the violation of the markov condition is reflected in the emergence of a new type of nonlocality in the fluctuations explicit solutions are obtained for some examples of driven random walks on the ring

time reversal and entropy there is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time reversal symmetry and the entropy production in such processes we explain on an elementary mathematical level the relations between entropy production phase space contraction and time reversal starting from a deterministic dynamics both closed and open systems in the transient and in the steady regime are considered the main result identifies under general conditions the statistical mechanical entropy production as the source term of time reversal breaking in the path space measure for the evolution of reduced variables this provides a general algorithm for computing the entropy production and to understand in a unified way a number of useful in equalities we also discuss the markov approximation important are a number of old theoretical ideas for connecting the microscopic dynamics with thermodynamic behavior

on a system of two dimensional recurrence equations summary the solution of a system of two dimensional recurrence equations is discussed particularly in the context of the auto correlation structure of a stationary first order autonormal scheme on the doubly infinite rectangular lattice a simple approximation in the region of primary interest is described

texture synthesis using 2 d noncausal autoregressive models the purpose of this paper is to illustrate the usefulness of two dimensional noncausal autoregressive ncar models for the synthesis of textures these models characterize the gray level at a pixel as a linear combination of gray levels at nearby locations in all directions and an additive white noise variable we first show that the class of ncar models is capable of generating a wide variety of image patterns posessing the local replication attribute an essential ingredient of many natural textures it is also shown that the theoretical variograms of many ncar models possess an oscillatory behavior a characteristic of the variograms of many natural textures next we give experimental results of synthesis of 64 64 textures resembling several real textures in the brodatz album the synthetic textures generated by 16 parameter ncar models retain most the visual characteristics of the original textures the variograms of the original and synthetic textures are also similar

an information theory approach to nonlinear nonequilibrium thermodynamics using the problem of ion channel thermodynamics as an example we illustrate the idea of building up complex thermodynamic models by successively adding physical information we present a new formulation of information algebra that generalizes methods of both information theory and statistical mechanics from this foundation we derive a theory for ion channel kinetics identifying a nonequilibrium process free energy functional in addition to the well known integrated work functionals the gibbs maxwell relation for the free energy functional is a green kubo relation applicable arbitrarily far from equilibrium that captures the effect of non local and time dependent behavior from transient thermal and mechanical driving forces comparing the physical significance of the lagrange multipliers to the canonical ensemble suggests definitions of nonequilibrium ensembles at constant capacitance or inductance in addition to constant resistance our result is that statistical mechanical descriptions derived from a few primitive algebraic operations on information can be used to create experimentally relevant and computable models by construction these models may use information from more detailed atomistic simulations two surprising consequences to be explored in further work are that in distinguishability factors are automatically predicted from the problem formulation and that a direct analogue of the second law for thermodynamic entropy production is found by considering information loss in stochastic processes the information loss identifies a novel contribution from the instantaneous information entropy that ensures non negative loss

large deviations in weakly interacting boundary driven lattice gases one dimensional boundary driven lattice gases with local interactions are studied in the weakly interacting limit the density profiles and the correlation functions are calculated to first order in the interaction strength for zero range and short range processes differing only in the specifics of the detailed balance dynamics furthermore the effective free energy large deviation function and the integrated current distribution are also found to this order from the former we find that the boundary drive generates long range correlations only for the short range dynamics while the latter provides support to an additivity principle recently proposed by bodineau and derrida

large deviation function for entropy production in driven one dimensional systems the large deviation function for entropy production is calculated by solving a time independent eigenvalue problem for a particle driven along a periodic potential in an intermediate force regime the large deviation function shows pronounced deviations from a gaussian behavior with a characteristic kink at zero entropy production such a feature can also be extracted from the analytical solution of the asymmetric random walk to which the driven particle can be mapped in a certain parameter range

bayesian non parametric models for spatially indexed data of mixed type we develop bayesian nonparametric models for spatially indexed data of mixed type our work is motivated by challenges that occur in environmental epidemiology where the usual presence of several confounding variables that exhibit complex interactions and high correlations makes it difficult to estimate and under stand the effects of risk factors on health outcomes of interest the modeling approach we adopt assumes that responses and confounding variables are manifestations of continuous latent variables and uses mul tivariate gaussians to jointly model these responses and confounding variables are not treated equally as relevant parameters of the distributions of the responses only are modeled in terms of explanatory variables or risk factors spatial dependence is introduced by allowing the weights of the nonparametric process priors to be location specific obtained as probit transformations of gaussian markov random fields con founding variables and spatial configuration have a similar role in the model in that they only in uence along with the responses the allocation probabilities of the areas into the mixture components thereby allowing for exible adjustment of the effects of observed confounders while allowing for the possibility of residual spatial structure possibly occurring due to unmeasured or undiscovered spatially varying factors aspects of the model are illustrated in simulation studies and an application to a real data set

bayesian analysis of agricultural field experiments the paper describes bayesian analysis for agricultural field experiments a topic that has received very little previous attention despite a vast frequentist literature adoption of the bayesian paradigm simplifies the interpretation of the results especially in ranking and selection also complex formulations can be analysed with comparative ease by using markov chain monte carlo methods a key ingredient in the approach is the need for spatial representations of the unobserved fertility patterns this is discussed in detail problems caused by outliers and by jumps in fertility are tackled via hierarchical f formulations that may find use in other contexts the paper includes three analyses of variety trials for yield and one example involving binary data none is entirely straightforward some numerical comparisons with frequentist analyses are made

analytic properties and covariance functions for a new class of generalized gibbs random fields spartan spatial random fields ssrfs are generalized gibbs random fields equipped with a coarse graining kernel that acts as a low pass filter for the fluctuations ssrfs are defined by means of physically motivated spatial interactions and a small set of free parameters interaction couplings this paper focuses on the fluctuation gradient curvature fgc ssrf model henceforth referred to as fgc ssrf this model is defined on the euclidean space r by means of interactions proportional to the squares of the field realizations as well as their gradient and curvature the permissibility criteria of fgc ssrfs are extended by considering the impact of a finite bandwidth kernel it is proved that the fgc ssrfs are almost surely differentiable in the case of finite bandwidth asymptotic explicit expressions for the spartan covariance function are derived for d 1 and d 3 both known and new covariance functions are obtained depending on the value of the fgc ssrf shape parameter nonlinear dependence of the covariance integral scale on the fgc ssrf characteristic length is established and it is shown that the relation becomes linear asymptotically the results presented in this paper are useful in random field parameter inference and in spatial interpolation of irregularly spaced samples

spatial analysis of field experiments an extension to two dimensions the one dimensional spatial analysis procedure proposed by gleeson and cullis 1987 biometrics 43 277 288 is extended to two dimensions using the subclass of separable lattice processes to model the errors residual maximum likelihood estimation of the models is described and diagnostics for testing model adequacy are derived results from the analysis of 24 sets of uniformity data indicate the frequent need for a two dimensional analysis even when the plot shape is highly rectangular these results also indicate the potential gain from using a two dimensional spatial analysis rather than a row column analysis an example is presented of the analysis of a field experiment on tobacco

current large deviations for asymmetric exclusion processes with open boundaries we study the large deviation functional of the current for the weakly asymmetric simple exclusion process in contact with two reservoirs we compare this functional in the large drift limit to the one of the totally asymmetric simple exclusion process in particular to the jensen varadhan functional conjectures for generalizing the jensen varadhan functional to open systems are also stated

current fluctuations in the one dimensional symmetric exclusion process with open boundaries we calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of n sites with open boundary conditions for large system size n the generating function of the integrated current depends on the densities a and b of the two reservoirs and on the fugacity z the parameter conjugated to the integrated current through a single parameter based on our expressions for these first four cumulants we make a conjecture which leads to a prediction for all the higher cumulants in the case a 1 and b 0 our conjecture gives the same universal distribution as the one obtained by lee levitov and yakovets for one dimensional quantum conductors in the metallic regime

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

non equilibrium current fluctuations in stochastic lattice gases we study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles more precisely we establish a large deviation principle for a space time fluctuation j of the empirical current with a rate functional i j we then estimate the probability of a fluctuation of the average current over a large time interval this probability can be obtained by solving a variational problem for the functional i we discuss several possible scenarios interpreted as dynamical phase transitions for this variational problem they actually occur in specific models we finally discuss the time reversal properties of i and derive a fluctuation relationship akin to the gallavotti cohen theorem for the entropy production