first order intrinsic autoregressions and the de wijs process summary we discuss intrinsic autoregressions for a first order neighbourhood on a two dimensional rectangular lattice and give an exact formula for the variogram that extends known results to the asymmetric case we obtain a corresponding asymptotic expansion that is more accurate and more general than previous ones and use this to derive the de wijs variogram under appropriate averaging a result that can be interpreted as a two dimensional spatial analogue of brownian motion obtained as the limit of a random walk in one dimension this provides a bridge between geostatistics where the de wijs process was once the most popular formulation and markov random fields and also explains why statistical analysis using intrinsic autoregressions is usually robust to changes of scale we briefly describe corresponding calculations in the frequency domain including limiting results for higher order autoregressions the paper closes with some practical considerations including applications to irregularly spaced data

asymptotic equivalence of empirical likelihood and bayesian map in this paper we are interested in empirical likelihood el as a method of estimation and we address the following two problems 1 selecting among various empirical discrepancies in an el framework and 2 demonstrating that el has a well defined probabilistic interpretation that would justify its use in a bayesian context using the large deviations approach a bayesian law of large numbers is developed that implies that el and the bayesian maximum a posteriori probability map estimators are consistent under misspecification and that el can be viewed as an asymptotic form of map estimators based on other empirical discrepancies are in general inconsistent under misspecification

a positivity preserving numerical method for stochastic r d model abstract the stochastic research and development r d model plays an important role in the growth rates of technological progress and capital accumulation however we can not obtain the explicit solution of stochastic r d model to explore a numerical approximate method preserving positivity for the r d model with uncertainty from the population growth we first construct an explicit euler maruyama em method and then verify it converges to the true solution with strong order 1 2 1 1 p but the em method may lead to a negative approximation which is unrealistic so we establish the balanced explicit method bem to overcome the defect of em method and give sufficient conditions to preserve the positivity of bem then the convergence order of bem is obtained finally numerical simulations are carried out to verify our theoretical work

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

hamiltonian monte carlo sampling in bayesian empirical likelihood computation summary we consider bayesian empirical likelihood estimation and develop an efficient hamiltonian monte carlo method for sampling from the posterior distribution of the parameters of interest the method proposed uses hitherto unknown properties of the gradient of the underlying log empirical likelihood function we use results from convex analysis to show that these properties hold under minimal assumptions on the parameter space prior density and the functions used in the estimating equations determining the empirical likelihood our method employs a finite number of estimating equations and observations but produces valid semiparametric inference for a large class of statistical models including mixed effects models generalized linear models and hierarchical bayes models we overcome major challenges posed by complex non convex boundaries of the support routinely observed for empirical likelihood which prevent efficient implementation of traditional markov chain monte carlo methods like random walk metropolis hastings sampling etc with or without parallel tempering a simulation study confirms that our method converges quickly and draws samples from the posterior support efficiently we further illustrate its utility through an analysis of a discrete data set in small area estimation

parameter estimation for differential equations a generalized smoothing approach summary we propose a new method for estimating parameters in models that are defined by a system of non linear differential equations such equations represent changes in system outputs by linking the behaviour of derivatives of a process to the behaviour of the process itself current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to the realization of statistical objectives such as inference and interval estimation the paper describes a new method that uses noisy measurements on a subset of variables to estimate the parameters defining a system of non linear differential equations the approach is based on a modification of data smoothing methods along with a generalization of profiled estimation we derive estimates and confidence intervals and show that these have low bias and good coverage properties respectively for data that are simulated from models in chemical engineering and neurobiology the performance of the method is demonstrated by using real world data from chemistry and from the progress of the autoimmune disease lupus

bayesian estimation and comparison of moment condition models in this article we develop a bayesian semiparametric analysis of moment condition models by casting the problem within the exponentially tilted empirical likelihood etel framework we use this f

fully simplified multivariate normal updates in non conjugate variational message passing fully simplified expressions for multivariate normal updates in non conjugate variational message passing approximate inference schemes are obtained the simplicity of these expressions means that the updates can be achieved very effciently since the multivariate normal family is the most common for approximating the joint posterior density function of a continuous parameter vector these fully simplified updates are of great practical benefit

evaluating logistic models for large contingency tables abstract this article discusses through three examples several new methods to aid in the analysis of large contingency tables the general goal is to give better understanding of specific contingency tables both by comparing how various log linear logistic models fit and through clearer interpretations of the resulting fits for model selection we show how to focus on a subset of simple good fitting models beginning with a plot of a goodness of fit statistic versus residual degrees of freedom for all of the fitted models to assess whether a particular model is adequate we demonstrate that certain plots of residuals can reveal interesting effects that are often otherwise hidden for model summarization and interpretation we plot odds ratio factors with confidence intervals to show the effects of explanatory variables in a concise and appealing way the first example involves the relationship of job satisfaction to demographic variables for craft employees of a large corporation the data presented c

a penalized empirical likelihood method in high dimensions we formulate a penalized empirical likelihood pel method for inference on the population mean when the dimension of the observations become unbounded with the sample size we derive the asymptotic distribution of the pel ratio statistic we show that the limit distribution of the proposed pel ratio statistic can vary widely depending on the correlation structure of the components of the observations that we classify as i non ergodic ii long range dependent and iii short range dependent the limit laws differ from the usual chi squared limit of the empirical likelihood ratio statistic in the finite dimensional case we propose a subsampling approximation for calibrating the pel ratio test statistic and establish its validity finite sample properties of the method are investigated through a simulation study joint work with deep mukhopadhyay

maximum sum rate of repeat accumulate interleave division system by fixed point analysis a multi user repeat accumulate interleave division raid system is considered for a multiple access channel mac with binary inputs equal power and symbol synchronization in the system a regular repeat accumulate ra code serially concatenated with block spreading is employed for each user at the receiver multi user message passing decoding is performed on a single factor graph over the mac with additive white gaussian noise awgn a fixed point analysis is developed to obtain the optimal code rate and the spreading length that give the maximum sum rate for an arbitrary small decoding error rate

exponential stability of equidistant euler maruyama approximations of stochastic differential delay equations our aim is to study under what conditions the exact and numerical solution based on equidistant nonrandom partitions of integration time intervals to a stochastic differential delay equation sdde share the property of mean square exponential stability our approach is trying to avoid the use of lyapunov functions or functionals we show that under a global lipschitz assumption an sdde is exponentially stable in mean square if and only if for some sufficiently small stepsize d the euler maruyama em method is exponentially stable in mean square we then replace the global lipschitz condition with a finite time convergence condition and establish the same if and only if result the important feature of this result is that it transfers the asymptotic problem into a finite time convergence problem replacing the exact and em numerical solution with stochastic processes we also discuss whether a family of stochastic processes share the stability property this new approach allows us to discuss i whether a family of sddes share the stability property and ii whether an sdde with variable time lag shares stability property with the modified em method as another application of this general approach we consider a linear sdde with variable time lag and establish an if and only if result it should also be mentioned that the questions addressed results proved as well as style of analysis borrow heavily from 14 but the computations involved to cope with time delay are nontrivial

empirical type likelihoods allowing posterior credible sets with frequentist validity higher order asymptotics summary with reference to a general class of empirical type likelihoods we develop higher order asymptotics for the frequentist coverage of bayesian credible sets based on posterior quantiles and highest posterior density these asymptotics in turn characterise members of the class that allow approximate frequentist validity of such sets it is seen that the usual empirical likelihood does not enjoy this property up to the order of approximation considered here

global stability in a population model with piecewise constant arguments abstract in this paper we investigate the global stability and the boundedness character of the positive solutions of the differential equation d x d t r x t 1 x t 0 x t 1 x t 1 where t 0 the parameters r 0 and 1 denote positive numbers and t denotes the integer part of t 0 we considered the discrete solution of the logistic differential equation to show the global asymptotic behavior and obtained that the unique positive equilibrium point of the differential equation is a global attractor with a basin that depends on the conditions of the coefficients furthermore we studied the semi cycle of the positive solutions of the logistic differential equation

analysis of sum product decoding of low density parity check codes using a gaussian approximation density evolution is an algorithm for computing the capacity of low density parity check ldpc codes under message passing decoding for memoryless binary input continuous output additive white gaussian noise awgn channels and sum product decoders we use a gaussian approximation for message densities under density evolution to simplify the analysis of the decoding algorithm we convert the infinite dimensional problem of iteratively calculating message densities which is needed to find the exact threshold to a one dimensional problem of updating the means of the gaussian densities this simplification not only allows us to calculate the threshold quickly and to understand the behavior of the decoder better but also makes it easier to design good irregular ldpc codes for awgn channels for various regular ldpc codes we have examined thresholds can be estimated within 0 1 db of the exact value for rates between 0 5 and 0 9 codes designed using the gaussian approximation perform within 0 02 db of the best performing codes found so far by using density evolution when the maximum variable degree is 10 we show that by using the gaussian approximation we can visualize the sum product decoding algorithm we also show that the optimization of degree distributions can be understood and done graphically using the visualization

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

local model uncertainty and incomplete data bias with discussion problems of the analysis of data with incomplete observations are all too familiar in statistics they are doubly difficult if we are also uncertain about the choice of model we propose a general formulation for the discussion of such problems and develop approximations to the resulting bias of maximum likelihood estimates on the assumption that model departures are small loss of efficiency in parameter estimation due to incompleteness in the data has a dual interpretation the increase in variance when an assumed model is correct the bias in estimation when the model is incorrect examples include non ignorable missing data hidden confounders in observational studies and publication bias in meta analysis doubling variances before calculating confidence intervals or test statistics is suggested as a crude way of addressing the possibility of undetectably small departures from the model the problem of assessing the risk of lung cancer from passive smoking is used as a motivating example

design of regular 2 d sub c ldpc codes over gf q using their binary images in this paper a method to design regular 2 dc ldpc codes over gf q with both good waterfall and error floor properties is presented based on the algebraic properties of their binary image first the algebraic properties of rows of the parity check matrix h associated with a code are characterized and optimized to improve the waterfall then the algebraic properties of cycles and stopping sets associated with the underlying tanner graph are studied and linked to the global binary minimum distance of the code finally simulations are presented to illustrate the excellent performance of the designed codes

approximate riemannian conjugate gradient learning for fixed form variational bayes variational bayesian vb methods are typically only applied to models in the conjugate exponential family using the variational bayesian expectation maximisation vb em algorithm or one of its variants in this paper we present an efficient algorithm for applying vb to more general models the method is based on specifying the functional form of the approximation such as multivariate gaussian the parameters of the approximation are optimised using a conjugate gradient algorithm that utilises the riemannian geometry of the space of the approximations this leads to a very efficient algorithm for suitably structured approximations it is shown empirically that the proposed method is comparable or superior in efficiency to the vb em in a case where both are applicable we also apply the algorithm to learning a nonlinear state space model and a nonlinear factor analysis model for which the vb em is not applicable for these models the proposed algorithm outperforms alternative gradient based methods by a significant margin

discrete time approximations of stochastic delay equations the milstein scheme in this paper we develop a strong milstein approximation scheme for solving stochastic delay differential equations sddes the scheme has convergence order 1 in order to establish the scheme we prove an infinite dimensional ito formula for tame functions acting on the segment process of the solution of an sdde it is interesting to note that the presence of the memory in the sdde requires the use of the malliavin calculus and the anticipating stochastic analysis of nualart and pardoux given the nonanticipating nature of the sdde the use of anticipating calculus methods in the context of strong approximation schemes appears to be novel

an approximate method via taylor series for stochastic functional differential equations abstract the subject of this paper is an analytic approximate method for stochastic functional differential equations whose coefficients are functionals sufficiently smooth in the sense of frechet derivatives the approximate equations are defined on equidistant partitions of the time interval and their coefficients are general taylor expansions of the coefficients of the initial equation it will be shown that the approximate solutions converge in the l p norm and with probability one to the solution of the initial equation and also that the rate of convergence increases when degrees in taylor expansions increase analogously to real analysis

bayesian and frequentist confidence intervals arising from empirical type likelihoods summary for a general class of empirical type likelihoods for the population mean higher order asymp totics are developed with a view to characterizing its members which allow for any given prior the existence of a confidence interval that has approximately correct posterior as well as fre quentist coverage in particular it is seen that the usual empirical likelihood always allows such a confidence interval while many of its variants proposed in the literature do not enjoy this property an explicit form of the confidence interval is also given

geometry of stochastic state vector reduction the state space of a quantum mechanical system is a complex projective space the space of rays in the associated hilbert space the state space comes equipped with a natural riemannian metric the fubini study metric and a compatible symplectic structure the operations of ordinary quantum mechanics can thus be reinterpreted in the language of differential geometry it is interesting in this spirit to scrutinize the probabilistic assumptions that are brought in at various stages in the analy sis of quantum dynamics particularly in connection with state vector reduction a promising approach to understanding reduction studied recently by a number of authors involves the use of nonlinear stochastic dynamics to modify the ordinary linear schrodinger evolution here we use stochastic differential geometry to give a systematic geometric formulation for such stochastic models of state vector collapse in this picture the conventional schrodinger evolution which corresponds to the unitary flow associated with a killing vector of the fubini study metric is replaced by a more general stochastic flow on the state manifold in the simplest example of such a flow the volatility term in the stochastic differential equation for the state trajectory is proportional to the gradient of the expectation of the hamiltonian the conservation of energy is represented by the requirement that the actual process followed by the expectation of the hamiltonian as the state evolves should be a martingale this requirement implies the existence of a nonlinear term in the drift vector of the state process which is always oriented opposite to the direction of in creasing energy uncertainty as a consequence the state vector necessarily collapses to an energy eigenstate and a martingale argument can be used to show that the probability of collapse to a given eigenstate from any particular initial state is in fact given by precisely the usual quantum mechanical probability

bayesian pseudo empirical likelihood intervals for complex surveys summary bayesian methods for inference on finite population means and other parameters by using sample survey data face hurdles in all three phases of the inferential procedure the formulation of a likelihood function the choice of a prior distribution and the validity of posterior inferences under the design based frequentist framework in the case of independent and identically distributed observations the profile empirical likelihood function of the mean and a non informative prior on the mean can be used as the basis for inference on the mean and the resulting bayesian empirical likelihood intervals are also asymptotically valid under the frequentist set up for complex survey data we show that a pseudo empirical likelihood approach can be used to construct bayesian pseudo empirical likelihood intervals that are asymptotically valid under the design based set up the approach proposed compares favourably with a full bayesian analysis under simple random sampling without replacement it is also valid under general single stage unequal probability sampling designs unlike a full bayesian analysis moreover the approach is very flexible in using auxiliary population information and can accommodate two scenarios which are practically important incorporation of known auxiliary population information for the construction of intervals by using the basic design weights calculation of intervals by using calibration weights based on known auxiliary population means or totals

generalized linear models incorporating population level information an empirical likelihood based approach summary in many situations information from a sample of individuals can be supplemented by population level information on the relationship between a dependent variable and explan atory variables inclusion of the population level information can reduce bias and increase the efficiency of the parameter estimates population level information can be incorporated via con straints on functions of the model parameters in general the constraints are non linear making the task of maximum likelihood estimation more difficult we develop an alternative approach exploiting the notion of an empirical likelihood it is shown that within the framework of gener alized linear models the population level information corresponds to linear constraints which are comparatively easy to handle we provide a two step algorithm that produces parameter estimates by using only unconstrained estimation we also provide computable expressions for the standard errors we give an application to demographic hazard modelling by combining panel survey data with birth registration data to estimate annual birth probabilities by parity

bayesian empirical likelihood summary research has shown that empirical likelihood tests have many of the same asymptotic properties as those derived from parametric likelihoods this leads naturally to the possibility of using empirical likelihood as the basis for bayesian inference different ways in which this goal might be accomplished are considered the validity of the resultant posterior inferences is examined as are frequentist properties of the bayesian empirical likelihood intervals

coding theorems for turbo code ensembles this paper is devoted to a shannon theoretic study of turbo codes we prove that ensembles of parallel and serial turbo codes are good in the following sense for a turbo code ensemble defined by a fixed set of component codes subject only to mild necessary restrictions there exists a positive number spl gamma sub 0 such that for any binary input memoryless channel whose bhattacharyya noise parameter is less than spl gamma sub 0 the average maximum likelihood ml decoder block error probability approaches zero at least as fast as n sup spl beta where spl beta is the interleaver gain exponent defined by benedetto et al in 1996

empirical likelihood for linear models empirical likelihood is a nonparametric method of inference it has sampling properties similar to the bootstrap but where the bootstrap uses resampling it profiles a multinomial likelihood supported on the sample its properties in i i d settings have been investigated in works by owen by hall and by diciccio hall and romano this article extends the method to regression problems fixed and random regressors are considered as are robust and heteroscedastic regressions to make the extension three variations on the original idea are considered it is shown that when some functionals of the distribution of the data are known one can get sharper inferences on other functionals by imposing the known values as constraints on the optimization the result is first order equivalent to conditioning on a sample value of the known functional the use of a euclidean alternative to the likelihood function is investigated a triangular array version of the empirical likelihood theorem is given the one way anova and heteroscedastic regression models are considered in detail an example is given in which inferences are drawn on the parameters of both the regression function and the conditional variance model

empirical likelihood for small area estimation abstract small areaestimation has become a topic of growingimportance inrecent years due to increasing demand for small area statistics fromboth the public and private sectors the current methodologies inthis area with possibly a handful of exceptions are all parametric be it bayesian or frequentist even the so called nonparamet ric procedures based on empirical best linear unbiased predictors eblup assume linearity of the estimators of small area means resampling methods like jacknife and bootstrap are used mostlyfor mean squared error estimation in this paper we propose analternative bayesian approach based on empirical likelihood whichdoes not require the assumption of either a parametric likelihoodor linearity of estimators the proposed method can also handleboth discrete and continuous data in a uni ed manner empiricallikelihood for both area and unit level models are introduced theimproved performance of our estimator is illustrated through twoexamples involving both discrete and continuous data key words and phrases area level exponentially tilted t prior unit level

estimation in parameter redundant models the likelihood surface resulting from a parameter redundant stochastic model is maximised along a completely flat ridge this ridge may be orthogonal to some parameter axes so that these parameters have unique maximum likelihood estimates for exponential family models we show how to determine which parameter combinations are estimable the approach requires the calculation of a derivative matrix and the determination of its null space both of which are readily achieved in computer algebra packages illustrative examples are drawn from the areas of compartment modelling and ring recovery analysis

spectral efficiency of cdma with random spreading the cdma channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods furthermore its analysis provides a comparison baseline for cdma channels with deterministic signature waveforms spanning one symbol period we analyze the spectral efficiency total capacity per chip as a function of the number of users spreading gain and signal to noise ratio and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading white gaussian background noise and equal power synchronous users are assumed the following receivers are analyzed a optimal joint processing b single user matched filtering c decorrelation and d mmse linear processing

the bayesian evidence scheme for regularizing probability density estimating neural networks training probability density estimating neural networks with the expectation maximization em algorithm aims to maximize the likelihood of the training set and therefore leads to overfitting for sparse data in this article a regularization method for mixture models with generalized linear kernel centers is proposed which adopts the bayesian evidence approach and optimizes the hyperparameters of the prior by type ii maximum likelihood this includes a marginalization over the parameters which is done by laplace approximation and requires the derivation of the hessian of the log likelihood function the incorporation of this approach into the standard training scheme leads to a modified form of the em algorithm which includes a regularization term and adapts the hyperparameters on line after each em cycle the article presents applications of this scheme to classification problems the prediction of stochastic time series and latent space models

particle approximations of the score and observed information matrix in state space models with application to parameter estimation particle methods are popular computational tools for bayesian inference in nonlinear non gaussian state space models for this class of models we present two particle algorithms to compute the score vector and observed information matrix recursively the first algorithm is implemented with computational complexity o n and the second with complexity o n 2 where n is the number of particles although cheaper the performance of the o n method degrades quickly as it relies on the approximation of a sequence of probability distributions whose dimension increases linearly with time in particular even under strong mixing assumptions the variance of the estimates computed with the o n method increases at least quadratically in time the more expensive o n 2 method relies on a nonstandard particle implementation and does not suffer from this rapid degradation it is shown how both methods can be used to perform batch and recursive parameter estimation

mean square exponential stability for stochastic control systems with discrete time state feedbacks and their numerical schemes in simulation aiming at the qualitative numerical simulation this article concerns the mean square exponential stability mses of the stochastic systems with discrete time state feedbacks and their numerical schemes a time delay dependent stability criterion is obtained for the underlying system the euler maruyama and backward euler maruyama schemes are established and their mses are proved under the same criterion which means that the numerical schemes preserve the stability of the continuous model the illustrative example at the end of this letter shows that the theoretical upper bound for the sampling period limited in the stability criterion is much greater than that obtained by the stability criteria from the literature

finite field spreading for multiple access channel as a generalization of the binary spreading scheme in conventional direct sequence code division multiple access ds cdma and interleave division multiple access idma a finite field spreading scheme is proposed for a synchronous multiple access channel mac with gaussian noise and equal power users for each user each information symbol over a finite field is spread into a length l field vector by l field multiplications at the receiver an iterative multi user decoding algorithm on a factor graph is developed to recover each user s information symbol to estimate the bit error rate performance of an uncoded finite field spreading system an extrinsic information transfer analysis of the finite field despreading is given this analysis shows that in addition to overcoming multi user interference the finite field spreading scheme can also provide an additional coding gain to overcome gaussian noise compared with the conventional spreading scheme this coding gain increases with the field order the finite field spreading serially concatenated with a nonbinary low density parity check ldpc code with field order 64 approaches the mac capacity within 0 26 db at a sum rate of 0 25

multivariate analysis design of experiments and survey sampling sampling designs and prediction methods for gaussian spatial processes design techniques for probabilistic sampling of items with variable monetary value small area estimation a bayesian perspective bayes sampling designs for selection procedures cluster coordinated composites of diverse datasets on several spatial scales for designing extensive environmental sample surveys prospectus on promising protocols corrected confidence sets for sequentially designed experiments ii examples resampling marked point processes graphical markov models in multivariate analysis robust regression with censored and truncated data multivariate calibration some consequences of random effects in multivariate survival models a unified methodology for constructing multivariate autoregressive models statistical model evaluation and information criteria multivariate rank tests asymptotic expansions of the distribution of some test statistics for elliptical populations a review of variance estimators with extensions to multivariate nonparametric regression models on affine invariant sign and rank tests in one and two sample multivariate problems correspondence and component analysis growth curve models dealing with uncertainties in queues and networks of queues optimal bayesian design for a logistic regression model geometric and algebraic approaches structure of weighing mattrices of small order and weight

stability of differential equations with piecewise constant arguments of generalized type abstract in this paper we continue to consider differential equations with piecewise constant argument of generalized type epcag m u akhmet integral manifolds of differential equations with piecewise constant argument of generalized type nonlinear anal tma 66 2007 367 383 a deviating function of a new form is introduced the linear and quasilinear systems are under discussion the structure of the sets of solutions is specified necessary and sufficient conditions for stability of the zero solution are obtained our approach can be fruitfully applied to the investigation of stability oscillations controllability and many other problems of epcag some of the results were announced at the international conference on hybrid systems and applications university of louisiana lafayette 2006

bayesian empirical likelihood for quantile regression bayesian inference provides a flexible way of combining data with prior information however quantile regression is not equipped with a parametric likelihood and therefore bayesian inference for quantile regression demands careful investigation this paper considers the bayesian empirical likelihood approach to quantile regression taking the empirical likelihood into a bayesian framework we show that the resultant posterior from any fixed prior is asymptotically normal its mean shrinks toward the true parameter values and its variance approaches that of the maximum empirical likelihood estimator a more interesting case can be made for the bayesian empirical likelihood when informative priors are used to explore commonality across quantiles regression quantiles that are computed separately at each percentile level tend to be highly variable in the data sparse areas e g high or low percentile levels through empirical likelihood the proposed method enables us to explore various forms of commonality across quantiles for efficiency gains by using an mcmc algorithm in the computation we avoid the daunting task of directly maximizing empirical likelihood the finite sample performance of the proposed method is investigated empirically where substantial efficiency gains are demonstrated with informative priors on common features across several percentile levels a theoretical framework of shrinking priors is used in the paper to better understand the power of the proposed method

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

numerical solutions of stochastic differential delay equations under local lipschitz condition in this paper a variant of the euler maruyama method is used to define the numerical solutions for stochastic differential delay equations sddes with variable delay the key aim is to show that the numerical solutions will converge to the true solutions of the sddes under the local lipschitz condition

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

riemann manifold langevin and hamiltonian monte carlo methods the paper proposes metropolis adjusted langevin and hamiltonian monte carlo sampling methods defined on the riemann manifold to resolve the shortcomings of existing monte carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations the methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for metropolis hastings or indeed hamiltonian monte carlo and metropolis adjusted langevin algorithms this allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the markov chain the methodology proposed exploits the riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold providing highly efficient convergence and exploration of the target density the performance of these riemann manifold monte carlo methods is rigorously assessed by performing inference on logistic regression models log gaussian cox point processes stochastic volatility models and bayesian estimation of dynamic systems described by non linear differential equations substantial improvements in the time normalized effective sample size are reported when compared with alternative sampling approaches matlab code that is available from http www ucl ac uk statistics research rmhmc allows replication of all the results reported

adjusted empirical likelihood with high order precision empirical likelihood is a popular nonparametric or semi parametric statistical method with many nice statistical properties yet when the sample size is small or the dimension of the accompanying estimating function is high the application of the empirical likelihood method can be hindered by low precision of the chi square approximation and by nonexistence of solutions to the estimating equations in this paper we show that the adjusted empirical likelihood is effective at addressing both problems with a specific level of adjustment the adjusted empirical likelihood achieves the high order precision of the bartlett correction in addition to the advantage of a guaranteed solution to the estimating equations simulation results indicate that the confidence regions constructed by the adjusted empirical likelihood have coverage probabilities comparable to or substantially more accurate than the original empirical likelihood enhanced by the bartlett correction

achievable information rates and the coding spreading tradeoff in finite sized synchronous cdma systems in this letter we compute achievable information rates for finite sized synchronous code division multiple access cdma systems and low density parity check ldpc codes are adopted to approach the achievable rates the associated coding spreading tradeoff problem is also considered using these results we assume binary random spreading sequences and the computed achievable rates are averaged over ensembles of spreading sequences unlike most prior papers which analyze the spectral efficiency of large cdma systems under gaussianity assumptions channel inputs and or multiple access interference we make no such assumptions in order to display the coding spreading tradeoff we plot the minimum required signal to noise ratio for reliable transmission as a function of information rate it is shown that the coding spreading tradeoff favors all coding i e no spreading when the optimal joint multiuser detector decoder is employed whereas for systems with a suboptimal multiuser detector and single user decoders there generally exists an optimal balance between coding and spreading we also provide simulation results on the performance of ldpc coded synchronous cdma systems which approach the information theoretic limits we have computed

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

the euler maruyama approximation of solutions to stochastic differential equations with piecewise constant arguments abstract in this paper we consider stochastic differential equations with piecewise constant arguments these equations describe hybrid dynamical systems that is combinations of continuous and discrete systems our aim is to establish the mean square convergence of the euler maruyama approximate solution under quite general conditions that is the global lipschitz condition and the linear growth condition which guarantee the existence and uniqueness of the true solution then we show that the initial equation is exponentially stable in mean square if and only if for some sufficiently small step size the euler maruyama method is exponentially stable in mean square the stability study does not involve the lyapunov functions nor functionals it should be pointed out that stochastic differential equations with piecewise constant arguments can be regarded as a class of stochastic differential equations with multiple time dependent delays which can be found in the literature however in the convergence analysis of the euler maruyama method of these equations it is required that the delay functions satisfy lipschitz continuity condition in the present paper the delay functions do not satisfy that condition so it represents an extension of results from the papers mao 2003 2007 using the technique similar to that from the first paper

empirical likelihood methods with weakly dependent processes this paper studies the method of empirical likelihood in models with weakly dependent processes in such cases if the likelihood function is formulated as if the data process were independent obviously empirical likelihood fails we propose to use empirical likelihood of blocks of observations to solve this problem in a nonparametric manner this method of blockwise empirical likelihood preserves the dependence of data and the resulting likelihood ratios can be used to construct asymptotically valid confidence intervals we consider general estimating equations for which an efficient estimator is derived by maximizing blockwise empirical likelihood we also introduce blocks of blocks empirical likelihood to conduct inference for parameters of the infinite dimensional joint distribution of data the smooth function model is used for such cases we show that blockwise empirical likelihood of the smooth function model with weakly dependent processes is bartlett correctable a wide variety of problems such as time series regressions and spectral densities can be treated using our methodology

bayesian empirical likelihood inference with complex survey data we propose a bayesian empirical likelihood approach to survey data analysis on a vector of finite population parameters defined through estimating equations our method allows overidentified estimating equation systems and is applicable to both smooth and non differentiable estimating functions our proposed bayesian estimator is design consistent for general sampling designs and the bayesian credible intervals are calibrated in the sense of having asymptotically valid design based frequentist properties under single stage unequal probability sampling designs with small sampling fractions large sample properties of the bayesian inference proposed are established for both non informative and informative priors under the design based framework we also propose a bayesian model selection procedure with complex survey data and show that it works for general sampling designs an efficient markov chain monte carlo procedure is described for the required computation of the posterior distribution for general vector parameters simulation studies and an application to a real survey data set are included to examine the finite sample performances of the methods proposed as well as the effect of different types of prior and different types of sampling design

convergence and stability of the split step theta method for stochastic differential equations with piecewise continuous arguments abstract in this paper we consider the stochastic differential equations with piecewise continuous arguments sdepcas in which both the drift and the diffusion coefficients do not satisfy the global lipschitz and linear growth conditions especially the diffusion coefficients are highly non linear growing it is proved that the split step theta sst method with 1 2 1 is strongly convergent to sdepcas under the local lipschitz monotone and one sided lipschitz conditions it is also obtained that the sst method with 1 2 1 preserves the exponential mean square stability of sdepcas under the monotone condition and some condition on the step size without any restriction on the step size there exists 1 2 1 such that the sst method with 1 is exponentially stable in mean square moreover for sufficiently small step size the rate constant can be reproduced some numerical simulations are presented to illustrate the analytical theory

an improved acceptance procedure for the hybrid monte carlo algorithm abstract the probability of accepting a candidate move in the hybrid monte carlo algorithm can be increased by considering a transition to be between windows of several states at the beginning and end of the trajectory with a particular state within the selected window then being chosen according to the boltzmann probabilities the detailed balance condition used to justify the algorithm still holds with this procedure provided the start state is randomly positioned within its window the new procedure is shown empirically to significantly improve the acceptance rate for a test system of uncoupled oscillators it also allows expectations to be estimated using data from all states in the windows rather than just states that are accepted

integral manifolds of differential equations with piecewise constant argument of generalized type abstract in this paper we introduce a general type of differential equations with piecewise constant argument epcag the existence of global integral manifolds of the quasilinear epcag is established when the associated linear homogeneous system has an exponential dichotomy the smoothness of the manifolds is investigated the existence of bounded and periodic solutions is considered a new technique of investigation of equations with piecewise argument based on an integral representation formula is proposed appropriate illustrating examples are given

extended empirical likelihood for estimating equations we derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood to the full parameter space under mild conditions the extended empirical likelihood has all the asymptotic properties of the original empirical likelihood the first order extended empirical likelihood is easy to use and substantially more accurate than the original empirical likelihood

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

bayesian calibration of computer models we consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models such models implemented as computer codes are often generic in the sense that by a suitable choice of some of the model s input parameters the code can be used to predict the behaviour of the system in a variety of specific applications however in any specific application the values of necessary parameters may be unknown in this case physical observations of the system in the specific context are used to learn about the unknown parameters the process of fitting the model to the observed data by adjusting the parameters is known as calibration calibration is typically effected by ad hoc fitting and after calibration the model is used with the fitted input values to predict the future behaviour of the system we present a bayesian calibration technique which improves on this traditional approach in two respects first the predictions allow for all sources of uncertainty including the remaining uncertainty over the fitted parameters second they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best fitting parameter values the method is illustrated by using data from a nuclear radiation release at tomsk and from a more complex simulated nuclear accident exercise

distance enumerator analysis for interleave division multi user codes consider an interleave division multi user coding model for a gaussian multiple access channel mac each user s message is encoded by a separate channel encoder followed by a user interleaver which is employed for user separation all the users codewords are jointly regarded as one multi user codeword and the distance between two multi user codewords is defined as the euclidean distance after the inter user superposition caused by the mac a distance enumerator analysis estimates the multi user maximum likelihood decoding performance by introducing user scramblers a multi user code ensemble is defined and its distance enumerator is calculated as concatenated multiple single user codes and a superposition code both finite length and asymptotic analyses are given and it is shown that interleave division multi user codes have much better distance properties than conventional random direct sequence code division multiple access in fact the codes achieve almost the same asymptotic uniquely decodable performance as a multi user random code

ricci curvature for metric measure spaces via optimal transport we dene a notion of a measured length space x having nonnegative n ricci curvature for n 2 1 1 or having1 ricci curvature bounded below byk fork2 r the denitions are in terms of the displacement convexity of certain functions on the associated wasserstein metric space p2 x of probability measures we show that these properties are preserved under measured gromov hausdor limits we give geometric and analytic consequences this paper has dual goals one goal is to extend results about optimal transport from the setting of smooth riemannian manifolds to the setting of length spaces a second goal is to use optimal transport to give a notion for a measured length space to have ricci curvature bounded below we refer to 11 and 44 for background material on length spaces and optimal transport respectively further bibliographic notes on optimal transport are in appendix f in the present introduction we motivate the questions that we address and we state the main results to start on the geometric side there are various reasons to try to extend notions of curvature from smooth riemannian manifolds to more general spaces a fairly general setting is that of length spaces meaning metric spaces x d in which the distance between two points equals the inmum of the lengths of curves joining the points in the rest of this introduction we assume that x is a compact length space alexandrov gave a good notion of a length space having curvature bounded below by k with k a real number in terms of the geodesic triangles in x in the case of a riemannian manifold m with the induced length structure one recovers the riemannian notion of having sectional curvature bounded below by k length spaces with alexandrov curvature bounded below by k behave nicely with respect to the gromovhausdor topology on compact metric spaces modulo isometries they form

unveiling turbo codes some results on parallel concatenated coding schemes a parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver the input bits to the first encoder are scrambled by the interleaver before entering the second encoder the codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders this construction can be generalized to any number of constituent codes parallel concatenated schemes employing two convolutional codes as constituent codes in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes have been previously shown to yield remarkable coding gains close to theoretical limits they have been named and are known as turbo codes we propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length the analytical bounding technique is then used to shed some light on some crucial questions which have been floating around in the communications community since the proposal of turbo codes