on the stability of the quenched state in mean field spin glass models while the gibbs states of spin glass models have been noted to have an erratic dependence on temperature one may expect the mean over the disorder to produce a continuously varying quenched state the assumption of such continuity in temperature implies that in the infinite volume limit the state is stable under a class of deformations of the gibbs measure the condition is satisfied by the parisi ansatz along with an even broader stationarity property the stability conditions have equivalent expressions as marginal additivity of the quenched free energy implications of the continuity assumption include constraints on the overlap distribution which are expressed as the vanishing of the expectation value for an infinite collection of multi overlap polynomials the polynomials can be computed with the aid of a real replica calculation in which the number of replicas is taken to zero

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

absence of self averaging of the order parameter in the sherrington kirkpatrick model we prove that if n is the sherrington kirkpatrick sk hamiltonian and the quantity bar q n n 1 sum left langle s l right rangle h 2 converges in the variance to a nonrandom limit asn then the mean free energy of the model converges to the expression obtained by sk since this expression is known not to be correct in the low temperature region our result implies the non self averaging of the order parameter of the sk model this fact is an important ingredient of the parisi theory which is widely believed to be exact we also prove that the variance of the free energy of the sk model converges to zero asn i e the free energy has the self averaging property

distributed sequential bayesian estimation of a diffusive source in wireless sensor networks we develop an efficient distributed sequential bayesian estimation method for applications relating to diffusive sources localizing a diffusive source determining its space time concentration distribution and predicting its cloud envelope evolution using wireless sensor networks potential applications include security environmental and industrial monitoring as well as pollution control we first derive the physical model of the substance dispersion by solving the diffusion equations under different environment scenarios and then integrate the physical model into the distributed processing technologies we propose a distributed sequential bayesian estimation method in which the state belief is transmitted in the wireless sensor networks and updated using the measurements from the new sensor node we propose two belief representation methods a gaussian density approximation and a new lpg function linear combination of polynomial gaussian density functions approximation these approximations are suitable for the distributed processing in wireless sensor networks and are applicable to different sensor network situations we implement the idea of information driven sensor collaboration and select the next sensor node according to certain criterions which provides an optimal subset and an optimal order of incorporating the measurements into our belief update reduces response time and saves energy consumption of the sensor network numerical examples demonstrate the effectiveness and efficiency of the proposed methods

quasi projective brauer characters abstract we study p brauer characters of a finite group g which are restrictions of generalized characters vanishing on p singular elements for a fixed prime p dividing the order of g such brauer characters are called quasi projective we show that for each irreducible brauer character there exists a minimal p power say p a such that p a is quasi projective the exponent a only depends on the cartan matrix of the block to which belongs moreover p a is bounded by the vertex of the module affording and equality holds in case that g is p solvable we give some evidence for the conjecture that a 0 occurs if and only if belongs to a block of defect 0 finally we study indecomposable quasi projective brauer characters of a block b this set is finite and corresponds to a minimal hilbert basis of the rational cone defined by the cartan matrix of b

modeling spatial extremes via ensemble of trees of pairwise copulas assessing the risk of extreme events in a spatial domain such as hurricanes floods and droughts presents a unique significance in practice unfortunately the existing extreme value statistical models are typically not feasible for practical large scale problems graphical models on the other hand are capable of handling sizable number of variables but have yet to be explored in the realm of extreme value analysis to bridge the gap an extreme value graphical model is introduced in this paper i e an ensemble of trees of pairwise copulas etpc in the proposed graphical model extreme value marginal distributions are stitched together by means of a pairwise copulas which in turn are the building blocks of the ensemble of trees novel linear complexity stochastic gradient based algorithms are then developed for learning the etpc model and inferring missing data as a result the etpc model is applicable to extreme value problems with thousands of variables it can be proven that under mild conditions the etpc model exhibits the favorable property of tail dependence between an arbitrary pair of sites variables consequently the model is able to reliably capture statistical dependence between extreme values at different sites experimental results for both synthetic and real data demonstrate the advantages of the etpc model in modeling fitting imputation and computational efficiency

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

on the distribution of overlaps in the sherrington kirkpatrick spin glass model this paper describes some of the analytic tools developed recently by ghirlanda and guerra in the investigation of the distribution of overlaps in the sherrington kirkpatrick spin glass model and of parisi s ultrametricity in particular we introduce to this task a simplified but also generalized model on which the gaussian analysis is made easier moments of the hamiltonian and derivatives of the free energy are expressed as polynomials of the overlaps under the essential tool of self averaging we describe with full rigour various overlap identities and replica independence that actually hold in a rather large generality the results are presented in a language accessible to probabilists and analysts

location estimation of a random signal source based on correlated sensor observations the problem of location estimation of a source of random signals using a network of sensors is considered a novel maximum likelihood estimation mle based approach using copula functions is proposed the measurements received at the sensors are often spatially correlated and characterized by a multivariate distribution using the theory of copulas the joint parametric density of sensor observations joint likelihood is approximated assuming only the knowledge of the marginal likelihood functions of the sensor observations the problem of selecting the best copula function to model the joint likelihood is approached as one of model selection and a model fusion strategy is used to reduce the effect of selection bias an example involving source localization of a poisson source is presented to illustrate the proposed approach and demonstrate its performance

model selection an integral part of inference we argue that model selection uncertainty should be fully incorporated into statistical inference whenever estimation is sensitive to model choice and that choice is made with reference to the data we consider different philosophies for achieving this goal and suggest strategies for data analysis we illustrate our methods through three examples the first is a poisson regression of bird counts in which a choice is to be made between inclusion of one or both of two covariates the second is a line transect data set for which different models yield substantially different estimates of abundance the third is a simulated example in which truth is known

robust distributed maximum likelihood estimation with dependent quantized data in this paper we consider the distributed maximum likelihood estimation mle with dependent quantized data under the assumption that the structure of the joint probability density function pdf is known but it contains unknown deterministic parameters the parameters may include different vector parameters corresponding to marginal pdfs and parameters that describe the dependence of observations across sensors since mle with a single quantizer is sensitive to the choice of thresholds due to the uncertainty of pdf we concentrate on mle with multiple groups of quantizers which can be determined by the use of prior information or some heuristic approaches to fend off against the risk of a poor outlier quantizer the asymptotic efficiency of the mle scheme with multiple quantizers is proved under some regularity conditions and the asymptotic variance is derived to be the inverse of a weighted linear combination of fisher information matrices based on multiple different quantizers which can be used to show the robustness of our approach as an illustrative example we consider an estimation problem with a bivariate non gaussian pdf that has applications in distributed constant false alarm rate cfar detection systems simulations show the robustness of the proposed mle scheme especially when the number of quantized measurements is small

the sherrington kirkpatrick model a challenge for mathematicians the sherrington kirkpatrick sk model for spin glasses is deceptively simple to state yet its rigorous study represents a considerable challenge we report here some modest progresses obtained through elementary methods even in the supposedly simple high temperature region a number of basic questions remain unsolved

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

quasi projective and quasi liftable characters we study ordinary characters of a finite group g which vanish on the p singular elements for a fixed prime p dividing the order of g such characters are called quasi projective we show that all quasi projective characters of g are characters of projective modules if and only if the ordinary irreducible characters of g can be ordered in such a way that the top square fragment of the decomposition matrix is diagonal finally we prove that the number of indecomposable quasi projective characters of g is finite and characterize them in case of blocks with cyclic defect groups

on posterior distributions for signals in gaussian noise with unknown covariance matrix a bayesian approach to estimate parameters of signals embedded in complex gaussian noise with unknown color is presented the study specifically focuses on a bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems by integrating out uncertainties regarding the noise color an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited several noninformative priors for the covariance matrix such as the reference prior the jeffreys prior and modifications to this are considered some of the priors result in analytical solutions whereas others demand numerical approximations in the linear signal model connections are made between the standard adaptive maximum likelihood aml estimate and a bayesian solution using the jeffreys prior with adjustments to the jeffreys prior correspondence to the regularized solution is also established this in turn enables a formal treatment of the regularization parameter simulations indicate that significant improvements compared to the aml estimator can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior the simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged

target location estimation in sensor networks with quantized data a signal intensity based maximum likelihood ml target location estimator that uses quantized data is proposed for wireless sensor networks wsns the signal intensity received at local sensors is assumed to be inversely proportional to the square of the distance from the target the ml estimator and its corresponding crameacuter rao lower bound crlb are derived simulation results show that this estimator is much more accurate than the heuristic weighted average methods and it can reach the crlb even with a relatively small amount of data in addition the optimal design method for quantization thresholds as well as two heuristic design methods are presented the heuristic design methods which require minimum prior information about the system prove to be very robust under various situations

radiological source detection and localisation using bayesian techniques the problem considered in this paper is detection and estimation of multiple radiation sources using a time series of radiation counts from a collection of sensors a bayesian framework is adopted source detection is approached as a model selection problem in which competing models are compared using partial bayes factors given the number of sources the posterior mean is the minimum mean square error estimator of the source parameters exact calculation of the partial bayes factors and the posterior mean is not possible due to the presence of intractable integrals importance sampling using progressive correction is proposed as a computationally efficient method for approximating these integrals previously proposed algorithms have been restricted to one or two sources a simulation analysis shows that the proposed methods can detect and accurately estimate the parameters of four sources with reasonable computational expense

maximum likelihood localization of a diffusive point source using binary observations in this paper we investigate the problem of localization of a diffusive point source of gas based on binary observations provided by a distributed chemical sensor network we motivate the use of the maximum likelihood ml estimator for this scenario by proving that it is consistent and asymptotically efficient when the density of the sensors becomes infinite we utilize two different estimation approaches ml estimation based on all the observations i e batch processing and approximate ml estimation using only new observations and the previous estimate i e real time processing the performance of these estimators is compared with theoretical bounds and is shown to achieve excellent performance even with a finite number of sensors