a note on bayes factors for log linear contingency table models with vague prior information spiegelhalter and smith 1982 hereafter ssproposed an approximate method for calculating the bayes factor for a log linear model mo for a contingency table against the saturated model m1 with vague prior information we adopt their notation and denote by ss n equation n of ss suppose x1 xk have a multinomial distribution with parameters 014 4k where xi 0 0 x4i 1 we write yt log x1 log xk 01 log 01 log dk and y diag x1 xk then if m1 is the saturated model and mo is the nested log linear model defined by setting the contrasts co1 0 where c is an s x k matrix with rank s and rows summing to zero the approximate bayes factor bo1 for mo against m1 is given by ss 32 this however is indeterminate if any of the cell frequencies in the table is zero this is because of the use by ss of a prior density proportional to h i if however we use instead the standard jeffreys prior density proportional to i1i 1 2 the problem no longer arises then by the arguments of ss and lindley 1964 the resulting bayes factor is still given by ss 32 with xi replaced by xi 2 in the definitions of y and y i 1 k and ss 33 replaced by c 1 2 s2 1 cct i 1 2 if this solution is adopted the prior is proper and so in principle the problem of assigning an arbitrary multiplicative constant for which the ss approach was primarily devised need not arise one could in theory simply apply bayes theorem directly and so obtain the bayes factor exactly however in practice this is difficult to do and i know of no general solution to the problem even for simpler more specific contingency table and related models such as those of independence or equiprobability finding the bayes factor exactly is not too easy see for example crook and good 1982 altham 1971 gunel and dickey 1974 gunel 1982 broniatowski 1981 and references therein the second purpose of this note is to point out that conditionally on mo

estimating the errors on measured entropy and mutual information abstract information entropy and the related quantity mutual information are used extensively as measures of complexity and to identify nonlinearity in dynamical systems expressions for the probability distribution of entropies and mutual informations calculated from finite amounts of data exist in the literature but the expressions have seldom been used in the field of nonlinear dynamics in this paper formulae for estimating the errors on observed information entropies and mutual informations are derived using the standard error analysis familiar to physicists their validity is demonstrated by numerical experiment for illustration the formulae are then used to evaluate the errors on the time lagged mutual information of the logistic map

assessing the order of dependence for partially exchangeable binary data abstract the problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences we obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts these tests are facilitated with a new monte carlo scheme asymptotic tests are also discussed in particular we show that the likelihood ratio tests have an asymptotic chi squared distribution thus generalizing the results of billingsley for the particular case of markov chains we apply these methods to several datasets and perform a simulation to study their properties

tractable inference and observation likelihood evaluation in latent structure influence models latent structure influence models lsims are a particular kind of coupled hidden markov models chmms against chmms lsims overcome the exponential growth of state space parameters by considering the influence model for coupled markov chains nevertheless the exact inference in lsims requires exponential complexity we propose a new recursive formulation to compute marginal forward and backward parameters by mathcal o t nc 2 instead of mathcal o tn text 2 c for c channels of n states apiece observing t data points this formulation is derived systematically and carefully to increase the inference accuracy furthermore a solution is presented for the evaluation problem of lsims based on the proposed marginal forward parameter this solution is essential in statistical multi channel time series classification the results show that the proposed algorithm is generally more accurate and reliable than other existing algorithms novelties in deriving the marginal backward parameter plays an important role in this superiority the hellinger distance is computed between the proposed and exact forward and one slice parameters for various simulation scenarios distances are small enough indicating that the proposed inference algorithm is sufficiently close to exact inference for various channels hidden state numbers and other parameters statistical multi channel time series classification is also considered for both proposed and exact algorithms classification results are almost similar indicating that the proposed approximate inference is proper and acceptable in the classification task finally the ieeg dataset s parameter learning indicates that the proposed inference algorithm leads to a higher log likelihood than the existing algorithms

decomposition of conditional probability for high order symbolic markov chains the main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet we elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high order markov chains we represent the conditional probability function as the sum of multilinear memory function monomials of different orders from zero up to the chain order this allows us to introduce a family of markov chain models and to construct artificial sequences via a method of successive iterations taking into account at each step increasingly high correlations among random elements at weak correlations the memory functions are uniquely expressed in terms of the high order symbolic correlation functions the proposed method fills the gap between two approaches namely the likelihood estimation and the additive markov chains the obtained results may have applications for sequential approximation of artificial neural network training

the tsallis entropy of natural information abstract estimating the information contained in natural data such as electroencephalography data is unusually difficult because the relationship between the physical data and the information that it encodes is unknown this unknown relationship is often called the encoding problem the present work provides a solution to this problem by deriving a method to estimate the tsallis entropy in natural data the method is based on two findings the first finding is that the physical instantiation of any information event that is the physical occurrence of a symbol of information must begin and end at a discontinuity or critical point maximum minimum or saddle point in the data the second finding is that in certain data types such as the encephalogram eeg the variance within of an eeg waveform event is directly proportional to its probability of occurrence these two outcomes yield two results the first is the easy binning of data into separate information events the second is the ability to estimate probabilities in two ways frequency counting and computing the variance within of an eeg waveform these results are used to derive a linear estimator of the tsallis entropy functional allowing it to be estimated without deducing the encoding this method for estimating the tsallis entropy is first used to estimate the information in simple signals the amount of information estimated is highly accurate the method is then applied to two problems in electroencephalography the first is distinguishing normal aging from very early alzheimer s disease mild cognitive impairment and the second is medication monitoring of alzheimer s disease treatment the former is done with an accuracy of 92 and the latter with an accuracy of 91 this detection accuracy is the highest published accuracy in the literature which suggests that this method for tsallis entropy estimation is both accurate and useful

estimating functions of probability distributions from a finite set of samples this paper addresses the problem of estimating a function of a probability distribution from a finite set of samples of that distribution a bayesian analysis of this problem is presented the optimal properties of the bayes estimators are discussed and as an example of the formalism closed form expressions for the bayes estimators for the moments of the shannon entropy function are derived then numerical results are presented that compare the bayes estimator to the frequency counts estimator for the shannon entropy we also present the closed form estimators all derived elsewhere for the mutual information mathrm ensuremath chi 2 covariance and some other statistics c 1995 the american physical society

exact significance test for markov order abstract we describe an exact significance test of the null hypothesis that a markov chain is n th order the procedure utilizes surrogate data to yield an exact test statistic distribution valid for any sample size surrogate data are generated using a novel algorithm that guarantees per shot a uniform sampling from the set of sequences that exactly match the n th order properties of the observed data using the test the markov order of tel aviv rainfall data is examined

tsallis conditional mutual information in investigating long range correlation in symbol sequences abstract the presence of long range correlation lrc as opposed to markov chain of a finite order is of primary interest in the study of symbol sequences such as dna among others methods using information theory have been developed for markov chain order estimation in this work we consider the tsallis entropy and define the tsallis conditional mutual information tcmi for markov chain order estimation which is more suitable to identify large orders suggesting effectively lrc the tcmi of order m for a tsallis parameter q is computed for increasing m and a significance test is performed for each m until tcmi is found non significant randomization and parametric significance tests for tcmi are developed for the latter the null distribution of tcmi is approximated with a gamma distribution deriving analytic expressions for its parameters we assess the accuracy of order estimation with the two tests for tcmi and compare them to the respective tests using the shannon entropy extended simulations on markov chains of different orders and structures of the transition probability matrix show that shannon and tsallis tests with parameter q 2 have similar performance for small orders when the problem becomes more demanding for higher markov chain orders and lrcs tsallis tests for q 2 have better approximation to the correct order with the sequence length n finally the tsallis tests are favorably compared to shannon tests to real dna sequences

context tree based image contour coding using a geometric prior efficient encoding of object contours in images can facilitate advanced image video compression techniques such as shape adaptive transform coding or motion prediction of arbitrarily shaped pixel blocks we study the problem of lossless and lossy compression of detected contours in images specifically we first convert a detected object contour into a sequence of directional symbols drawn from a small alphabet to encode the symbol sequence using arithmetic coding we compute an optimal variable length context tree vct mathcal t via a maximum a posterior map formulation to estimate symbols conditional probabilities map can avoid overfitting given a small training set mathcal x of past symbol sequences by identifying a vct mathcal t with high likelihood p mathcal x mathcal t of observing mathcal x given mathcal t using a geometric prior p mathcal t stating that image contours are more often straight than curvy for the lossy case we design fast dynamic programming dp algorithms that optimally trade off coding rate of an approximate contour hat text x given a vct mathcal t with two notions of distortion of hat text x with respect to the original contour x to reduce the size of the dp tables a total suffix tree is derived from a given vct mathcal t for compact table entry indexing reducing complexity experimental results show that for lossless contour coding our proposed algorithm outperforms state of the art context based schemes consistently for both small and large training datasets for lossy contour coding our algorithms outperform comparable schemes in the literature in rate distortion performance

a mixture of transition models for heterogeneous longitudinal ordinal data with applications to longitudinal bacterial vaginosis data markov models used to analyze transition patterns in discrete longitudinal data are based on the limiting assumption that individuals follow the common underlying transition process however when one is interested in diseases with different disease or severity subtypes explicitly modeling subpopulation specific transition patterns may be appropriate we propose a model which captures heterogeneity in the transition process through a finite mixture model formulation and provides a framework for identifying subpopulations at different risks we apply the procedure to longitudinal bacterial vaginosis bv study data and demonstrate that the model fits the data well further we show that under the mixture model formulation we can make the important distinction between how covariates affect transition patterns unique to each of the subpopulations and how they affect which subgroup a participant will belong to practically covariate effects on subpopulation specific transition behavior and those on subpopulation membership can be interpreted as effects on short term and long term transition behavior we further investigate models with higher order subpopulation specific transition dependence

nash model relation to horton order ratios the nash model of the instantaneous unit hydrograph iuh is parameterized in terms of horton order ratios of a catchment on the basis of a geomorphologic model of catchment response the shape parameter of the nash model is found to depend on horton s numbers ra rb and rl of a catchment thus catchment geomorphology can provide a synthesis of the shape of the hydrologic response the scale parameter of the nash model results to be a time varying character depending on both geomorphology and average streamflow velocity along the stream network thus the time scale of the iuh could account for the variability of the hydrologic response for different storms and throughout a storm

higher order multivariate markov chains and their applications abstract markov chains are commonly used in modeling many practical systems such as queuing systems manufacturing systems and inventory systems they are also effective in modeling categorical data sequences in a conventional n th order multivariate markov chain model of s chains and each chain has the same set of m states the total number of parameters required to set up the model is o m ns such huge number of states discourages researchers or practitioners from using them directly in this paper we propose an n th order multivariate markov chain model for modeling multiple categorical data sequences such that the total number of parameters are of o ns 2 m 2 the proposed model requires significantly less parameters than the conventional one we develop efficient estimation methods for the model parameters an application to demand predictions in inventory control is also discussed

relative entropy and identification of gibbs measures in dynamical systems in this work we explore the idea of using the relative entropy of ergodic measures for the identification of gibbs measures in dynamical systems the question we face is how to estimate the thermodynamic potential together with a grammar from a sample produced by the corresponding gibbs state

entropy and long range memory in random symbolic additive markov chains the goal of this paper is to develop an estimate for the entropy of random symbolic sequences with elements belonging to a finite alphabet as a plausible model we use the high order additive stationary ergodic markov chain with long range memory supposing that the correlations between random elements of the chain are weak we express the conditional entropy of the sequence by means of the symbolic pair correlation function we also examine an algorithm for estimating the conditional entropy of finite symbolic sequences we show that the entropy contains two contributions i e the correlation and the fluctuation the obtained analytical results are used for numerical evaluation of the entropy of written english texts and dna nucleotide sequences the developed theory opens the way for constructing a more consistent and sophisticated approach to describe the systems with strong short range and weak long range memory

on some criteria for estimating the order of a markov chain tong 1975 has proposed a procedure for estimating the order of a markov chain based on akaike s information criterion aic in this paper the asymptotic distribution of the aic estimator is derived and it is shown that the estimator is inconsistent as an alternative to the aic procedure the bayesian information criterion bic proposed by schwarz 1978 is shown to be consistent these two procedures yield different estimated orders when applied to specific samples of meteorological observations for parameters based on these meteorological examples the aic and bic procedures are compared by means of simulation for finite samples the results obtained have practical implications concerning whether in the routine fitting of precipitation data it is necessary to consider higher than first order markov chains

markov chain order estimation with conditional mutual information abstract we introduce the conditional mutual information cmi for the estimation of the markov chain order for a markov chain of k symbols we define cmi of order m i c m as the mutual information of two variables in the chain being m time steps apart conditioning on the intermediate variables of the chain we find approximate analytic significance limits based on the estimation bias of cmi and develop a randomization significance test of i c m where the randomized symbol sequences are formed by random permutation of the components of the original symbol sequence the significance test is applied for increasing m and the markov chain order is estimated by the last order for which the null hypothesis is rejected we present the appropriateness of cmi testing on monte carlo simulations and compare it to the akaike and bayesian information criteria the maximal fluctuation method peres shields estimator and a likelihood ratio test for increasing orders using divergence the order criterion of cmi testing turns out to be superior for orders larger than one but its effectiveness for large orders depends on data availability in view of the results from the simulations we interpret the estimated orders by the cmi testing and the other criteria on genes and intergenic regions of dna chains

a stochastic model of dimensionless thunderstorm rainfall a concise stochastic model for the nondimensional thunderstorm rainfall process at a point is proposed the accumulated precipitation process for individual thunderstorms is nondimensionalized by dividing the precipitation at any time by the total precipitation and the elapsed time by the total duration the dimensionless process is divided into 100 equal time increments and the depth increments are rescaled to range between 0 and 1 the sequence of rescaled increments z1 z2 z9 are assumed to represent a nonhomogeneous markov process in discrete time with continuous state space the expected value of the kth rescaled increment given the k 1st increment is assumed to be a linear function of that increment and the marginal distribution of the first increment and the conditional distributions are assumed to be described by the beta distribution an analyses of data for 275 thunderstorms observed at the walnut gulch experimental watershed in southeastern arizona showed that the proposed model structure is a good approximation for this region the number of model parameters can be reduced from 26 to a minimum of 10 by approximating the 2 parameters in the conditional expectation function and the conditional beta parameter as polynomial functions of the dimensionless time likelihood ratio tests and the akaike information criterion suggest that the dependence parameters are independent of storm amount and duration but the conditional beta parameter k is larger for short duration storms than for long duration storms a 13 parameter model is recommended for disaggregating thunderstorm rainfall in southeastern arizona

testing the order of discrete markov chains using surrogate data tests of the null hypothesis that a symbolic sequence is of nth markov order are described these tests are based on resampling methods similar to the method of surrogate data used to test continuous time series for nonlinear structure the size and power of these symbolic surrogate tests are estimated using binary and heptary test sequences of known order conditioning on a sufficient statistic under the null hypothesis yields an estimated true size which closely approximates the nominal size and increases the power of the test with respect to the unconditional test we apply one method to a symbolic sequence derived from the rossler system and to a binary and heptary representation of an interspike interval sequence of an electroreceptor of the weakly electric eel apteronotus leptorhynchus

on the relation between various entropy concepts and the valoric interpretation abstract the valoric interpretation developed already by clausius helmholtz and ostwald is taken as the basis for a reinterpretation of the various entropy concepts developed by clausius boltzmann gibbs shannon and kolmogorov as the key points we consider the value of energy with respect to work and the value of entropy with respect to informmation processing

human brain dynamics the analysis of eeg signals with tsallis information measure we undertake the study of human eeg signals by recourse to a wavelet based multiresolution analysis as adapted to an information measure scenario dierent information measures are employed it is shown that non extensive ones seem to be of particular usefulness their use opens up perspectives of building up automatic detection devices conjectures concerning general characteristics of focal epilepsy are formulated on the basis of a tsallis type of analysis c 1999 elsevier science b v all rights reserved

method for generating long range correlations for large systems we propose a new method to generate a sequence of random numbers with long range power law correlations that overcomes known difficulties associated with large systems the new method presents an improvement on the commonly used methods we apply the algorithm to generate enhanced diffusion isotropic and anisotropic self affine surfaces and isotropic and anisotropic correlated percolation

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

best linear unbiased design hyetograph under the conditions of system linearity and stationarity of the precipitation process we derive the hyetograph associated with any given flood discharge q using best linear unbiased estimation blue theory the blue hyetograph depends explicitly on the correlation characteristics of the rainfall process and the instantaneous unit hydrograph iuh of the basin when the correlation time of the rainfall process is short relative to the dispersion of the iuh the shape of the blue hyetograph is the mirror image of the iuh itself in the opposite case the design hyetograph is the mirror image of the rainfall correlation function the procedure is extended from lumped to semidistributed and distributed basins in the latter case we obtain simultaneous design hyetographs for each subbasin or each site in the basin the analytical findings and the possibility of regionalization are verified using synthetic and recorded rainfall time series with excellent agreement in both cases because of its simplicity robustness and theoretical basis the proposed procedure should be appealing for practical use particularly when not only the peak but the entire flood hydrograph is required

newton noda iteration for finding the perron pair of a weakly irreducible nonnegative tensor we present a newton noda iteration nni for computing the perron pair of a weakly irreducible nonnegative mth order tensor mathscr a a by combining the idea of newton s method with the idea of the noda iteration the method requires the selection of a positive parameter theta k k in the kth iteration and produces a scalar sequence approximating the spectral radius of mathscr a a and a positive vector sequence approximating the perron vector we propose a halving procedure to determine the parameters theta k k starting with theta k 1 k 1 for each k such that the scalar sequence is monotonically decreasing convergence of this sequence to the spectral radius of mathscr a a and convergence of the vector sequence to the perron vector is guaranteed for any initial positive unit vector as long as the sequence theta k k so chosen is bounded below by a positive constant in this case we always have theta k 1 k 1 near convergence and the convergence is quadratic very often the halving procedure will return theta k 1 k 1 i e no halving is actually used for each k if the tensor is semisymmetric m ge 4 m 4 and theta k 1 k 1 then the computational work in the kth iteration of nni is roughly the same as that for one iteration of the ng qi zhou algorithm which is linearly convergent for the smaller class of weakly primitive tensors

guessing probability distributions from small samples we propose a new method for the calculation of the statistical properties e g the entropy of unknown generators of symbolic sequences the probability distributionp k of the elementsk of a population can be approximated by the frequenciesf k of a sample provided the sample is long enough so that each elementk occurs many times our method yields an approximation if this precondition does not hold for a givenf k we recalculate the zipf ordered probability distribution by optimization of the parameters of a guessed distribution we demonstrate that our method yields reliable results

two general models that generate long range correlation abstract in this paper we study two models that generate sequences with lrc long range correlation for the ift inverse fourier transform model our conclusion is the low frequency part leads to lrc while the high frequency part tends to eliminate it therefore a typical method to generate a sequence with lrc is multiplying the spectrum of a white noise sequence by a decaying function a special case is analyzed the linear combination of a smooth curve and a white noise sequence in which the dfa plot consists of two line segments for the patch model our conclusion is long subsequences leads to lrc while short subsequences tend to eliminate it therefore we can generate a sequence with lrc by using a fat tailed pdf probability distribution function of the length of the subsequences a special case is also analyzed if a patch model with long subsequences is mixed with a white noise sequence the dfa plot will consist of two line segments we have checked known models and actual data and found they are all consistent with this study

some applications of the useful mutual information abstract the useful mutual information statistic is considered and its asymptotic properties are investigated either considering random sampling or stratified random sampling under different assumptions it is shown that the asymptotic distribution of this statistic is either normal or a linear form in gc 2 variables finally its application to testing hypotheses of independence in multinomial populations is given

determining and interpreting the order of a two state markov chain application to models of daily precipitation we illustrate the result that lumping together some of the states of a many state first order markov chain does not in general give a first order markov chain with a smaller number of states if a series generated in this way is nevertheless assumed to have been produced by a two state markov chain standard statistical procedures using the akaike and bayesian information criteria may indicate that it should be fitted by a higher order than first stochastic models based on a markov chain are often used to model precipitation series it is normal to classify days as dry and wet and fit a two state process in some cases second or higher order chains are preferred by reference to information criteria in the light of the foregoing we suggest that this might be because a many state process possibly of only first order would actually be a better choice than a two state process

statistical analysis of gene and intergenic dna sequences abstract much of the on going statistical analysis of dna sequences is focused on the estimation of characteristics of coding and non coding regions that would possibly allow discrimination of these regions in the current approach we concentrate specifically on genes and intergenic regions to estimate the level and type of correlation in these regions we apply various statistical methods inspired from nonlinear time series analysis namely the probability distribution of tuplets the mutual information and the identical neighbour fit the methods are suitably modified to work on symbolic sequences and they are first tested for validity on sequences obtained from well known simple deterministic and stochastic models then they are applied to the dna sequence of chromosome 1 of arabidopsis thaliana the results suggest that correlations do exist in the dna sequence but they are weak and that intergenic sequences tend to be more correlated than gene sequences the use of statistical tests with surrogate data establish these findings in a rigorous statistical manner

a model for high order markov chains on introduit un modele pour des chaines de markov du leme ordre qui comporte seulement un parametre additionnel pour chaque retard

dynamical complexity detection in pre seismic emissions using nonadditive tsallis entropy abstract we investigate within the framework of nonextensive tsallis entropy particular aspects of the relation between signal analysis and signals originating in a very special nonlinear system the focal area of an impending earthquake the tsallis like time dependent entropy is shown to be a rather powerful tool for providing a novel quantitative strategy for monitoring the focal area states just before the earthquake occurrence

global entropy solutions to weakly nonlinear gas dynamics abstract entropy weak solutions with bounded periodic initial data are considered for the system of weakly nonlinear gas dynamics through a modified glimm scheme an approximate solution sequence is constructed and then a priori estimates are provided with the methods of approximate characteristics and approximate conservation laws which gives not only the existence and uniqueness but also the uniform total variation bounds for the entropy solutions

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

unit hydrograph approximations assuming linear flow through topologically random channel networks the instantaneous unit hydrograph iuh of a drainage basin is derived in terms of fundamental basin characteristics z where parameterizes the link channel segment length distribution and is a vector of hydraulic parameters z is one of three basin topological properties n n d or n m where n is magnitude number of first order streams d is diameter mainstream length and m is order the iuh is derived based on assumptions that the links are independent and identically distributed random variables and that the network is a member of a topologically random population linear routing schemes including translation diffusion and general linear routing are used and constant drainage density is assumed by using n as the fundamental basin characteristics asymptotic for large n considerations lead to a weibull probability density function for the iuh with time to peak given by tp 2n where is mean link length and is a scalar hydraulic parameter usually average celerity this asymptotic iuh is identical for all linear routing schemes

correlation function inadequacy in random sequence entropy measures considering symbolic and numerical random sequences in the framework of the additive markov chain approach we establish a relation between their correlation functions and conditional entropies we express the entropy by means of the two point probability distribution functions and then evaluate the entropy for the numerical random chain in terms of the correlation function we show that such approximation gives a satisfactory result only for special types of random sequences in general case the conditional entropy of numerical sequences obtained in the two point distribution function approach is lower we derive the conditional entropy of the additive markov chain as a sum of the kullback leibler mutual information and give an example of random sequence with the exactly zero correlation function and the nonzero correlations

asymptotics of the partition function of a general markov random field on an infinite rectangular lattice abstract we investigate theoretically and numerically the asymptotics of the partition function of a general markov random field mrf on an infinite rectangular lattice we first propose the general local energy function lef parameterized mrf then we prove that the thermodynamic limit of the free energy of the mrf can be exactly characterized by the perron root of the fundamental transfer matrix of a particular markov additive process map this matrix possesses a special structure and many interesting properties that enable parallel computation of the perron root and may be beneficial for deriving an analytical form of the free energy we also develop another transfer matrix for numerical computation of the desired perron root specifically the former is a site to site transfer matrix on a twisted cylindrical lattice while the latter is the one associated with a row to row transition on a vertical strip numerical results show that our methods exhibit consistent finite size scaling behavior even for small values of the lattice width this study reveals that the fundamental transfer matrix is an alternative direction of research on the analysis of the partition function of general mrfs within the scope of matrix algebra

modeling flat stretches bursts and outliers in time series using mixture transition distribution models abstract the class of mixture transition distribution mtd time series models is extended to general non gaussian time series in these models the conditional distribution of the current observation given the past is a mixture of conditional distributions given each one of the last p observations they can capture non gaussian and nonlinear features such as flat stretches bursts of activity outliers changepoints in a single unified model class they can also represent time series defined on arbitrary state spaces univariate or multivariate continuous discrete or mixed which need not even be euclidean they perform well in the usual case of gaussian time series without obvious nonstandard behaviors the models are simple analytically tractable easy to simulate readily estimated the stationarity and autocorrelation properties of the models are derived a simple em algorithm is given and shown to work well for estimation the models are applied to several real and simulated datasets with satisfacto

decay of almost periodic solutions of conservation laws we consider the asymptotic behavior of solutions of systems of inviscid or viscous conservation laws in one or several space variables which are almost periodic in the space variables in a generalized sense introduced by stepanoff and wiener which extends the original one of h bohr we prove that if u x t is such a solution whose inclusion intervals at time t with respect to 0 satisfy l epsiv t t 0 as t and such that the scaling sequence u t x t u t x t t is pre compact as t in l loc 1 d 1 then u x t decays to its mean value which is independent of t as t the decay considered here is in l 1 loc of the variable x t which implies as we show that as t where m x denotes taking the mean value with respect to x in many cases we show that if the initial data are almost periodic in the generalized sense then so also are the solutions we also show in these cases how to reduce the condition on the growth of the inclusion intervals l t with t as t for fixed 0 to a condition on the growth of l 0 with as 0 which amounts to imposing restrictions only on the initial data we show with a simple example the existence of almost periodic non periodic functions whose inclusion intervals satisfy any prescribed growth condition as 0 the applications given here include inviscid and viscous scalar conservation laws in several space variables some inviscid systems in chromatography and isentropic gas dynamics as well as many viscous 2 2 systems such as those of nonlinear elasticity and eulerian isentropic gas dynamics with artificial viscosity among others in the case of the inviscid scalar equations and chromatography systems the class of initial data for which decay results are proved includes in particular the l generalized limit periodic functions our procedures can be easily adapted to provide similar results for semilinear and kinetic relaxations of systems of conservation laws

approximate confidence intervals for the parameters of a stationary binary markov chain the power divergence family of test statistics introduced by cressie and read 1984 is used to obtain approximate confidence intervals for the parameters of a stationary first order binary markov chain intervals based on inverting the likelihood ratio pearson and freeman tukey statistics are included in this family small sample comparisons are used to select the best intervals for the different parameters the results show that the best power divergence intervals for the probability of success and in particular the likelihood ratio interval have error rates closer to nominal levels than the sample proportion based intervals suggested by crow 1979 the properties of power divergence joint confidence regions for the transition probabilities are also explored

spectral analysis for categorical time series scaling and the spectral envelope summary many studies produce categorical time series in which harmonic analysis is of interest although there exist time domain approaches for the analysis of categorical time series such as markov chains or link function based regression models there is apparently little statistical theory or methodology for analyzing qualitative valued time series in the frequency domain the purpose of this paper is to initiate the development of a general framework for the frequency domain analysis of categorical time series in doing so we discuss the scaling of categorical time series and introduce a new concept that we call the spectral envelope of a categorical time series we demonstrate our methodology on a data set from a problem in molecular biology

application of statistical information criteria for optimal fuzzy model construction theoretical studies have shown that fuzzy models are capable of approximating any continuous function on a compact domain to any degree of accuracy however constructing a good fuzzy model requires finding a good tradeoff between fitting the training data and keeping the model simple a simpler model is not only easily understood but also less likely to overfit the training data even though heuristic approaches to explore such a tradeoff for fuzzy modeling have been developed few principled approaches exist in the literature due to the lack of a well defined optimality criterion in this paper we propose several information theoretic optimality criteria for fuzzy models construction by extending three statistical information criteria 1 the akaike information criterion aic 1974 2 the bhansali downham information criterion bdic 1977 and 3 the information criterion of schwarz 1978 and rissanen 1978 sric we then describe a principled approach to explore the fitness complexity tradeoff using these optimality criteria together with a fuzzy model reduction technique based on the singular value decomposition svd the role of these optimality criteria in fuzzy modeling is discussed and their practical applicability is illustrated using a nonlinear system modeling example

long range memory elementary 1d cellular automata dynamics and nonextensivity abstract we numerically study the dynamics of elementary 1d cellular automata ca where the binary state i t 0 1 of a cell i does not only depend on the states in its local neighborhood at time t 1 but also on the memory of its own past states i t 2 i t 3 i t we assume that the weight of this memory decays proportionally to with 0 the limit corresponds to the usual ca since the memory function is summable for 1 and nonsummable for 0 1 we expect pronounced changes of the dynamical behavior near 1 this is precisely what our simulations exhibit particularly for the time evolution of the hamming distance h of initially close trajectories we typically expect the asymptotic behavior h t t 1 1 q where q is the entropic index associated with nonextensive statistical mechanics in all cases the function q exhibits a sensible change at 1 we focus on the class ii rules 61 99 and 111 for rule 61 q 0 for 0 c 1 3 and q 0 for c whereas the opposite behavior is found for rule 111 for rule 99 the effect of the long range memory on the spread of damage is quite dramatic these facts point at a rich dynamics intimately linked to the interplay of local lookup rules and the range of the memory finite size scaling studies varying system size n indicate that the range of the power law regime for h t typically diverges n z with 0 z 1

tsallis like information measures and the analysis of complex signals abstract a tsallis like information measure that elaborates upon those of the tsallis type is shown to be a rather powerful tool for the analysis of complex non stationary signals as exemplified by the henon map and eegs the ensuing results could be of importance concerning the automatic detection of epileptic spikes

long time existence of entropy solutions to the one dimensional non isentropic euler equations with periodic initial data the non isentropic euler system with periodic initial data in mathbb r 1 is studied by analyzing wave interactions in a framework of specially chosen riemann invariants generalizing glimm s functionals and applying the method of approximate conservation laws and approximate characteristics an mathcal o varepsilon 2 lower bound is established for the life span of the entropy solutions with initial data that possess varepsilon variation in each period

some models for the analysis of association in multiway cross classifications having ordered categories abstract goodman recently presented a class of models for the analysis of association between two discrete ordinal variables the association was measured in terms of the odds ratios in 2 2 subtables formed from adjacent rows and adjacent columns of the cross classification and models were devised that allowed the odds ratios to depend on an overall effect on row effects on column effects and on other effects this article presents some generalizations of this approach appropriate for multiway cross classifications including a models for the analysis of conditional association b models for the analysis of partial association and c models for the analysis of symmetric association three cross classifications are analyzed with these models and methods and rather simple interpretations of the association in each are provided

symbolic stochastic dynamical systems viewed as binary n step markov chains a theory of systems with long range correlations based on the consideration of binary n step markov chains is developed in the model the conditional probability that the ith symbol in the chain equals zero or unity is a linear function of the number of unities among the preceding n symbols the correlation and distribution functions as well as the variance of the number of symbols in the words of arbitrary length l are obtained analytically and numerically a self similarity of the studied stochastic process is revealed and the similarity group transformation of the chain parameters is presented the diffusion fokker planck equation governing the distribution function of the l words is explored if the persistent correlations are not extremely strong the distribution function is shown to be the gaussian with the variance being nonlinearly dependent on l the applicability of the developed theory to the coarse grained written and dna texts is discussed

decay of entropy solutions of nonlinear conservation laws we are concerned with the asymptotic behavior of entropy solutions of nonlinear conservation laws the main objective of this paper is to present an analytical approach and to explore its applications to studying the large time behavior of periodic entropy solutions of hyperbolic conservation laws the asymptotic decay of periodic solutions of nonlinear hyperbolic conservation laws is an important nonlinear phenomenon it is observed that the genuine nonlinearity of equations forces the waves of each characteristic family to interact vigorously and to cancel each other the insightful analysis of glimm lax gl for scalar equations and 2 2 systems has indicated that the resultant mutual cancellation of interacting shock and rarefaction waves of the same family induces the decay of periodic solutions such a result was first shown by lax l1 in 1957 for one dimensional convex scalar conservation laws dafermos d1 applying his uniform processes proved the decay result for the case that the set of inflection points of the flux does not have an accumulation point the glimm lax theory gl indicates that for 2 2 strictly hyperbolic and genuinely nonlinear systems any periodic glimm solution decays like o 1 t this result was proved by using the approximate characteristic method in the glimm difference solutions provided that the oscillation of the corresponding initial data is small recently using the method of generalized characteristics dafermos d3 showed that any periodic solution with local bounded variation and small oscillation for 2 2 systems decays asymptotically with the same detailed structure pas found by lax l1 for the

wavelet analysis and nonlinear dynamics in a nonextensive setting abstract we undertake the study of signals originated in time dependent nonlinear systems by recourse to a wavelet based multiresolution analysis as adapted to a nonextensive tsallis scenario diverse applications are discussed it is shown that the tsallis environment provides one with more detailed information than the conventional shannon one

methods and criteria for model selection model selection is an important part of any statistical analysis and indeed is central to the pursuit of science in general many authors have examined the question of model selection from both frequentist and bayesian perspectives and many tools for selecting the best model have been suggested in the literature this paper considers the various proposals from a bayesian decision theoretic perspective

a stochastic model of dimensionless hyetograph a very simple statistical model is proposed to describe the time distribution of rainfall within a rainy event the modeled process is the dimensionless hyetograph h tj that represents the fraction of rainfall accumulated over the time interval 0 tj where tj is a fraction of the total duration in any rainy episode lasting n 1 units of time the sequence h t1 h tn is described as an ordered sample from the beta distribution dimensionless rainfall from hourly data at three stations in southern spain show little dependence on rainfall duration amount of precipitation or period of the year these results though not essential to the model structure simplify its formulation reducing the number of parameters other features of the historical records such as correlations maximum dimensionless hourly precipitation or frequency curves are reasonably well reproduced by the model