semiclassical solutions for choquard equations with berestycki lions type conditions abstract this paper is concerned with existence of multiple semiclassical states for a class of choquard equation under the classic berestycki lions type assumptions assumed on the nonlinearity we obtain multiplicity of semiclassical solutions for the equation by using a method of penalization argument we study further the concentration phenomena of such solutions and show that they converge to the least energy solutions of the associated limit problem as the parameter e goes to 0

on parametric density estimation summary the paper makes a critical assessment of aitchison s criterion of density estimation it seems not to satisfy certain intuitive requirements a new criterion based on decisions theoretic considerations is introduced it is shown through examples that the judgement about the choice of density estimates is seriously dependent on the criterion chosen some other density estimates are introduced which look similar to bayesian predictive density estimates without using a prior distribution

invariant subset and set stability of boolean networks under arbitrary switching signals this study investigates the set stability of switched boolean networks bns with arbitrary switching signals based on invariant subsets set stability determines whether a bn converges to a given subset while arbitrary switching signals can be used to characterize uncertainties and disturbances an algorithm is proposed to calculate the largest invariant subset contained in any given set as this is the key step in establishing the set stability criterion based on this algorithm a necessary and sufficient condition for set stability is obtained the result is then used to solve the robust output synchronization problem and the robust node synchronization problem for bns in the presence of uncertainties and disturbances examples are presented to demonstrate the use of the proposed approach

on the sensitivity to noise of a boolean function in this paper we generate upper and lower bounds for the sensitivity to noise of a boolean function using relaxed assumptions on input choices and noise the robustness of a boolean network to noisy inputs is related to the average sensitivity of that function the average sensitivity measures how sensitive to changes in the inputs the output of the function is the average sensitivity of boolean functions can indicate whether a specific random boolean network constructed from those functions is ordered chaotic or in critical phase we give an exact formula relating the sensitivity to noise and the average sensitivity of a boolean function the analytic approach is supplemented by numerical results that illustrate the overall behavior of the sensitivities as various boolean functions are considered it is observed that for certain parameter combinations the upper estimates in this paper are sharper than other estimates in the literature and that the lower estimates are very close to the actual values of the sensitivity to noise of the selected boolean functions

on coherence in parametric density estimation summary in parametric density estimation the existence of a prior distribution on the parameter dictates the use of the corresponding predictive density function as estimate this paper argues that in a decision theory approach to parameter density estimation any loss function introduced should lead to this predictive result for situations where prior information is available the kullbackleibler directed divergence has this coherence property whereas the corresponding symmetric divergence does not the role of a recently suggested sequential improvement criterion in density estimation is also discussed

singularly perturbed critical choquard equations abstract in this paper we study the semiclassical limit for the singularly perturbed choquard equation e 2 u v x u e 3 r 3 q y g u y x y d y q x g u in r 3 where 0 3 e is a positive parameter v q are two continuous real function on r 3 and g is the primitive of g which is of critical growth due to the hardy littlewood sobolev inequality under suitable assumptions on g we first establish the existence of ground states for the critical choquard equation with constant coefficients next we establish existence and multiplicity of semi classical solutions and characterize the concentration behavior by variational methods

modeling intrinsic noise in random boolean networks abstract noise has crucial effects on biological processes chemical reactions and various chaotic systems this study explores the dynamical properties of noise in random boolean networks in which the stochasticity may cause significant deviations from deterministic descriptions such noise is intrinsic and results from the discrete dynamics of finite populations by using methods from statistical physics and nonlinear dynamics this study illustrates the dynamical characteristics of the inherent noise furthermore a modified mean field model is formulated to mimic the stochastic dynamics revealed by the discrete systems the proposed idea of modeling intrinsic noise can be potentially applied to other discrete systems belonging to the category of random boolean networks

multiplicity and concentration results for fractional choquard equations doubly critical case abstract in this paper we consider the following fractional choquard equation e 2 s s u v x u e i f u f u x r n where n 3 s 0 1 and 0 n e 0 is a parameter i is the riesz potential and f u 1 2 u 2 1 2 u 2 where 2 n n and 2 n n 2 s are lower and upper critical exponents in the sense of the hardy littlewood sobolev inequality firstly by the refined sobolev inequality with morrey norm we show a generalization of lions type theorem secondly combining this theorem with variational methods we show the multiplicity and concentration of positive solutions for above equation moreover the multiplicity and concentration results are obtained in the case where f u has the lower critical exponent 2 which remains unsolved in the existing literature

goodness of prediction fit for multivariate linear models abstract using both frequentist and bayesian techniques predicting densities are derived for future observations from a multivariate linear model with matrix normal error terms all the candidates belong to a general location scale family of predicting densities an analytic comparison is undertaken using a kullback leibler loss by citing an optimal member of a subclass including most of these predicting densities as members the subclass is based on an invariant student t random matrix and the optimal member is the bayesian predictive density corresponding to a jeffreys noninformative prior information based numerical comparisons illustrate the nature of the dominance

on the generalization of the likelihood function and the likelihood principle abstract the parametric likelihood and likelihood principle lp play a central role in parametric methodology and in the foundations of statistics the main purpose of this article is to extend the concepts of likelihood and lp to general inferential aims and models covering for example prediction and empirical bayes models the likelihood function is the joint distribution of the data and the unobserved variables of inferential interest considered as a function of the parameters and these inferential variables lp is based on this likelihood and the principles of sufficiency sp and conditionality cp are modified such that the equivalence sp and cp lp is valid generalizing birnbaum s theorem

strongly interacting bumps for the schrodinger newton equations we study concentrated bound states of the schrodinger newton equations h2 e x u 0 0 x r3 u 12 2 0 x r3 x 0 u x 0 as x moroz et al an analytical approach to the schrodinger newton equations nonlinearity 12 201 1999 proved the existence and uniqueness of ground states of u 0 0 x r3 u 12 2 0 x r3 x 0 u x 0 as x we first prove that the linearized operator around the unique ground state radial solution 0 u0 with 0 r ae r r 1 o 1 as r x u0 r b r 1 o 1 as r x for some a b 0 has a kernel whose dimension is exactly 3 corresponding to the translational modes using this result we further show that if for some positive integer k the points pi r3 i 1 2 k with pi pj for i j are all local minimum or local maximum or nondegenerate critical points of e p then for h small enough there exist solutions of the schrodinger newton equations with k bumps which concentrate at pi we also prove that given a local maximum point p0 of e p the

an optimal prediction function for the normal linear model abstract a prediction density function g for the normal linear model is derived this function is shown to dominate three well known prediction densities by first constructing a specified class of densities that includes these three and then proving that g is the optimal member of this class in the sense of minimizing a criterion based on the kullback leibler divergence g coincides with a bayesian prediction density assuming diffuse prior

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

a simple predictive density function abstract an easily computable predictive density is considered although involving a plain maximum likelihood technique it coincides with the posterior predictive density with a noninformative prior for standard situations achievements are comparable with classical inference

geometry of exponential family with competing risks and censored data abstract employing the differential geometrical methods in statistics suggested by amari 1985 and amari et al 1987 considering the exponential family with censored data and competing risks as a manifold of a statistical model the geometry of the manifold is investigated based on two information sources as an application of the geometry the asymptotic expansions of the bootstrap prediction bayesian prediction and their risk evaluations are investigated the results show that these expansions are related to the coefficients of connections and metric tensors and the predictive density function is the estimative density function in the asymptotic sense finally taking rayleigh distribution and prostatic cancer data as examples some computation and simulation results are presented to illustrate our main results

existence and concentration of ground state solutions for a critical nonlocal schrodinger equation in r2 we study the following singularly perturbed nonlocal schrodinger equation e2 u v x u e 2 1 x f u f u inr2 where v x is a continuous real function on r2 f s is the primitive of f s 0 2 and e is a positive parameter assuming that the nonlinearity f s has critical exponential growth in the sense of trudinger moser we establish the existence and concentration of solutions by variational methods

frequentist prediction intervals and predictive distributions summary we consider parametric frameworks for the prediction of future values of a random variable y based on previously observed data x simple pivotal methods for obtaining calibrated prediction intervals are presented and illustrated frequentist predictive distri butions are defined as confidence distributions and their utility is demonstrated a simple pivotal based approach that produces prediction intervals and predictive distributions with well calibrated frequentist probability interpretations is introduced and efficient simulation methods for producing predictive distributions are considered properties related to an average kullback leibler measure of goodness for predictive or estimated distributions are given the predictive distributions here are shown to be optimal in certain settings with invariance structure and to dominate plug in distributions under certain conditions

a hopf s lemma and a strong minimum principle for the fractional p laplacian abstract our propose here is to provide a hopf lemma and a strong minimum principle for weak supersolutions of p s u c x u p 2 u in where is an open set of r n s 0 1 p 1 c c and p s is the fractional p laplacian

predictive likelihood inference with applications summary conditional and marginal predictive likelihood are defined and used in predicting un observed or missing data a distinction is made between predictive and estimative goals of a data analysis such methodology and distinctions are illustrated in the context of outlier theory and mixed model ano va the prediction of unobserved or missing data is considered from a likelihood perspective a general predictive likelihood is proposed for such purposes and contrasted with parametric likelihood the resulting maximum likelihood predictor is also compared with the limiting imputation from the em algorithm the new methodology is illustrated and contrasted with estimative likelihood analysis in the context of outlier theory and mixed model ano va predictions are proposed that are based on conditional and marginal predictive likelihoods for the unobserved data which are predictive adaptations of the methods developed by kalbfleisch and sprott 1970 1973 these authors were concerned with the elimination of nuisance parameters in order to make inference about another set of structural parameters prediction in the frame work of parametric distributions involves the elimination of all parameters in such a way that inference about the unobserved data is possible therefore in the predictive setting all para meters are nuisance parameters and the unobserved data now play a role similar to that of the structural parameters various predictive approaches to statistical inference have been advocated principally by geisser 1971 1975 stone 1974 aitchison and dunsmore 1975 and guttman 1970 a survey is provided by geisser 1980 and a brief overview in a parametric setting is presented in the next section following this a conditional likelihood approach is developed and shown to be closely related to the lauritzen 1974 hinkley 1979 likelihood method but specified in a manner allowing for a wider range of applicability a marginal predictive likelihood procedure is also specified which when applicable essentially agrees with the conditional likelihood procedure for the examples considered for a general account of likelihood based inference see fraser

robust predictive distributions for exponential families summary the bootstrap predictive distribution considered by harris 1989 is modified by replacing the maximum likelihood estimator of the unknown parameter by its minimum hellinger distance estimator the predictive distribution thus obtained is asymptotically superior to the corresponding estimative distribution in terms of the average kullback leibler divergence when the true distribution is in the natural exponential family simulation results are provided for the binomial and normal distributions which suggest that the proposed predictive distributions are robust and can perform better than the likelihood based methods under data contamination

fractional kirchhoff type equation with hardy littlewood sobolev critical exponent abstract in this paper we consider the following fractional kirchhoff type equation a b r n r n u x u y 2 x y n 2 s d x d y s u i u 2 h u 2 h 2 u in r n where n 3 s 0 1 a 0 b 0 0 n and 2 h n n 2 s is the hardy littlewood sobolev critical exponent and i is the riesz potential we establish the existence nonexistence and multiplicity of nontrivial solutions to above equation

a note on schrodinger newton systems with decaying electric potential abstract we prove the existence of solutions for the singularly perturbed schrodinger newton system 2 v x u 0 2 u 4 2 0 in r 3 with an electric potential v that decays polynomially fast at infinity the solution concentrates as 0 around structurally stable critical points of the electric potential as a particular case isolated strict extrema of v are allowed

stable and unstable attractors in boolean networks boolean networks at the critical point have been a matter of debate for many years as e g the scaling of numbers of attractors with system size recently it was found that this number scales superpolynomially with system size contrary to a common earlier expectation of sublinear scaling we point out here that these results are obtained using deterministic parallel update where a large fraction of attractors are an artifact of the updating scheme this limits the significance of these results for biological systems where noise is omnipresent here we take a fresh look at attractors in boolean networks with the original motivation of simplified models for biological systems in mind we test the stability of attractors with respect to infinitesimal deviations from synchronous update and find that most attractors are artifacts arising from synchronous clocking the remaining fraction of attractors are stable against fluctuating delays the average number of these stable attractors grows sublinearly with system size in the numerically tractable range

approximate predictive likelihood summary a predictive likelihood is given which approximates both bayes and maximum likeli hood predictive inference by expansion of a posterior likelihood this synthesizes and extends previous results and is widely applicable the approximation usually differs from exact bayes posterior predictive density by op n 2 and from exact predictive likelihood by op n 1 but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot be found the results are applied to the prediction various treatments of the likelihood function form the basis of parametric inference but until recently few non bayesian attempts have been made to define versions of it suitable for prediction however lauritzen 1974 hinkley 1979 and more recently butler 1986 have proposed rather similar definitions of predictive likelihood based on the idea of conditioning on the value of a sufficient statistic unfortunately they apply only when sufficiency provides a genuine reduction of the data moreover even if for a given problem an exact predictive likelihood exists the calculations needed to derive it can be onerous this paper provides approximations to hinkley lauritzen predictive likelihood accur ate to op n 1 in many cases which are applicable in situations where maximum likelihood estimation is regular they also apply to problems which admit no exact predictive likelihood because sufficiency provides no real reduction of the data the approximations are derived from a posterior predictive density and may if prior informa tion is available be regarded as bayesian procedures their construction requires only the repeated maximization of a likelihood and evaluation of the observed information matrix at the maximum and is fast and accurate using usual numerical maximization methods there is a close connexion with the approximations to posterior moments and marginal densities given by tierney kadane 1986 who suggest the same approxima tion as used here but give no detailed results for prediction section 2 of this paper shows how laplace s method for integrals may be applied to a posterior predictive density to yield approximate predictive likelihood section 3 discusses a connection with conditional inference essentially the same approximation

entropy of complex relevant components of boolean networks boolean network models of strongly connected modules are capable of capturing the high regulatory complexity of many biological gene regulatory circuits we study numerically the previously introduced basin entropy a parameter for the dynamical uncertainty or information storage capacity of a network as well as the average transient time in random relevant components as a function of their connectivity we also demonstrate that basin entropy can be estimated from time series data and is therefore also applicable to nondeterministic networks models

topology regulates pattern formation capacity of binary cellular automata on graphs abstract we study the effect of topology variation on the dynamic behavior of a system with local update rules we implement one dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree dependent rules each containing a single parameter we observe that changes in graph topology induce transitions between different dynamic domains wolfram classes without a formal change in the update rule along with topological variations we study the pattern formation capacities of regular random small world and scale free graphs pattern formation capacity is quantified in terms of two entropy measures which for standard cellular automata allow a qualitative distinction between the four wolfram classes a mean field model explains the dynamic behavior of random graphs implications for our understanding of information transport through complex network based systems are discussed

regularity results on a class of doubly nonlocal problems abstract the purpose of this article is twofold first an issue of regularity of weak solution to the problem p see below is addressed secondly we investigate the question of h s versus c 0 weighted minimizers of the functional associated to problem p and then give applications to existence and multiplicity results

the stabilizing effect of noise on the dynamics of a boolean network abstract in this paper we explore both numerically and analytically the robustness of a synchronous boolean network governed by rule 126 of cellular automata in particular we explore whether or not the introduction of noise into the system has any discernable effect on the evolution of the system this noise is introduced by changing the states of a given number of nodes in the system according to certain rules new mathematical models are developed for this purpose we use matlab to run the numerical simulations including iterations of the real system and the model computation of lyapunov exponents lye and generation of bifurcation diagrams we provide a more in depth fixed point analysis through analytic computations paired with a focus on bifurcations and delay plots to identify the possible attractors we show that it is possible either to attenuate or to suppress entirely chaos through the introduction of noise and that the perturbed system may exhibit very different long term behavior than that of the unperturbed system

information geometry of generalized bayesian prediction using alpha divergences as loss functions in this paper the methods of information geometry are employed to investigate a generalized bayes rule for prediction taking alpha divergences as the loss functions optimality and asymptotic properties of the generalized bayesian predictive densities are considered we show that the bayesian predictive densities minimize a generalized bayes risk we also find that the asymptotic expansions of the densities are related to the coefficients of the alpha connections of a statistical manifold in addition we discuss the difference between two risk functions of the generalized bayesian predictions based on different priors finally using the non informative priors i e jeffreys and reference priors uniform prior and conjugate prior two examples are presented to illustrate the main results

random boolean network model exhibiting deterministic chaos this paper considers a simple boolean network with n nodes each node s state at time t being determined by a certain number of parent nodes which may vary from one node to another this is an extension of a model studied by andrecut and ali int j mod phys b 15 17 2001 who consider the same number of parents for all nodes we make use of the same boolean rule as andrecut and ali provide a generalization of the formula for the probability of finding a node in state 1 at a time t and use simulation methods to generate consecutive states of the network for both the real system and the model the results match well we study the dynamics of the model through sensitivity of the orbits to initial values bifurcation diagrams and fixed point analysis we show that the route to chaos is due to a cascade of period doubling bifurcations which turn into reversed period halving bifurcations for certain combinations of parameter values

predictive fit for natural exponential families summary the paper examines predictive distributions concentrating on measuring their fit to the true distribution by average kullback leibler divergence the notion of an averaged bootstrap predictive distribution is introduced this predictive distribution is shown to be asymptotically superior to the estimative distribution in terms of average kullbackleibler divergence when the true distribution is in a natural exponential family smallsample results are presented for the poisson and binomial distributions which suggest that the bootstrap distribution performs well in these cases

on an exact probability matching property of right invariant priors summary the paper considers priors which are right invariant with respect to the haar measure it is shown that the posterior coverage probabilities of certain invariant bayesian predictive regions exactly match the corresponding frequentist probabilities several examples are given to illustrate the main result

dynamical phase transition in a neural network model with noise an exact solution the dynamical organization in the presence of noise of a boolean neural network with random connections is analyzed for low levels of noise the system reaches a stationary state in which the majority of its elements acquire the same value it is shown that under very general conditions there exists a critical value gc of the noise below which the network remains organized and above which it behaves randomly the existence and nature of the phase transition are computed analytically showing that the critical exponent is 1 2 the dependence of gc on the parameters of the network is obtained these results are then compared with two numerical realizations of the network

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

asynchronous random boolean network model based on elementary cellular automata rule 126 this paper considers a simple boolean network with n nodes each node s state at time t being determined by a certain number k of parent nodes which is fixed for all nodes the nodes with randomly assigned neighborhoods are updated based on various asynchronous schemes we make use of a boolean rule that is a generalization of rule 126 of elementary cellular automata we provide formulas for the probability of finding a node in state 1 at a time t for the class of asynchronous random boolean networks arbn in which only one node is updated at every time step and for the class of generalized arbns garbn in which a random number of nodes can be updated at each time point we use simulation methods to generate consecutive states of the network for both the real system and the models under the various schemes the results match well we study the dynamics of the models through sensitivity of the orbits to initial values bifurcation diagrams and fixed point analysis we show both theoretically and by example that the arbns generate an ordered behavior regardless of the updating scheme used whereas the garbns have behaviors that range from order to chaos depending on the type of random variable used to determine the number of nodes to be updated and the parameter combinations

on asymptotic properties of predictive distributions summary second order asymptotic theory of predictive distributions is investigated it is shown that estimative distributions with asymptotically efficient estimators can be improved to predictive distributions that do not belong to the model the model is assumed to be a multidimensional curved exponential family predictive distributions can be constructed by shifting estimative distributions in a direction orthogonal to the model the average kullback leibler divergence from the true distribution to a predictive distribution is represented as the sum of two components one of them depends on the choice of the estimative distribution and the other depends on the shift orthogonal to the model the optimal shift orthogonal to the model is obtained a quantity that can be regarded as the mixture mean curvature of the model in the space of all probability distributions is introduced the difference in average kullback leibler divergence between an estimative distribution and the optimal predictive distribution obtained by shifting it can be regarded as the mixture mean curvature of the model an asymptotic expression for bayesian predictive distributions is also obtained

dynamical behavior and influence of stochastic noise on certain generalized boolean networks abstract this study considers a simple boolean network with n nodes each node s state at time t being determined by a certain number of parent nodes the network is analyzed when the connectivity k is fixed or variable making use of a boolean rule that is a generalization of rule 22 of elementary cellular automata a generalized formula for providing the probability of finding a node in state 1 at time t is determined we show typical behaviors of the iterations and we study the dynamics of the network through lyapunov exponents bifurcation diagrams and fixed point analysis we conclude that the network may exhibit stability or chaos depending on the underlying parameters in general high connectivity is associated with a convergence to zero of the probability of finding a node in state 1 at time t we also study analytically and numerically the dynamics of the network under a stochastic noise procedure we show that under a smaller probability of disturbing the nodes through the noise procedure the system tends to exhibit more nodes in the same state for many parameter combinations there is no critical value of the noise parameter below which the network remains organized and above which it behaves randomly

measures for information propagation in boolean networks boolean networks provide a large scale model of gene regulatory and neuronal networks in this paper we study what kinds of boolean networks best propagate and process signals i e information in the presence of stochasticity and noise we first examine two existing approaches that use mutual information and find that these approaches do not capture well the phenomenon studied we propose a new measure for information propagation based on perturbation avalanches in boolean networks and find that the measure is maximized in dynamically critical networks and in subcritical networks if noise is present

existence of groundstates for a class of nonlinear choquard equations we prove the existence of a nontrivial solution h n to the nonlinear choquard equation i in n where i is a riesz potential under almost necessary conditions on the nonlinearity in the spirit of berestycki and lions this solution is a groundstate if moreover is even and monotone on 0 then is of constant sign and radially symmetric

improved minimax predictive densities under kullback leibler loss let x n p u x i and y n p v y i be independentp dimensional multivariate normal vectors with common unknown mean based on only observing x x we consider the problem of obtaining a predictive density p y x for y that is close to p y as measured by expected kullback leibler loss a natural procedure for this problem is the formal bayes predictive density p u y x under the uniform prior u 1 which is best invariant and minimax we show that any bayes predictive density will be minimax if it is obtained by a prior yielding a marginal that is superharmonic or whose square root is superharmonic this yields wide classes of minimax procedures that dominate p u y x including bayes predictive densities under superharmonic priors fundamental similarities and differences with the parallel theory of estimating a multivariate normal mean under quadratic loss are described

a note on modified estimative prediction limits and distributions in this paper a modification of the estimative prediction limit is derived for which the coverage probability equals the target value to third order accuracy under ordinary repeated sampling it provides an explicit approximate solution to the equation given by barndorff nielsen cox 1996 which determines an upper prediction limit for an unobserved random variable the corresponding predictive density is specified in a simple closed form and its main properties are emphasised

capturing the intangible concept of information abstract the purpose of this article is to discuss the intricacies of quantifying information in some statistical problems the aim is to develop a general appreciation for the meanings of information functions rather than their mathematical use this theme integrates fundamental aspects of the contributions of kullback lindley and jaynes and bridges chaos to probability modeling a synopsis of information theoretic statistics is presented in the form of a pyramid with shannon at the vertex and a triangular base that signifies three distinct variants of quantifying information discrimination information kullback mutual information lindley and maximum entropy information jaynes examples of capturing information by the maximum entropy me method are discussed it is shown that the me approach produces a general class of logit models capable of capturing various forms of sample and nonsample information diagnostics for quantifying information captured by the me logit models are given and decom

a simple predictive density based on the p formula the predictive density proposed by harris 1989 is based on integrating the density for a new observation with respect to the estimated sampling distribution of the maximum likelihood estimator of the unknown parameter this has good properties but is rather complicated to compute even for simple models an approximation to the harris proposal is considered which consists of approximating the sampling distribution of the maximum likelihood estimator of the unknown parameter by barndorff nielsen s 1983 p formula and then using a laplace approximation with o n 1 correction terms for integrating out the parameter the result can generally be expressed in terms of standard likelihood derivatives and takes a quite simple form for exponential families and for location models

estimability and likelihood inference for generalized linear mixed models using data cloning maximum likelihood estimation for generalized linear mixed models glmm an important class of statistical models with substantial applications in epidemiology medical statistics and many other fields poses significant computational difficulties in this article we use data cloning a simple computational method that exploits advances in bayesian computation in particular the markov chain monte carlo method to obtain maximum likelihood estimators of the parameters in these models this method also leads to a simple estimator of the asymptotic variance of the maximum likelihood estimators determining estimability of the parameters in a mixed model is in general a very difficult problem data cloning provides a simple graphical test to not only check if the full set of parameters is estimable but also and perhaps more importantly if a specified function of the parameters is estimable one of the goals of mixed models is to predict random effects we suggest a frequentist method to obtain predict

on efficient probability forecasting systems we study the asymptotic behaviour of probability forecasting systems and discuss their usefulness as inferential tools for statistical problems such as model verification and selection our theoretical setting is the prequential or predictive sequential framework proposed by dawid 1984 we study especially the notion of prequential efficiency of a forecasting system and present some new results we focus on plug in or estimative forecasting systems where the forecast distribution is generated by replacing the unknown parameter with an estimate

synchronization of stochastically coupled cellular automata we analyze the dynamics of two coupled elementary cellular automata with complex spatiotemporal dynamics the coupling mechanism characterized by a probability p is stochastic from numerical simulations we find that a sharp transition to full synchronization of the two cellular automata occurs at a critical value of p this transition admits an approximate semianalytical description in terms of the evolution of the difference automaton and is found both for symmetric and asymmetric coupling it is argued that the behavior of cellular automata under coupling may inspire a classification of their individual dynamics s1063 651x 98 51407 9