to what class of fractals does the alexander orbach conjecture apply discussion de la decouverte numerique recente d alexander et orbach selon laquelle pour un agregat infini naissant en percolation le rapport d f d w dimension fractale de l agregat dimension fractale d une marche aleatoire dans l agregat est approximativement independant de d pour d 1

marginal likelihood estimation via power posteriors model choice plays an increasingly important role in statistics from a bayesian perspective a crucial goal is to compute the marginal likelihood of the data for a given model however this is typically a difficult task since it amounts to integrating over all model parameters the aim of the paper is to illustrate how this may be achieved by using ideas from thermodynamic integration or path sampling we show how the marginal likelihood can be computed via markov chain monte carlo methods on modified posterior distributions for each model this then allows bayes factors or posterior model probabilities to be calculated we show that this approach requires very little tuning and is straightforward to implement the new method is illustrated in a variety of challenging statistical settings

approximate bayes factors and accounting for model uncertainty in generalised linear models summary ways of obtaining approximate bayes factors for generalised linear models are described based on the laplace method for integrals we propose a new approximation which uses only the output of standard computer programs for estimating generalised linear models this appears to be quite accurate a reference set of proper priors is suggested both to represent the situation where there is not much prior information and to assess the sensitivity of the results to the prior distribution the methods can be used when the dispersion parameter is unknown when there is overdispersion to compare link functions and to compare error distributions and variance functions the methods can be used to implement the bayesian approach to accounting for model uncertainty we describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important software to implement the methods is available at no cost from statlib

measurement error in linear autoregressive models time series data are often subject to measurement error usually the result of needing to estimate the variable of interest although it is often reasonable to assume that the measurement error is additive i e the estimator is conditionally unbiased for the missing true value the measurement error variances often vary as a result of changes in the population process over time and or changes in sampling effort in this article we address estimation of the parameters in linear autoregressive models in the presence of additive and uncorrelated measurement errors allowing heteroscedasticity in the measurement error variances we establish the asymptotic properties of naive estimators that ignore measurement error and propose an estimator based on correcting the yule walker estimating equations we also examine a pseudo likelihood method based on normality assumptions and computed using the kalman filter we review other techniques that have been proposed including two that require no information about

on the predictability of discrete dynamical systems iii abstract given an integer n 2 a metrizable compact topological n manifold x with boundary and a finite positive borel measure on x we prove that most homeomorphisms f x x are non sensitive almost everywhere on x moreover we also prove that for most homeomorphisms f x x the non wandering set f has measure zero

bias reduction of autoregressive estimates in time series regression model through restricted maximum likelihood abstract this article considers maximum likelihood ml and restricted maximum likelihood reml estimation of time series regression models with autoregressive ar p noise approximate biases of the ml and reml estimators of the ar parameters based on their approximate representations are derived in addition a bias result for the ml estimator mle of the error variance is established numerical results are presented to illustrate the biases of the mle and reml estimator for the ar parameters and simulation results are provided to assess the adequacy of our approximations the impact of bias of the ar estimates on testing of linear trend in a regression trend model is also investigated for a time series of short or moderate sample length the reml estimator is generally much less biased than the mle consequently the reml approach leads to more accurate inferences for the regression parameters

asymptotic properties of estimators for autoregressive models with errors in variables let x t t z be an observable strictly stationary sequence of random variables and let x t u t e t where u t is an ar p and e t is a strictly stationary sequence representing errors of measurement in x t with e e 1 0 under some broad assumptions on e t we establish the consistency properties as well as the rates of convergence for the standard estimators for the autoregressive parameters computed from a set of modified yule walker equations

under reported data analysis with inar hidden markov chains in this work we deal with correlated under reported data through inar 1 hidden markov chain models these models are very flexible and can be identified through its autocorrelation function which has a very simple form a naive method of parameter estimation is proposed jointly with the maximum likelihood method based on a revised version of the forward algorithm the most probable unobserved time series is reconstructed by means of the viterbi algorithm several examples of application in the field of public health are discussed illustrating the utility of the models copyright 2016 john wiley sons ltd

turbulence amalgamation and generic automorphisms of homogeneous structures we study topological properties of conjugacy classes in polish groups with emphasis on automorphism groups of homogeneous countable structures we first consider the existence of dense conjugacy classes the topological rokhlin property we then characterize when an automorphism group admits a comeager conjugacy class answering a question of truss and apply this to show that the homeomorphism group of the cantor space has a comeager conjugacy class answering a question of akin hurley and kennedy finally we study polish groups that admit comeager conjugacy classes in any dimension in which case the groups are said to admit ample generics we show that polish groups with ample generics have the small index property generalizing results of hodges hodkinson lascar and shelah and arbitrary homomorphisms from such groups into separable groups are automatically continuous moreover in the case of oligomorphic permutation groups they have uncountable cofinality and the bergman property these results in particular apply to automorphism groups of many stable 0 categorical structures and of the random graph in this connection we also show that the infinite symmetric group s has a unique non trivial separable group topology for several interesting groups we also establish serre s properties fh and fa

topological properties of percolation clusters percolation properties including the total cluster mass s the shell mass b and the linear geometrical size r are studied as a function of the topological chemical distance parameter l all critical exponents are shown to be related to an apparently new exponent nu defined by r approximately lv critical exponents are calculated exactly for percolation clusters on the cayley tree a model for 6d percolation for which s approximately l2 b approximately l and r2 approximately l for diffusion on such clusters one finds that l3 approximately t numerical estimates of the exponents are obtained for other dimensions a conjecture which relates nu to beta and nu is discussed

structure of clusters generated by random walks the authors study the cluster structure resulting from a nearest neighbour random walk embedded in a d dimensional space each bond visited by the random walks is regarded as belonging to the cluster the diffusion exponent and the fracton dimensional of the fractal cluster in d 3 is found to be dw 3 5 or 0 1 and d 0 57 or 0 02 using a method of exact enumeration of random walks on these fractals

structural and dynamical properties of random walk clusters the authors study the structural and dynamical properties of the clusters generated by a nearest neighbour random walk embedded in a d dimensional space they have focused on the non trivial case in which the cluster is generated in d 3 the structure of this cluster is characterised by loops for all length scales on the one hand and by the fact that deadends are negligible upon scaling on the other hand the cluster is very dilute and is characterised by fractal dimension df 2 and chemical dimension d1 1 29 or 0 04 from these results it follows that v identical to dldf approximately 2 3 which is consistent with the formula v 2 d 2 or d or 4 obtained using a flory type argument the dynamical diffusion exponents dw and dlw were calculated using the exact enumeration method and found to be dw 3 45 or 0 10 and dlw 2 28 or 0 05 the results suggest that the effect of loops is small but not negligible they also calculated the fracton dimensionality of the cluster and obtained ds 1 14 or 0 02 a scaling function is presented for the end to end mean square displacement of a random walk performed on a random walk cluster this scaling function is supported by their numerical results

approximate and real trajectories for generic dynamical systems abstract in this paper we show that generic dynamical systems have a weak shadowing property namely that for a generic dynamical system in the space of discrete continuous dynamical systems on a compact manifold m with the usual c 0 topology given 0 there exists a 0 such that trajectories are close to real trajectories there are no dimensional restrictions on this result we also give some results on the inverse problem of tracing real trajectories by trajectories these problems are motivated by questions regarding the validity of numerical solutions of differential equations

on li yorke pairs the li yorke definition of chaos proved its value for interval maps in this paper it is considered in the setting of general topological dynamics we adopt two opposite points of view on the one hand sufficient conditions for li yorke chaos in a topological dynamical system are given we solve a long standing open question by proving that positive entropy implies li yorke chaos on the other hand properties of dynamical systems without li yorke pairs are investigated in addition to having entropy 0 they are minimal when transitive and the property is stable under factor maps arbitrary products and inverse limits finally it is proved that minimal systems without li yorke pairs are disjoint from scattering systems

limit sets of typical continuous functions abstract given a metrizable compact topological n manifold x with boundary and a finite positive borel measure on x we prove that for the typical continuous function f x x it is true that for every point x in a full measure subset of x the limit set f x is a cantor set of hausdorff dimension zero f maps f x homeomorphically onto itself each point of f x has a dense orbit in f x and f is non sensitive at each point of f x moreover the function x f x is continuous almost everywhere

dynamical entropy in banach spaces we introduce a version of voiculescu brown approximation entropy for isometric automorphisms of banach spaces and develop within this framework the connection between dynamics and the local theory of banach spaces as discovered by glasner and weiss our fundamental result concerning this contractive approximation entropy or ca entropy characterizes the occurrence of positive values both geometrically and topologically this leads to various applications for example we obtain a geometric description of the topological pinsker factor and show that a c algebra is type i if and only if every multiplier inner automorphism has zero ca entropy we also examine the behaviour of ca entropy under various product constructions and determine its value in many examples including isometric automorphisms of l p for 1 p and noncommutative tensor product shifts

graph theoretic structure of maps of the cantor space abstract in this paper we develop unifying graph theoretic techniques to study the dynamics and the structure of spaces h 0 1 n and c 0 1 n the space of homeomorphisms and the space of self maps of the cantor space respectively using our methods we give characterizations which determine when two homeomorphisms of the cantor space are conjugate to each other we also give a new characterization of the comeager conjugacy class of the space h 0 1 n the existence of this class was established by kechris and rosendal and a specific element of this class was described concretely by akin glasner and weiss our characterization readily implies many old and new dynamical properties of elements of this class for example we show that no element of this class has a li yorke pair implying the well known glasner weiss result that there is a comeager subset of h 0 1 n each element of which has topological entropy zero our analogous investigation in c 0 1 n yields a surprising result there is a comeager subset of c 0 1 n such that any two elements of this set are conjugate to each other by an element of h 0 1 n our description of this class also yields many old and new results concerning dynamics of a comeager subset of c 0 1 n

good measures on cantor space while there is up to homeomorphism only one cantor space i e one zero dimensional perfect compact nonempty metric space there are many measures on cantor space which are not topologically equivalent the clopen values set for a full nonatomic measure is the countable dense subset u u is clopen of the unit interval it is a topological invariant for the measure for the class of good measures it is a complete invariant a full nonatomic measure is good if whenever u v are clopen sets with u v there exists w a clopen subset of v such that w u these measures have interesting dynamical properties they a re exactly the measures which arise from uniquely ergodic minimal systems on cantor space for some of them there is a unique generic measure preserving homeomorphism that is within the polish group of such homeomorphisms there is a dense g conjugacy class

generically there is but one self homeomorphism of the cantor set we describe a self homeomorphism r of the cantor set x and then show that its conjugacy class in the polish group h x of all homeomorphisms of x forms a dense g subset of h x we also provide an example of a locally compact second countable topological group which has a dense conjugacy class

random walk on a random walk the authors investigate the random walk of a particle on a one dimensional chain which has been constructed by a random walk procedure exact expressions are given for the mean square displacement and the fourth moment after n steps the probability density after n steps is derived in the saddle point approximation for large n these quantities have also been studied by numerical simulation the extension to continuous time has been made where the particle jumps according to a poisson process the exact solution for the self correlation function has been obtained in the fourier and laplace domain the resulting frequency dependent diffusion coefficient and incoherent dynamical structure factor have been discussed the model of random walk on a random walk is applied to self diffusion in the concentrated one dimensional lattice gas where the correct asymptotic behavior is found

weak shadowing for discrete dynamical systems on nonsmooth manifolds abstract in j math anal appl 189 1995 409 423 corless and pilyugin proved that weak shadowing is a c 0 generic property in the space of discrete dynamical systems on a compact smooth manifold m in our paper we give another proof of this theorem which does not assume that m has a differential structure moreover our method also works for systems on some compact metric spaces that are not manifolds such as a hilbert cube or generally a countably infinite cartesian product of manifolds with boundary and a cantor set

shifts of finite type as fundamental objects in the theory of shadowing shifts of finite type and the notion of shadowing or pseudo orbit tracing are powerful tools in the study of dynamical systems in this paper we prove that there is a deep and fundamental relationship between these two concepts let x be a compact totally disconnected space and f x rightarrow x a continuous map we demonstrate that f has shadowing if and only if the system f x is conjugate to the inverse limit of a directed system satisfying the mittag leffler condition and consisting of shifts of finite type in particular this implies that in the case that x is the cantor set f has shadowing if and only if f x is the inverse limit of a sequence satisfying the mittag leffler condition and consisting of shifts of finite type moreover in the general compact metric case where x is not necessarily totally disconnected we prove that f has shadowing if f x is a factor of the inverse limit of a sequence satisfying the mittag leffler condition and consisting of shifts of finite type by a quotient that almost lifts pseudo orbits

the topological rohlin property and topological entropy for a compact metric space x let g h x denote the group of self homeomorphisms with the topology of uniform convergence the group g acts on itself by conjugation and we say that x satisfies the topological rohlin property if this action has dense orbits we show that the hilbert cube the cantor set and with a slight modification also even dimensional spheres satisfy this property we also show that zero entropy is generic for homeomorphisms of the cantor set whereas it is infinite entropy which is generic for homeomorphisms of cubes of dimension d 2 and the hilbert cube

generic automorphisms of homogeneous structures let g be a permutation group on the set usually we take n o we seek a notion of genericity for members of g the idea is that a member of g should be generic if it is in some sense typical we argue that the following is the correct definition suppose that g is endowed with a metric so that it becomes a complete metric space it follows that the baire category theorem holds and we may use the notions of meagre and comeagre sets

chaos among self maps of the cantor space glasner and weiss have shown that a generic homeomorphism of the cantor space has zero topological entropy hochman has shown that a generic transitive homeomorphism of the cantor space has the property that it is topologically conjugate to the universal odometer and hence far from being chaotic in any sense we show that a generic self map of the cantor space has zero topological entropy moreover we show that a generic self map of the cantor space has no periodic points and hence is not devaney chaotic nor devaney chaotic on any subsystem however we exhibit a dense subset of the space of all self maps of the cantor space each element of which has infinite topological entropy and is devaney chaotic on some subsystem

pseudo maximum likelihood estimation the asymptotic distribution gong and samaniego 1981 define pseudo maximum likelihood estimation and derive the asymptotic distribution of the resulting estimates this note gives a simpler and more elegant expression for the asymptotic variance of a pseudo maximum likelihood estimate

a marginal moment matching approach for fitting endemic epidemic models to underreported disease surveillance counts count data are often subject to underreporting especially in infectious disease surveillance we propose an approximate maximum likelihood method to fit count time series models from the endemic epidemic class to underreported data the approach is based on marginal moment matching where underreported processes are approximated through completely observed processes from the same class moreover the form of the bias when underreporting is ignored or taken into account via multiplication factors is analyzed notably we show that this leads to a downward bias in model based estimates of the effective reproductive number a marginal moment matching approach can also be used to account for reporting intervals which are longer than the mean serial interval of a disease the good performance of the proposed methodology is demonstrated in simulation studies an extension to time varying parameters and reporting probabilities is discussed and applied in a case study on weekly rotavirus gastroenteritis counts in berlin germany

resistance of random walks unrestricted lattice random walks in which a unit conductor is placed along each bond traversed are considered the mean end to end resistance is studied as a function of the number of steps in the walk and the spatial dimension a critical scaling law is found whose exponent is consistently given by four different calculational schemes

rigorous exponent inequalities for random walks the exponents for the resistance of a random walk path and the random walk on a random walk problem are related to a number of other exponents for random walks some rigorous inequalities for these exponents are then established

pseudo maximum likelihood estimation theory and applications abstract pseudo maximum likelihood estimation easily extends to k parameter models and is of interest in problems in which the likelihood surface is ill behaved in higher dimensions but well behaved in lower dimensions several signal plus noise or convolution models are examined which exhibit such behavior and satisfy the regularity conditions of the asymptotic theory for specific models a numerical comparison of asymptotic variances suggests that a psuedo maximum likelihood estimate of the signal parameter is uniformly more efficient than estimators that have been advanced by previous authors a number of other potential applications are noted

an asymptotic theory for weighted least squares with weights estimated by replication summary we consider a heteroscedastic linear regression model with replication to estimate the variances one can use the sample variances or the sample average squared errors from a regression fit we study the large sample properties of these weighted least squares estimates with estimated weights when the number of replicates is small the estimates are generally inconsistent for asymmetrically distributed data if sample variances are used based on m replicates the weighted least squares estimates are inconsistent for m 2 replicates even when the data are normally distributed with between 3 and 5 replicates the rates of convergence are slower than the usual square root of n with m 6 replicates the effect of estimating the weights is to increase variances by m 5 m 3 relative to weighted least squares estimates with known weights

heteroskedasticity autocorrelation robust standard errors using the bartlett kernel without truncation in this paper we analyze heteroskedasticity autocorrelation hac robust tests constructed using the bartlett kernel without truncation we show that while such an hac estimator is not consistent asymptotically valid testing is still possible we show that tests using the bartlett kernel without truncation are exactly equivalent to recent hac robust tests proposed by kiefer vogelsang and bunzel 2000 econometrica 68 pp 695 714

bayesian parameter inference for dynamic infectious disease modelling rotavirus in germany understanding infectious disease dynamics using epidemic models based on ordinary differential equations requires the calibration of model parameters from data a commonly used approach in practice to simplify this task is to fix many parameters on the basis of expert or literature information however this not only leaves the corresponding uncertainty unexamined but often also leads to biased inference for the remaining parameters because of dependence structures inherent in any given model in the present work we develop a bayesian inference framework that lessens the reliance on such external parameter quantifications by pursuing a more data driven calibration approach this includes a novel focus on residual autocorrelation combined with model averaging techniques in order to reduce these estimates dependence on the underlying model structure we applied our methods to the modelling of age stratified weekly rotavirus incidence data in germany from 2001 to 2008 using a complex susceptible infectious susceptible type model complemented by the stochastic reporting of new cases as a result we found the detection rate in the eastern federal states to be more than four times higher compared with that of the western federal states 19 0 vs 4 3 and also the infectiousness of symptomatically infected individuals was estimated to be more than 10 times higher than that of asymptomatically infected individuals 95 credibility interval 8 1 19 6 not only do these findings give valuable epidemiological insight into the transmission processes we were also able to examine the considerable impact on the model predicted transmission dynamics when fixing parameters beforehand