the analysis of rates using poisson regression models models are considered in which the underlying rate at which events occur can be represented by a regression function that describes the relation between the predictor variables and the unknown parameters estimates of the parameters can be obtained by means of iteratively reweighted least squares irls when the events of interest follow the poisson distribution the irls algorithm is equivalent to using the method of scoring to obtain maximum likelihood ml estimates the general poisson regression models include log linear quasilinear and intrinsically nonlinear models the approach considered enables one to concentrate on describing the relation between the dependent variable and the predictor variables through the regression model standard statistical packages that support irls can then be used to obtain ml estimates their asymptotic covariance matrix and diagnostic measures that can be used to aid the analyst in detecting outlying responses and extreme points in the model space applications of these methods to epidemiologic follow up studies with the data organized into a life table type of format are discussed the method is illustrated by using a nonlinear model derived from the multistage theory of carcinogenesis to analyze lung cancer death rates among british physicians who were regular cigarette smokers

acoustic propagation in non uniform waveguides revisiting webster equation using evanescent boundary modes the scattering of an acoustic wave propagating in a non uniform waveguide is inspected by revisiting improved multimodal methods in which the introduction of additional modes so called boundary mo

verhulst lotka volterra vlv model of ideological struggle abstract a model for ideological struggles is formulated the underlying set is a closed one like a country but in which the population size is variable in time the dynamics of the struggle is described by model equations of verhulst lotka volterra kind several ideologies compete to increase their number of adepts such followers can be either converted from one ideology to another or become followers of an ideology though being previously ideologically free a reverse process is also allowed two kinds of conversions are considered unitary conversion e g by means of mass communication tools or binary conversion e g by means of interactions between people it is found that the steady state when it exists depends on the number of ideologies moreover when the number of ideologies increases some tension arises between them this tension can change in the course of time we propose to measure the ideology tensions through an appropriately defined scale index finally it is shown that a slight change in the conditions of the environment can prevent the extinction of some ideology after almost collapsing the ideology can spread again and can affect a significant part of the country s population two kinds of such resurrection effects are described as phoenix effects

approximately exact inference for the common odds ratio in several 2 2 tables abstract the conditional maximum likelihood estimator mle of the common odds ratio in a sequence of independent 2 2 tables is known to be superior to the mantel haenszel estimator in terms of asymptotic efficiency and has the further advantage that its exact distribution is known however a long standing barrier to the widespread use of this estimator has been computational intractability in particular the calculation of significance levels confidence sets and power based on the exact distribution requires fast and efficient algorithms an important class of such algorithms form the basis of statxact a software package able to solve various aspects of the exact inference problem for a sequence of several 2 2 tables in real time we provide an alternative methodology by developing several useful saddlepoint approximations to the exact distribution of the conditional mle the approximations are derived from an interesting representation for hypergeometric random variables as a sum of independent

saddlepoint approximations as smoothers reference stat article 2002 001doi 10 1093 biomet 89 4 933view record in web of science record created on 2006 04 21 modified on 2017 05 12

the screening of species in a darwinistic tree like model of evolution abstract numerical and theoretical investigations of a tree like model of self organized critical evolution are presented the screening of species from the evolution process is numerically studied critical exponents for i the avalanche distribution ii the correlation function iii the order parameter and iv the fraction of unscreened species are given a mean field approximation is developed this theory is quite accurate for describing the critical state but is not able to describe the transient regimes i e the self organized slowing down of both order parameter and fraction of unscreened species towards the critical state

the likelihood ratio approximation to the conditional distribution of the maximum likelihood estimator in the discrete case summary the likelihood ratio approximation also called barndorff nielsen s approximation and often denoted by p provides a highly accurate approximation to the conditional density of a maximum likelihood estimator 0 given an ancillary statistic in this paper the properties of p are considered for the case in which the underlying random variables have a lattice distribution and 0 has a discrete but not necessarily lattice distribution if 0 has a lattice distribution then p provides a valid approximation to the density of 0 with respect to counting measure if the distribution of 0 is non lattice then p is still a valid approximation to the conditional density of 0 however the dominating measure is no longer counting measure

scaling properties of the surface of the eden model in d 2 3 4 the surface of the eden model is investigated numerically by finite size scaling using a strip geometry three different versions are studied and it shows that the one mostly used previously exhibits strong finite size corrections in two dimensions it is found that the surface thickness simply grows as the square root of the width of the strip for infinitely long strips this result as well as the results in d 3 and d 4 suggest that the surface of the eden shares some properties with the equilibrium models used to describe the roughening transition moreover it is found that the surface thickness scales differently with the height of the cluster for infinitely large strips

stability of high order perturbative methods for the computation of dirichlet neumann operators abstract in this paper we present results on the stability of perturbation methods for the evaluation of dirichlet neumann operators dno defined on domains that are viewed as complex deformations of a basic simple geometry in such cases geometric perturbation methods based on variations of the spatial domains of definition have long been recognized to constitute efficient and accurate means for the approximation of dno and in fact several numerical implementations have been previously proposed inspired by our recent analytical work here we demonstrate that the convergence of these algorithms is quite generally limited by numerical instability indeed we show that these standard perturbative methods for the calculation of dno suffer from significant ill conditioning which is manifest even for very smooth boundaries and whose severity increases with boundary roughness moreover and again motivated by our previous work we introduce an alternative perturbative approach that we show to be numerically stable this approach can be interpreted as a reformulation of classical perturbative algorithms in suitable independent variables and thus it allows for both direct comparison and the possibility of analytic continuation of the perturbation series it can also be related to classical preconditioned spectral approaches and as such it retains in finite arithmetic the spectral convergence properties of classical perturbative methods albeit at a higher computational cost as it does not take advantage of possible dimensional reductions still as we show an alternative approach such as the one we propose may be mandated in cases where substantial information is contained in high order harmonics and or perturbation coefficients of the solution

mean loglikelihood and higher order approximations summary higher order approximations to p values can be obtained from the log likelihood function and a reparameterization that can be viewed as a canonical parameter in an exponential family approximation to the model this approach clarifies the connection between skovgaard 1996 and fraser et al 1999a and shows that the skovgaard approximation can be obtained directly using the mean log likelihood function

likelihood for component parameters for a statistical model with data likelihood for the scalar or vector full parameter 0 of dimension p say is typically well defined and easily computed in this paper we investigate likelihood for a component parameter 0 of dimension d p and make use of the recent likelihood theory that has been successful in producing highly accurate third order p values for scalar parameters of continuous models the theory leads under moderate regularity to a definitive third order determination of likelihood for a component parameter 0 of dimension d where 1 d p we use the simple location model on the plane with standard normal errors to motivate the development the example exhibits most of the key characteristics of the general case and the recent theory then extends the determination of likelihood to the general context for the scalar interest parameter case with d 1 the usual determinations are typically of second order accuracy the example indicates how the new determination achieves third order accuracy the implementation is straightforward and uses familiar ingredients to other determinations such as the full maximum likelihood value o the constrained value o given 0 and the observed information j o for a complementing nuisance parameter 0 it does however require a special version of the nuisance information j o a version calibrated relative to a symmetric choice of the exponential type reparameterisation 0 underlying the recent theory but this is easily computed various examples are given and the motivating example is discussed in detail

asymptotics and the theory of inference asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable more importantly asymptotic analysis can also provide insight into the inference process itself suggesting what information is available and how this information may be extracted the development of likelihood inference over the past twenty some years provides an illustration of the interplay between techniques of approximation and statistical theory

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

the boundary of life for a self organized critical evolution the role of the interaction range abstract the dynamics of a tree like evolution is investigated as a function of the range k of the interactions between competing entities which are located at the extremities of the branches speciation branching events are supposed to be driven by extremal dynamics extinction events are allowed and controlled by a parameter r a transition between self organized critical and frozen evolution occurs at some well defined critical value rc k surprisingly the critical rc value behaves as a power of the range k rc k with an exponent 0 46 0 03 moreover the asymptotic case k is herein exactly solved the dynamics for k is not critical and does not present any transition in contrast with finite k cases

is the improved likelihood ratio statistic really improved in the discrete case summary on the basis of some numerical studies we argue that bartlett adjustment of the likelihood ratio statistic for discrete data does not in general yield an improvement in the asymptotic error rate of the chi squared approximation also we argue that the small sample effect of the bartlett adjustment is unclear and that it is in no way comparable with the improvement obtained for continuous data

improved multimodal method for the acoustic propagation in waveguides with a wall impedance and a uniform flow we present an efficient multimodal method to describe the acoustic propagation in the presence of a uniform flow in a waveguide with locally a wall impedance treatment the method relies on a variational formulation of the problem which allows to derive a multimodal formulation within a rigorous mathematical framework notably to properly account for the boundary conditions on the walls being locally the myers condition and the neumann condition otherwise also the method uses an enriched basis with respect to the usual cosine basis able to absorb the less converging part of the modal series and thus to improve the convergence of the method using the cosine basis the modal method has a low convergence 1 n with n the order of truncation using the enriched basis the improvement in the convergence is shown to depend on the mach number from 1 n5 to roughly 1 n1 5 for m 0 to m close to unity the case of a continuously varying wall impedance is considered and we discuss the limiting case of piecewise constant impedance which defines pressure edge conditions at the impedance discontinuities

improving on exact tests by approximate conditioning summary the often conservative nature for discrete data of so called exact tests seems usually the result of unnecessarily precise conditioning we consider avoiding this by conditioning only approximately on the sufficient statistics for nuisance parameters modest relaxation of conditioning results in small loss in terms of the rationale for conditional inference but can greatly reduce the difficulties caused by discreteness exact calculation of p values based on approximate conditioning is possible but unattractive both in terms of the amount of calculation involved and in requiring explicit specification of the extent to which conditioning is to be relaxed it is shown that there is a highly accurate easily computed and very natural asymptotic approximation that avoids these difficulties

evolution on trees a brief review about the extinctions of species and the case of genocide in a darwinistic punctuated equilibrium evolution model abstract numerical and theoretical investigations of species evolution in presence of extinction rules are recalled in the framework of punctuated equilibrium evolution models previous results on the bak sneppen model are mentioned together with extensions taking into account a variable number of species conditions for limited growth due to species interactions external fields or intrinsic population density conditions have already been considered an original genocide model is presented as a step towards describing effects due to the extinction of species critical exponents for i the avalanche distribution ii the steady state approach and iii the tree size are given a mean field approximation is shown to be quite accurate for describing the critical state the screening of species from the evolution process is not numerically studied

changes of a continuous character caused by gene flow a monte carlo study abstract we introduce a model of a large sexual population in which partners for reproduction are chosen randomly without any bias this large population is composed of two groups of local populations living in different environments and being in contact we propose a dynamic equation describing like the existing one for the allele frequency the temporal changes of a continuous character due to gene flow i e the transfer of the allels resulting from migration of individuals between the populations and natural selection we show that the gene flow can be described by the linear term in the proposed equation and the natural selection by the nonlinear term additional killing rule introduces a random factor into our model we discuss the role of both factors gene flow and selection on the structure of the population i e spatial distribution of the considered character and the resulting from it existence of hybrid zones we use the standard monte carlo simulations

phenomenological theory of mortality evolution its singularities universality and superuniversality the probability to survive to the age x universally increases with the mean lifespan x for species as remote as humans and flies for a given x the rate of its evolution with x is constant except for the narrow vicinity of a certain x x which equals 75 years for humans and 32 days for flies and which is independent of age population and living conditions at x x the evolution rate jumps to a different value its next jump is predicted at x 87 years for humans and 59 days for flies such singularities are well known in physics and mathematics as phase transitions in the considered case different population phases have significantly different survival evolution rates the evolution is rapid life expectancy may double within a lifespan of a single generation survival probability depends on age x and mean longevity x only for instance survival curves of 1896 swedes and 1947 japanese with approximately equal x are very close although they are related to different races in different countries at different periods in their different history with no adjustable parameters its presented universal law quantitatively agrees with all lifetable data according to this law the impact of all factors but age reduces to the mean lifespan only in advanced and old age this law is superuniversal it is approximately the same for species as remote as humans and flies it yields survival probability that linearly depends on the mean lifespan x as a result when human x almost doubles from 35 5 to 69 3 years life expectancy at 70 years increases from 8 to 9 5 years only other implications of the universal law are also considered

a simple general formula for tail probabilities for frequentist and bayesian inference summary we describe a simple general formula for approximating the p value for testing a scalar parameter in the presence of nuisance parameters the formula covers both frequentist and bayesian contexts and does not require explicit nuisance parameterisation implementation is discussed in terms of computer algebra packages examples are given and the relationship to barndorff nielsen s approximation is discussed

determination of lamb mode eigenvalues an original method is presented to determine the complex lamb wave spectrum by using a numerical spectral method applied to the elasticity equations this method presents the advantage to directly determine complex wave numbers for a given frequency via a classical matricial eigenvalue problem and allows the wave numbers to be determined at relatively high frequencies i e corresponding to many propagating modes it does not need initial guess values for the wave numbers contrary to the usual method of root finding of the rayleigh lamb frequency equations dispersion relation in the complex plane results are presented and the method is discussed

simple model of evolution with variable system size a simple model of biological extinction with variable system size is presented that exhibits a power law distribution of extinction event sizes the model is a generalization of a model recently introduced by newman proc r soc lond b265 1605 1996 both analytical and numerical analysis show that the exponent of the power law distribution depends only marginally on the growth rate g at which new species enter the system and is equal to the one of the original model in the limit g to infty a critical growth rate g c can be found below which the system dies out under these model assumptions stable ecosystems can only exist if the regrowth of species is sufficiently fast

consistent coupled mode theory of sound propagation for a class of nonseparable problems this article examines the effects of boundary condition approximations that arise whenever the coupled mode theories of a d pierce j acoust soc am 37 19 27 1965 and d m milder j acoust soc am 46 1259 1263 1969 are applied to propagation problems involving range dependent boundaries this boundary condition approximation requires that the depth derivative rather than the normal derivative of the field be continuous across a sloping interface the approximation is necessary in order to carry out the partial separation of depth and range variables effected in the mathematical formulation of the theory this article will show that a consequence of this approximation is that conventional coupled mode theory applied to dissipationless media with nonhorizontal boundaries does not conserve energy it is shown that a correction to coupled mode theory can be derived such that the proper boundary conditions are satisfied and energy is conserved to first order in the local bottom slope moreover the corrections are not prohibitive in terms of added computational complexity numerical examples are presented which illustrate the nonconservation of energy effect and the corrections to the theory

improved likelihood inference for discrete data reference stat article 2006 001doi 10 1111 j 1467 9868 2006 00548 xview record in web of science record created on 2006 04 21 modified on 2017 05 12

phyllotaxis an interdisciplinary phenomenon abstract regular phyllotaxis is largely non uniform in the sense that 1 2 and the golden mean are the most frequently observed values of the characteristic parameter divergence the different approaches to this enigmatic phenomenon form a fascinating chapter in the history of science more recently different models have been independently suggested in an attempt to recreate the phenomenon these are dynamic systems in discrete time founded on a simple inhibiting hypothesis ih we analyse the divergences selected by these models and consequently we investigate the ih capability to account for regular phyllotaxis this capability is conditional it depends on the convex concave shape of the elementary inhibitions and involves considering the ih from a statistical standpoint our conclusions are essentially new and they partly conflict with previous predictions because of its generality our analysis applies to botanical as well as to physical systems such as vortex networks

numerical simulation of gravity waves abstract we present a new spectral method to simulate numerically the waterwave problem in a channel for a fluid of finite or infinite depth it is formulated in terms of the free surface elevation and the velocity potential the numerical method is based on the reduction of this problem to a lower dimensional computation involving surface variables alone to accomplish this we describe the taylor expansion of the dirichlet neumann operator in homogeneous powers of the surface elevation each term is a concatenation of fourier multipliers with powers of and its derivatives and is valid uniformly in wavenumber these are easily calculated using the fast fourier transform the method is illustrated by computing the long time evolution of modulated wave packets and of approximations to the stokes steady wave train by imposing a surface pressure we observe surface steepening in large amplitude evolution and wake and bow wave development for flows with a close to critical froude number finally we give an example of nonlinear evolution of the distribution of energy among normal modes

exact semi separation of variables in waveguides with non planar boundaries series expansions of unknown fields nzn in elongated waveguides are commonly used in acoustics optics geophysics water waves and other applications in the context of coupled mode theories

an empirical adjustment to the likelihood ratio statistic consider a model parameterised by a scalar parameter of interest and a nuisance parameter inference about may be based on the signed square root of the likelihood ratio statistic r the statistic r is asymptotically distributed according to a standard normal distribution with error o n 1 2 to reduce the error of this normal approximation several modifications to r have been proposed such as barndorff nielsen s modified directed likelihood statistic r in this paper an approximation to r is proposed that can be calculated numerically for a wide range of models this approximation is shown to agree with r with error of order o p n 1 the results are illustrated on several examples

mean field theory for a simple model of evolution a simple dynamical model for darwinian evolution on its slowest time scale is analyzed its mean field theory is formulated and solved a random neighbor version of the model is simulated as is a one dimensional version in one dimension the dynamics can be described in terms of a repetitious random walker and anomalous diffusion with exponent 0 4 in all cases the model self organizes to a robust critical attractor

accurate directional inference for vector parameters in linear exponential families we consider inference on a vector valued parameter of interest in a linear exponential family in the presence of a finite dimensional nuisance parameter based on higher order asymptotic theory for likelihood we propose a directional test whose p value is computed using one dimensional integration the work simplifies and develops earlier research on directional tests for continuous models and on higher order inference for discrete models and the examples include contingency tables and logistic regression examples and simulations illustrate the high accuracy of the method which we compare with the usual likelihood ratio test and with an adjusted version due to skovgaard in high dimensional settings such as covariance selection the approach works essentially perfectly whereas its competitors can fail catastrophically