on p stability in groups and fusion systems the aim of this paper is to generalise the notion of p stability p is an odd prime in finite group theory to fusion systems we first compare the different definitions of p stability for groups and examine properties of p stability concerning subgroups and factor groups motivated by glauberman s theorem we study the question of how qd p is involved in finite simple groups we show that with a single exception a simple group involving qd p has a subgroup isomorphic to either qd p or a central extension of qd p by a cyclic group of order p then we define p stability for fusion systems and characterise some of its properties we prove a fusion theoretic version of thompson s maximal subgroup theorem we introduce the notion of section p stability both for groups and fusion systems and prove a version of glauberman s theorem to fusion systems we also examine relationship between solubility and p stability for fusion systems and determine the simple groups whose fusion systems are qd p free

the powers and strengths of tests for multinomials and contingency tables abstract the strength of a significance test is defined as a weighted average of the power especially if the weights are a prior density the concept is a compromise between neyman pearsonian and bayesian methods and is applied to tests for multinomial equiprobability and for no association in contingency tables the differences of the power functions of two criteria x 2 and g are illustrated for the trinomial where g arose earlier from a partially bayesian approach other methods for apprehending power functions of several variables are discussed for 2 2 contingency tables with equal row or column totals the power and strength functions of several statistics are equal

a center manifold for second order semilinear differential equations on the real line and applications to the existence of wave trains for the gurtin mccamy equation

simple fusion systems and the solomon 2 local groups we introduce a notion of simple fusion systems which imitates the corresponding notion for finite groups and show that the fusion system on the sylow 2 subgroup of a 7 dimensional spinor group over a field of characteristic 3 considered by ron solomon 18 and by ran levi and bob oliver 11 is simple in this sense

quasiperiodic solutions for dissipative boussinesq systems in this paper we analyze the behavior of the solution of the dissipative boussinesq systems partial t u partial x v alpha partial xxx v beta partial xxt u partial x uv partial t v partial x u c partial xxx u beta partial xxt v v partial x v where c 0 are parameters those systems model two dimensional small amplitude long wavelength water waves for 1 this equation is ill posed and most initial conditions do not lead to solutions nevertheless we show that for almost every c and almost every 1 it admits solutions that are quasiperiodic in time the proof uses the fact that the equation leaves invariant a smooth center manifold and for the restriction of the boussinesq system to the center manifold uses arguments of classical perturbation theory by considering the hamiltonian formulation of the problem and studying the birkhoff normal form

bayesian goodness of fit testing using infinite dimensional exponential families we develop a nonparametric bayes factor for testing the fit of a parametric model we begin with a nominal parametric family which we then embed into an infinite dimensional exponential family the new model then has a parametric and nonparametric component we give the log density of the nonparametric component a gaussian process prior an asymptotic consistency requirement puts a restriction on the form of the prior leaving us with a single hyperparameter for which we suggest a default value based on simulation experience then we construct a bayes factor to test the nominal model versus the semiparametric alternative finally we show that the bayes factor is consistent the proof of the consistency is based on approximating the model by a sequence of exponential families

subcentric linking systems for part of this research the author was supported by the danish national research foundation through the centre for symmetry and deformation dnrf92

the robustness and sensitivity of the mixed dirichlet bayesian test for independence in contingency tables a mixed dirichlet prior was previously used to model the hypotheses of independence and dependence in contingency tables thus leading to a bayesian test for independence each dirichlet has a main hyperparameter kappa and the mixing is attained by assuming a hyperprior for kappa this hyperparameter can be regarded as a flattening or shrinking constant we here review the method generalize it and check the robustness and sensitivity with respect to variations in the hyperpriors and in their hyperhyperparameters the hyperpriors examined included generalized log students with various numbers of degrees of freedom nu when nu is as large as 15 this hyperprior approximates a log normal distribution and when nu 1 it is a log cauchy our experiments caused us to recommend the log cauchy hyperprior or of course any distribution that closely approximates it the user needs to judge values for the upper and lower quartiles or any two quantiles of kappa but we find that the outcome is robust with respect to fairly wide variations in these judgments

stable and unstable manifolds for hyperbolic bi semigroups we show the existence of local lipschitzian stable and unstable manifolds for the ill posed problem of perturbations of hyperbolic bi semigroups we do not assume backward nor forward uniqueness of solutions we do not use cut off functions because we do not assume global smallness conditions on the nonlinearities we introduce what we call dichotomous flows which recovers the symmetry between the past and the future thus we need to prove only a stable manifold theorem we modify the conley mcgehee moeckel approach to avoid appealing to wazewski principle and brouwer degree theory hence we allow both the stable and unstable directions to be infinite dimensional we apply our theorem to the elliptic system u u g u u in an infinite cylinder r

posterior predictive p values extending work of rubin this paper explores a bayesian counterpart of the classical p value namely a tail area probability of a test statistic under a null hypothesis the bayesian formulation using posterior predictive replications of the data allows a test statistic to depend on both data and unknown nuisance parameters and thus permits a direct measure of the discrepancy between sample and population quantities the tail area probability for a test statistic is then found under the joint posterior distribution of replicate data and the nuisance parameters both conditional on the null hypothesis this posterior predictive p value can also be viewed as the posterior mean of a classical p value averaging over the posterior distribution of nuisance parameters under the null hypothesis and thus it provides one general method for dealing with nuisance parameters two classical examples including the behrens fisher problem are used to illustrate the posterior predictive p value and some of its interesting properties which also reveal a new bayesian interpretation for some classical p values an application to multiple imputation inference is also presented a frequency evaluation shows that in general if the replication is defined by new nuisance parameters and new data then the type i frequentist error of an level posterior predictive test is often close to but less than and will never exceed 2

nilpotent fusion systems abstract let p be a prime and let f be a saturated fusion system over a finite p group p a fusion system f is said to be nilpotent if f f p p we give various criteria for a saturated fusion system f to be nilpotent which generalize the analogous criteria for a finite group to be p nilpotent

stability of some waves in the dissipative boussinesq system abstract in this paper we study analytically a class of waves in the variant of the classical dissipative boussinesq system given by t u x v x x x v x x t u x u v t v x u c x x x u x x t v v x v where c 0 is a small parameter and 0 1 this equation is ill posed and most initial conditions do not lead to solutions nevertheless we show that for almost every c and almost every 1 it contains solutions that are defined for large values of time and they are very close of order o to a linear torus for long times of order o 1 the proof uses the fact that the equation leaves invariant a smooth center manifold and for the restriction of the system to the center manifold uses arguments of classical perturbation theory by considering the hamiltonian formulation of the problem the birkhoff normal form and neckhoroshev type estimates

large sample significance levels from multiply imputed data using moment based statistics and an f reference distribution abstract we present a procedure for computing significance levels from data sets whose missing values have been multiply imputed data this procedure uses moment based statistics m 3 repeated imputations and an f reference distribution when m we show first that our procedure is essentially the same as the ideal procedure in cases of practical importance and second that its deviations from the ideal are basically a function of the coefficient of variation of the canonical ratios of complete to observed information for small m our procedure s performance is largely governed by this coefficient of variation and the mean of these ratios using simulation techniques with small m we compare our procedure s actual and nominal large sample significance levels and conclude that it is essentially calibrated and thus represents a definite improvement over previously available procedures furthermore we compare the large sample power of the procedure as a function of m and other factors such as the di

analogues of goldschmidt s thesis for fusion systems we extend the results of david goldschmidt s thesis concerning fusion in nite groups to saturated fusion systems t 2 syl 2 g then the exponent of z t and hence of t is bounded by a function of the nilpotence class of t he also includes in the write up a fusion factorization result for an arbitrary nite group involving 0 1 z and the thompson subgroup in this paper we generalize these results to arbitrary saturated fusion systems throughout this paper unless otherwise in dicated p denotes an arbitrary prime number n a nonnegative integer and p a nontrivial nite p group theorem 1 suppose p is of nilpotence class at most n p 1 1 andf is a saturated fusion system on p with op f 1 then z p has exponent at most p n

on the efficient calculation of a linear combination of chi square random variables with an application in counting string vacua linear combinations of chi square random variables occur in a wide range of fields unfortunately a closed analytic expression for the probability density function is not yet known starting out from an analytic expression for the density of the sum of two gamma variables a computationally efficient algorithm to numerically calculate the linear combination of chi square random variables is developed an explicit expression for the error bound is obtained the proposed technique is shown to be computationally efficient i e only polynomial in growth in the number of terms compared to the exponential growth of most other methods it provides a vast improvement in accuracy and shows only logarithmic growth in the required precision in addition it is applicable to a much greater number of terms and currently the only way of computing the distribution for hundreds of terms as an application the exponential dependence of the eigenvalue fluctuation probability of a random matrix model for 4d supergravity with n scalar fields is found to be of the asymptotic form exp 0 35n

a characteristic subgroup for fusion systems abstract as a counterpart for the prime 2 to glauberman s zj theorem stellmacher proves that any nontrivial 2 group s has a nontrivial characteristic subgroup w s with the following property for any finite 4 free group g with s a sylow 2 subgroup of g and with o 2 g self centralizing the subgroup w s is normal in g we generalize stellmacher s result to fusion systems a similar construction of w s can be done for odd primes and gives rise to a glauberman functor

local control in fusion systems of p blocks of finite groups abstract if p is an odd prime b a p block of a finite group g such that sl 2 p is not involved in n g q e c g q for any b subpair q e then n g z j p controls b fusion where p is a defect group of b this is a block theoretic analogue of glauberman s zj theorem several results of general interest about fusion and blocks are also proved

existence of traveling waves of invasion for ginzburg landau type problems in infinite cylinders we study a class of systems of reaction diffusion equations in infinite cylinders which arise within the context of ginzburg landau theories and describe the kinetics of phase transformation in second order or weakly first order phase transitions with non conserved order parameters we use a variational characterization to study the existence of a special class of traveling wave solutions which are characterized by a fast exponential decay in the direction of propagation our main result is a simple verifiable criterion for existence of these traveling waves under the very general assumptions of non linearities we also prove boundedness regularity and some other properties of the obtained solutions as well as several sufficient conditions for existence or non existence of such traveling waves and give rigorous upper and lower bounds for their speed in addition we prove that the speed of the obtained solutions gives a sharp upper bound for the propagation speed of a class of disturbances which are initially sufficiently localized we give a sample application of our results using a computer assisted approach

lindley s paradox 1982 lindley s paradox journal of the american statistical association vol 77 no 378 pp 325 334

bayesian motivated tests of function fit and their asymptotic frequentist properties we propose and analyze nonparametric tests of the null hypothesis that a function belongs to a specified parametric family the tests are based on bic approximations bic to the posterior probability of the null model and may be carried out in either bayesian or frequentist fashion we obtain results on the asymptotic distribution of bic under both the null hypothesis and local alternatives one version of bic call it bic uses a class of models that are orthogonal to each other and growing in number without bound as sample size n tends to infinity we show that n 1 bic converges in distribution to a stable law under the null hypothesis we also show that bic can detect local alternatives converging to the null at the rate log n n a particularly interesting finding is that the power of the bic based test is asymptotically equal to that of a test based on the maximum of alternative log likelihoods simulation results and an example involving variable star data illustrate desirable features of the proposed tests

saturated fusion systems with parabolic families abstract let g be a group a finite p subgroup s of g is a sylow p subgroup if every finite p subgroup of g is conjugate to a subgroup of s in this paper we examine the relations between the fusion system over s which is given by conjugation in g and a certain chamber system c on which g acts chamber transitively with chamber stabilizer n g s next we introduce the notion of a fusion system with a parabolic family and we show that a chamber system can be associated to such a fusion system we determine some conditions the chamber system has to fulfill in order to assure the saturation of the underlying fusion system we give an application to fusion systems with parabolic families of classical type

existence of quasiperiodic solutions of elliptic equations on rn 1 via center manifold and kam theorems abstract we consider elliptic equations on r n 1 of the form 1 x u u y y g x u 0 x y r n r where g x u is a sufficiently regular function with g 0 0 we give sufficient conditions for the existence of solutions of 1 which are quasiperiodic in y and decaying as x uniformly in y such solutions are found using a center manifold reduction and results from the kam theory we discuss several classes of nonlinearities g to which our results apply

testing a point null hypothesis the irreconcilability of p values and evidence abstract the problem of testing a point null hypothesis or a small interval null hypothesis is considered of interest is the relationship between the p value or observed significance level and conditional and bayesian measures of evidence against the null hypothesis although one might presume that a small p value indicates the presence of strong evidence against the null such is not necessarily the case expanding on earlier work especially edwards lindman and savage 1963 and dickey 1977 it is shown that actual evidence against a null as measured say by posterior probability or comparative likelihood can differ by an order of magnitude from the p value for instance data that yield a p value of 05 when testing a normal mean result in a posterior probability of the null of at least 30 for any objective prior distribution objective here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null other definiti

generalized p values in significance testing of hypotheses in the presence of nuisance parameters abstract this article examines some problems of significance testing for one sided hypotheses of the form h 0 0 versus h 1 0 where is the parameter of interest in the usual setting let x be the observed data and let t x be a test statistic such that the family of distributions of t x is stochastically increasing in define cx as x t x t x 0 the p value is p x sup 0 pr x cx in the presence of a nuisance parameter there may not exist a nontrivial cx with a p value independent of we consider tests based on generalized extreme regions of the form cx x t x x t x x and conditions on t x x are given such that the p value p x sup 0 pr x cx is free of the nuisance parameter where t is stochastically increasing in we provide a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions a problem for which the fixed level testing approach

on the null distribution of bayes factors in linear regression abstractwe show that under the null the 2log bayesfactor is asymptotically distributed as a weighted sum of chi squared random variables with a shifted mean this claim holds for bayesian multi linear regression with a family of conjugate priors namely the normal inverse gamma prior the g prior and the normal prior our results have three immediate impacts first we can compute analytically a p value associated with a bayes factor without the need of permutation we provide a software package that can evaluate the p value associated with bayes factor efficiently and accurately second the null distribution is illuminating to some intrinsic properties of bayes factor namely how bayes factor quantitatively depends on prior and the genesis of bartlett s paradox third enlightened by the null distribution of bayes factor we formulate a novel scaled bayes factor that depends less on the prior and is immune to bartlett s paradox when two tests have an identical p value the test with a larger powe

large scale multiple testing under dependence summary the paper considers the problem of multiple testing under dependence in a compound decision theoretic framework the observed data are assumed to be generated from an underlying two state hidden markov model we propose oracle and asymptotically optimal datadriven procedures that aim to minimize the false non discovery rate fnr subject to a constraint on the false discovery rate fdr it is shown that the performance of a multiple testing procedure can be substantially improved by adaptively exploiting the dependence structure among hypotheses and hence conventional fdr procedures that ignore this structural information are inefficient both theoretical properties and numerical performances of the procedures proposed are investigated it is shown that the procedures proposed control fdr at the desired level enjoy certain optimality properties and are especially powerful in identifying clustered non null cases the new procedure is applied to an influenza like illness surveillance study for detecting the timing of epidemic periods

mixtures of g priors for bayesian variable selection zellner s g prior remains a popular conventional prior for use in bayesian variable selection despite several undesirable consistency issues in this article we study mixtures of g priors as an alternative to default g priors that resolve many of the problems with the original formulation while maintaining the computational tractability that has made the g prior so popular we present theoretical properties of the mixture g priors and provide real and simulated examples to compare the mixture formulation with fixed g priors empirical bayes approaches and other default procedures please see arnold zellner s letter and the author s response

control of fusion and solubility in fusion systems abstract in this article we consider control of fusion quotients and p soluble fusion systems for control of fusion we prove the three main theorems in the literature in a new largely elementary way significantly shortening their proofs to prove one of these and a theorem of aschbacher that the product of strongly closed subgroups is strongly closed we produce a consolidated treatment of quotients collating and expanding the constructions previously available we include analogues of the isomorphism theorems for fusion systems we move on to p soluble fusion systems and prove that they are constrained allowing us to effectively characterize fusion systems of p soluble groups this leads us to recast thompson factorization for q d p free fusion systems and consider it for more general fusion systems

fractional bayes factors for model comparison bayesian comparison of models is achieved simply by calculation of posterior probabilities of the models themselves however there are difficulties with this approach when prior information about the parameters of the various models is weak partial bayes factors offer a resoiution of the problem by setting aside part of the data as a training sampie the training sampie is used to obtain an initiai informative posterior distribution of the parameters in each model model comparison is then based on a bayes factor calculated from the remaining data properties of partial bayes factors are discussed particularly in the context of weak prior information and they are found to have advantages over other proposed methods of model comparison a new variant of the partial bayes factor the fractional bayes factor is advocated on grounds of consistency simplicity robustness and coherence

abundance of entire solutions to nonlinear elliptic equations by the variational method abstract we study entire bounded solutions to the equation u u u 3 0 in r 2 our approach is purely variational and is based on concentration arguments and symmetry considerations this method allows us to construct in an unified way several types of solutions with various symmetries radial breather type rectangular triangular hexagonal etc both positive and sign changing it is also applicable for more general equations in any dimension

analysis of structural equation model with ignorable missing continuous and polytomous data the main purpose of this article is to develop a bayesian approach for structural equation models with ignorable missing continuous and polytomous data joint bayesian estimates of thresholds structural parameters and latent factor scores are obtained simultaneously the idea of data augmentation is used to solve the computational difficulties involved in the posterior analysis in addition to the real missing data latent variables and latent continuous measurements underlying the polytomous data are treated as hypothetical missing data an algorithm that embeds the metropolis hastings algorithm within the gibbs sampler is implemented to produce the bayesian estimates a goodness of fit statistic for testing the posited model is presented it is shown that the proposed approach is not sensitive to prior distributions and can handle situations with a large number of missing patterns whose underlying sample sizes may be small computational efficiency of the proposed procedure is illustrated by simulation studies and a real example

information about hyperparameters in hierarchical models abstract we consider situations in which the prior distribution of a parameter vector 1 in the distribution of an observable random vector x contains a hyperparameter vector 2 the experimenter specifies another distribution for 2 that contains hyperparameters 3 and so forth one wants to learn about the hyperparameters at each level of this hierarchical model we show that for many measures of information the gain in information decreases as one moves to higher levels of hyperparameters these results are illustrated for univariate normal models and a general linear hierarchical model examples of measures of information are given for which this property does not hold

on bayesian analysis of generalized linear models using jeffreys s prior abstract generalized linear models glm s have proved suitable for modeling various kinds of data consisting of exponential family response variables with covariates bayesian analysis of such data requires specification of a prior for the regression parameters in the model used uniform priors are very commonly used as conventional noninformative priors we show however that uniform priors for glm s can lead to improper posterior distributions thus making them undesirable alternative reference priors may be constructed from jeffreys s rule in this article we give two theorems that support the use of jeffreys s priors for glm s with intrinsically fixed or known scale parameters these theorems provide i sufficient and ii necessary and sufficient conditions for the propriety of the i posterior and ii prior distributions as well as for the existence of moments implications of these theorems for some commonly used glm s are discussed finally an illustrative example is given for the binomial

subgroup families controlling p local finite groups a p local finite group consists of a finite p group s together with a pair of categories which encode conjugacy relations among subgroups of s and which are modelled on the fusion in a sylow p subgroup of a finite group it contains enough information to define a classifying space which has many of the same properties as p completed classifying spaces of finite groups in this paper we examine which subgroups control this structure more precisely we prove that the question of whether an abstract fusion system mathcal f over a finite p group s is saturated can be determined by just looking at smaller classes of subgroups of s we also prove that the homotopy type of the classifying space of a given p local finite group is independent of the family of subgroups used to define it in the sense that it remains unchanged when that family ranges from the set of mathcal f centric mathcal f radical subgroups at a minimum to the set of mathcal f quasicentric subgroups at a maximum finally we look at constrained fusion systems analogous to p constrained finite groups and prove that they in fact all arise from groups

asymptotic distribution of p values in composite null models abstract we investigate the compatibility of a null model h 0 with the data by calculating a p value that is the probability under h 0 that a given test statistic t exceeds its observed value when the null model consists of a single distribution the p value is readily obtained and it has a uniform distribution under h 0 on the other hand when the null model depends on an unknown nuisance parameter one must somehow get rid of e g by estimating it to calculate a p value various proposals have been suggested to remove each yielding a different candidate p value but unlike the simple case these p values typically are not uniformly distributed under the null model in this article we investigate their asymptotic distribution under h 0 we show that when the asymptotic mean of the test statistic t depends on the posterior predictive p value of guttman and rubin and the plug in p value are conservative i e their asymptotic distributions are more concentrated around 1 2 than a uni

existence of quasiperiodic solutions for the second order approximation boussinesq system abstract in this paper we study analytically a class of waves in the variant of the classical second order approximation boussinesq system given by t u b x x t u c x x x x t u x v x u v 1 3 2 b x x x v b x x x u v b x u x x v a x x x x x v t v b x x t v c x x x x t v x u 1 2 x x x u v x v x u x x u b x v x x v d x x x x x u where a b c d are some real constants this equation is ill posed and most initial conditions do not lead to solutions nevertheless we show that for almost every a b c and d it admits solutions that are quasiperiodic in time

control of transfer and weak closure in fusion systems we show that k1 and k 1 control transfer in every fusion system on a finite p group when p 5 and that they control weak closure of elements in every fusion system on a finite p group when p 3 this generalizes results of g glauberman concerning finite groups

realisability of p stable fusion systems abstract the aim of this paper is to investigate p stable fusion systems where p is an odd prime we examine realisable fusion systems and prove a generalisation of a result of g glauberman then we prove that p stability is determined by the normaliser systems of centric radical subgroups finally we prove that all p stable fusion systems are realisable provided there exists a stable p functor

model equivalence tests in a parametric framework in empirical research one commonly aims to obtain evidence in favor of restrictions on parameters appearing as an economic hypothesis a consequence of economic theory or an econometric modeling assumption i propose a new theoretical framework based on the kullback leibler information to assess the approximate validity of multivariate restrictions in parametric models i construct tests that are locally asymptotically maximin and locally asymptotically uniformly most powerful invariant the tests are applied to three different empirical problems

analysis of variance why it is more important than ever analysis of variance anova is an extremely important method in exploratory and confirmatory data analysis unfortunately in complex problems e g split plot designs it is not always easy to set up an appropriate anova we propose a hierarchical analysis that automatically gives the correct anova comparisons even in complex scenarios the inferences for all means and variances are performed under a model with a separate batch of effects for each row of the anova table we connect to classical anova by working with finite sample variance components fixed and random effects models are characterized by inferences about existing levels of a factor and new levels respectively we also introduce a new graphical display showing inferences about the standard deviations of each batch of effects we illustrate with two examples from our applied data analysis first illustrating the usefulness of our hierarchical computations and displays and second showing how the ideas of anova are helpful in understanding a previously fit hierarchical model

exponential dichotomies for solitary wave solutions of semilinear elliptic equations on infinite cylinders in applications solitary wave solutions of semilinear elliptic equations u g u u 0 x y r in infinite cylinders frequently arise as travelling waves of parabolic equations as such their bifurcations are an interesting issue interpreting elliptic equations on infinite cylinders as dynamical systems inxhas proved very useful still there are major obstacles in obtaining for instance bifurcation results similar to those for ordinary differential equations in this article persistence and continuation of exponential dichotomies for linear elliptic equations is proved with this technique at hands lyapunov schmidt reduction near solitary waves can be applied as an example existence of shift dynamics near solitary waves is shown if a perturbation h x u u periodic inxis added

zj theorems for fusion systems for p an odd prime we generalise the glauberman thompson p nilpotency theorem 5 ch 8 theorem 3 1 to arbitrary fusion systems we define a notion of qd p free fusion systems and show that if f is a qd p free fusion system on some finite p group p then f is controlled by w p for any glauberman functor w generalising glauberman s zj theorem 3 to arbitrary fusion systems

adaptive revised standards for statistical evidence johnson 1 argues for decreasing the bar of statistical significance from 0 05 and 0 01 to 0 005 and 0 001 respectively there is growing evidence that the canonical fixed standards of significance are inappropriate however the author simply proposes other fixed standards the essence of the problem of classical testing of significance lies in its goal of minimizing type ii error false negative for a fixed type i error false positive a real departure instead would be to minimize a weighted sum of the two errors as proposed by jeffreys 2 significance levels 1 1to whom correspondence should be addressed e mail luis pericchi at upr edu 1 xref corresp 1 1

on the bayesian interpretation of the harmonic mean p value i read with much interest the article by wilson 1 on the harmonic mean p value hmp for combining statistical significance tests i congratulate the author on a thorough discussion of this proposal however i would like to point out that good 2 had suggested the hmp already in 1958 see also refs 3 and 4 and references therein good 2 distinguishes tests in parallel from tests in series where the latter lead to fisher s method while the former lead to the hmp both good ref 2 p 804 and wilson section 5 of supporting information for ref 1 use the theorem of weighted averages of bayes factors 5 to derive the hmp good s argument is based on his empirical observation that the bayes factor against 1 1email leonhard held at uzh ch 1 xref corresp 1 1

bayesianly justifiable and relevant frequency calculations for the applied statistician a common reaction among applied statisticians is that the bayesian statistician s energies in an applied problem must be directed at the a priori elicitation of one model specification from which an optimal design and all inferences follow automatically by applying bayes s theorem to calculate conditional distributions of unknowns given knowns i feel however that the applied bayesian statistician s tool kit should be more extensive and include tools that may be usefully labeled frequency calculations three types of bayesianly justifiable and relevant frequency calculations are presented using examples to convey their use for the applied statistician

the gluing problem in the fusion systems of the symmetric alternating and linear groups a solution to linckelmann s gluing problem in all fusion systems of blocks yields an alternative formulation of alperin s weight conjecture using bredon equivariant cohomology techniques we solve the gluing problem in fusion systems of blocks which are isomorphic to the fusion systems of the symmetric groups or the alternating groups or gld q or sld q at the defining characteristic

the bayes non bayes compromise a brief review abstract various compromises that have occurred between bayesian and non bayesian methods are reviewed a citation is provided that discusses the inevitability of compromises within the bayesian approach one example deals with the masses of elementary particles but no knowledge of physics will be assumed

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

time reversal symmetry in dynamical systems a survey abstract in this paper we survey the topic of time reversal symmetry in dynamical systems we begin with a brief discussion of the position of time reversal symmetry in physics after defining time reversal symmetry as it applies to dynamical systems we then introduce a major theme of our survey namely the relation of time reversible dynamical sytems to equivariant and hamiltonian dynamical systems we follow with a survey of the state of the art on the theory of reversible dynamical systems including results on symmetric periodic orbits local bifurcation theory homoclinic orbits and renormalization and scaling some areas of physics and mathematics in which reversible dynamical systems arise are discussed in an appendix we provide an extensive bibliography on the topic of time reversal symmetry in dynamical systems

a reduction theorem for fusion systems of blocks let k be an algebraically closed field of characteristic p and g a finite group an interesting question for fusion systems is whether they can be obtained from the local structure of a block of the group algebra kg in this paper we develop some methods to reduce this question to the case when g is a central p extension of a simple group as an application of our result we obtain that the exotic examples of fusion systems discovered by ruiz and viruel a ruiz a viruel the classification of p local finite groups over the extra special group of order p3 and exponent p math z 248 2004 45 65 do not occur as fusion systems of p blocks of finite groups

stability of some solutions for elliptic equations on a cylindrical domain we study analytically a class of solutions for the elliptic equation formula 1 where 0 and e is a small parameter this equation is ill posed and most initial conditions do not lead to solutions nevertheless we show that for almost every 0 it contains solutions that are defined for large values of time and they are very close of order o e to a linear torus for long times of order o e 1 the proof uses the fact that the equation leaves invariant a smooth centre manifold and for the restriction of the system to the centre manifold uses arguments of classical perturbation theory by considering the hamiltonian formulation of the problem the birkhoff normal form and neckhoroshev type estimates 1 embed graphic 1 gif

performing likelihood ratio tests with multiply imputed data sets summary existing procedures for obtaining significance levels from multiply imputed data either i require access to the completed data point estimates and variance covariance matrices which may not be available in practice when the dimensionality of the estimand is high or ii directly combine p values with less satisfactory results taking advantage of the well known relationship between the wald and log likelihood ratio test statistics we propose a complete data log likelihood ratio based procedure it is shown that for any number of multiple imputations the proposed procedure is equivalent in large samples to the existing procedure based on the point estimates and the variance covariance matrices yet it only requires the point estimates and evaluations of the complete data log likelihood ratio statistic as a function of these estimates and the completed data the proposed procedure therefore is especially attractive with highly multiparameter incomplete data problems since it does not involve the computation of any matrices

the homotopy theory of fusion systems the main goal of this paper is to identify and study a certain class of spaces which in many ways behave like p completed classifying spaces of finite groups these spaces occur as the classifying spaces of certain algebraic objects which we call p local finite groups a p local finite group consists roughly speaking of a finite p group s and fusion data on subgroups of s encoded in a way explained below our starting point is our earlier paper blo on p completed classifying spaces of finite groups together with the axiomatic treatment by lluis puig pu pu2 of systems of fusion among subgroups of a given p group the p completion of a space x is a space xp which isolates the properties of x at the prime p and more precisely the properties which determine its mod p cohomology for example a map of spaces x f y induces a homotopy equivalence xp y p if and only if f induces an isomorphism in mod p cohomology and h xp fp h x fp in favorable cases if x is p good when g is a finite group the p completion bgp of its classifying space encodes many of the properties of g at p for example not only the mod p cohomology of bg but also the sylow p subgroup of g together with all fusion among its subgroups are determined up to isomorphism by the homotopy type of bgp our goal here is to give a direct link between p local structures and homotopy types which arise from them this theory tries to make explicit the essence of what it means to be the p completed classifying space of a finite group and at the same time yields new spaces which are not of this type but which still enjoy most of the properties a space of the form bgp would have we hope that the ideas presented here will have further applications and generalizations in algebraic topology but this theory also fits well with certain aspects of modular representation theory in particular it may give a way of constructing classifying spaces for blocks in the group ring of a finite group over an algebraically closed field of characteristic p a saturated fusion system f over a p group s consists of a set homf p q of monomorphisms for each pair of subgroups p q s which form a category under composition include all monomorphisms induced by conjugation in s and satisfy certain other axioms formulated by puig definitions 1 1 and 1 2 below in particular these axioms are satisfied by the conjugacy homomorphisms in a finite group we refer to pu and pu2 for more details of puig s work on saturated