regular orbits on symplectic modules let g be a finite group and let v be a faithful kg module k a field the question is does v contain a regular g orbit the problem has been widely studied in the literature in l berger proves that the answer is positive when a is nilpotent c 1 c free for every p and char k 1 a in 6 hargraves drops the condition of being a c c free for odd primes which are not mersenne primes a simplified proof of the main results of hargraves may be found in fleischmann s paper 3 in s gow shows that the conclusion holds when a is nilpotent char k j j a 1 and both 1 a i and char k are odd in io turull studies the case in which a is supersolvable and v is a completely reducible a module theorem 2 2 of lo extends berger s result in z the author studies a particular situation in which char k 1 1 a it is proven that if h k is a p chief factor of a solvable group g p odd and a is a p subgroup of g acting faithfully on h k then h k contains a regular a orbit the nilpotent case is open in this note we suppose that v is endowed with a g invariant nonsingular symplectic form this allows us to obtain stronger results

anova under unequal error variances by taking a generalized approach to findingp values the classical f test of the one way anova is extended to the case of unequal error variances the relationship of this result to other solutions in the literature is discussed an exact test for comparing variances of a number of populations is also developed scheff6 s procedure of multiple comparison is extended to the case of unequal variances the possibility and the approach that one can take to extend the results to simple designs involving more than one factor are briefly discussed

on finite groups in which coprime commutators are covered by few cyclic subgroups the coprime commutators j and j were recently introduced as a tool to study properties of finite groups that can be expressed in terms of commutators of elements of coprime orders every element of a finite group g is both a 1 commutator and a 0 commutator now let j 2 and let x be the set of all elements of g that are powers of j 1 commutators an element g is a j commutator if there exist a x and b g such that g a b and a b 1 for j 1 let y be the set of all elements of g that are powers of j 1 commutators an element g is a j commutator if there exist a b y such that g a b and a b 1 the subgroups of g generated by all j commutators and all j commutators are denoted by j g and j g respectively for every j 2 the subgroup j g is precisely the last term g of the lower central series of g while for every j 1 the subgroup j g is precisely the last term of the lower central series of j 1 g that is j g j 1 g in the present paper we prove that if g possesses m cyclic subgroups whose union contains all j commutators of g then j g contains a subgroup of m bounded order which is normal in g and has the property that j g is cyclic if j 2 and g possesses m cyclic subgroups whose union contains all j commutators of g then the order of j g is m bounded

langevin dynamics with constraints and computation of free energy differences in this paper we consider langevin processes with mechanical constraints the latter are a fundamental tool in molecular dynamics simulation for sampling purposes and for the computation of free energy differences the results of this paper can be divided into three parts i we propose a simple discretization of the constrained langevin process based on a standard splitting strategy we show how to correct the scheme so that it samples em exactly the canonical measure restricted on a submanifold using a metropolis rule in the spirit of the generalized hybrid monte carlo ghmc algorithm moreover we obtain in some limiting regime a consistent discretization of the overdamped langevin brownian dynamics on a submanifold also sampling exactly the correct canonical measure with constraints the corresponding numerical methods can be used to sample without any bias a probability measure supported by a submanifold ii for free energy computation using thermodynamic integration we rigorously prove that the longtime average of the lagrange multipliers of the constrained langevin dynamics yields the gradient of a rigid version of the free energy associated with the constraints a second order time discretization using the lagrange multipliers is proposed iii the jarzynski crooks fluctuation relation is proved for langevin processes with mechanical constraints evolving in time an original numerical discretization without time step error is proposed numerical illustrations are provided for ii and iii

fixed point free action on groups of odd order let a be a finite abelian group that acts fixed point freely on a finite solvable group g assume that g is odd and a is of squarefree exponent coprime to 6 we show that the fitting length of g is bounded by the length of the longest chain of subgroups of a

comparing the means and variances of a bivariate log normal distribution for a bivariate log normal distribution a confidence interval is developed for the ratio of the means the generalized confidence interval approach is used for this purpose and the procedure is applicable regardless of the sample size it is also noted that the same approach can be used to obtain a confidence interval for the ratio of the variances a modified signed log likelihood ratio procedure is also described for computing confidence intervals the coverage probabilities of the proposed confidence intervals are estimated by monte carlo and the generalized confidence intervals are found to exhibit satisfactory performance even for small sample sizes numerical results also show that the corresponding test procedures provide larger power compared with the modified signed log likelihood ratio test two examples are given one dealing with the comparison of the means and variances of health care costs and the other dealing with testing mean equivalence in quantitative assays copyright 2007 john wiley sons ltd

a comparison of several exact and approximate tests for structural shift under heteroscedasticity abstract it is known that the chow test for equality of regression coefficients is not robust to heteroscedasticity much recent attention has been paid to this problem by way of new tests the bulk of the new procedures are justified only asymptotically and little has been done to examine finite sample properties even less attention has been focused on comparisons of tests under either the null or alternative hypotheses in this paper we redress these shortcomings and also contribute by suggesting additional tests the results indicate that there are tests available with good sampling characteristics some of which are computationally easy to carry out from both the standpoint of the researcher s time and computation time

on distributions of ratios a large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables if the denominator variable is positive then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random variables if in addition the joint characteristic function of numerator and denominator is known then standard fourier inversion techniques can be used to reconstruct the distribution function from it most research in this field has been based on this correspondence but which breaks down when both numerator and denominator are supported on the entire real line the present manuscript derives inversion formulae and saddlepoint approximations that remain valid in this case and reduce to known results when the denominator is almost surely positive applications include the iv est imator of a structural parameter in a just identified equation

fiducial generalized confidence intervals generalized pivotal quantities gpqs and generalized confidence intervals gcis have proven to be useful tools for making inferences in many practical problems although gcis are not guaranteed to have exact frequentist coverage a number of published and unpublished simulation studies suggest that the coverage probabilities of such intervals are sufficiently close to their nominal value so as to be useful in practice in this article we single out a subclass of generalized pivotal quantities which we call fiducial generalized pivotal quantities fgpqs and show that under some mild conditions gcis constructed using fgpqs have correct frequentist coverage at least asymptotically we describe three general approaches for constructing fgpqs a recipe based on invertible pivotal relationships and two extensions of it and demonstrate their usefulness by deriving some previously unknown gpqs and gcis it is fair to say that nearly every published gci can be obtained using one of these recipes as an inte

generalized p values and confidence intervals for variance components applications to army test and evaluation various mixed models that are relevant for analyzing army test data are described along with several hypothesis testing and interval estimation problems the problems come up in the context of inv

testing reliability in a stress strength model when x and y are normally distributed we consider the stress strength problem in which a unit of strength x is subjected to environmental stress y an important problem in stress strength reliability concerns testing hypotheses about the reliability parameter r p x yl in this article we consider situations in which x and y are independent and have normal distributions or can be transformed to normality we do not require the two population variances to be equal our approach leads to test statistics which are exact p values that are represented as one dimensional integrals on the basis of the p value one can also construct approximate confidence intervals for the parameter of interest we also present an extension of the testing procedure to the case in which both strength and stress depend on covariates for comparative purposes the bayesian solution to the problem is also presented we use data from a rocket motor experiment to illustrate the procedure

good action on a finite group abstract let g and a be finite groups with a acting on g by automorphisms in this paper we introduce the concept of good action namely we say the action of a on g is good if h h b c h b for every subgroup b of a and every b invariant subgroup h of g this definition allows us to prove a new noncoprime hall higman type theorem if a is a nilpotent group acting on the finite solvable group g with c g a 1 a long standing conjecture states that h g l a where h g is the fitting height of g and l a is the number of primes dividing the order of a counted with multiplicities as an application of our result we prove the main theorem of this paper which states that the above conjecture is true if a and g have odd order the action of a on g is good and some other fairly general conditions are satisfied

frobenius groups of automorphisms with almost fixed point free kernel abstract let fh be a frobenius group with kernel f and complement h acting coprimely on the finite solvable group g by automorphisms we prove that if c g h is of fitting length n then the index of the n th fitting subgroup f n g in g is bounded in terms of c g f and f this generalizes a result of khukhro and makarenko 6 which handles the case n 1

confidence intervals for steady state availability of a system with exponential operating time and lognormal repair time long run availability of a system assuming lognormal repair times and exponential failure times is considered with many repairable systems the time to repair is well characterized by a lognormal distribution however due to the difficulties associated with the lognormal distribution repair times are often modeled using the lognormal distribution assuming that the variance of the lognormal distribution is known or by using some other distribution such as the exponential distribution instead of the lognormal distribution in this paper using the generalized p value approach we propose confidence intervals and exact tests for steady state availability of systems using the two parameter lognormal distribution for repair time and exponential distribution for operating time here both parameters of the lognormal distribution are assumed to be unknown a couple of examples are given to illustrate the proposed procedures a simulation study is given to demonstrate the performance of the proposed procedure results are extended for the long run availability of a system consisting of several independent parallel sub systems

hybrid monte carlo methods for sampling probability measures on submanifolds probability measures supported on submanifolds can be sampled by adding an extra momentum variable to the state of the system and discretizing the associated hamiltonian dynamics with some stochastic perturbation in the extra variable in order to avoid biases in the invariant probability measures sampled by discretizations of these stochastically perturbed hamiltonian dynamics a metropolis rejection procedure can be considered the so obtained scheme belongs to the class of generalized hybrid monte carlo ghmc algorithms we show here how to generalize to ghmc a procedure suggested by goodman holmes cerfon and zappa for metropolis random walks on submanifolds where a reverse projection check is performed to enforce the reversibility of the algorithm for any timesteps and hence avoid biases in the invariant measure we also provide a full mathematical analysis of such procedures as well as numerical experiments demonstrating the importance of the reverse projection check on simple toy examples

generalized p values and the multivariate behrens fisher problem abstract tsui and weerahandi 1989 defined generalized p values for testing statistical hypothesis in the presence of nuisance parameters and applied to obtain an exact solution to the univariate behrens fisher problem johnson and weerahandi 1988 provided a bayesian solution to the multivariate behrens fisher problem with the help of the cauchy schwarz inequality we provide an upper bound for the generalized p value for the multivariate case also we extend the result of tsui and weerahandi to present a second upper bound

conservative stochastic differential equations mathematical and numerical analysis we consider stochastic differential equations on the whole euclidean space possessing a scalar invariant along their solutions the stochastic dynamics therefore evolves on a hypersurface of the ambient space using orthogonal coordinate systems we show the existence and uniqueness of smooth solutions of the kolmogorov equation under some ellipticity conditions over the invariant hypersurfaces if we assume moreover the existence of an invariant measure we show the exponential convergence of the solution towards its average in the second part we consider numerical approximation of the stochastic differential equation and show the convergence and numerical ergodicity of a class of projected schemes in the context of molecular dynamics this yields numerical schemes that are ergodic with respect to the microcanonical measure over isoenergy surfaces

on groups in which engel sinks are cyclic abstract for an element g of a group g an engel sink is a subset e g such that for every x g all sufficiently long commutators x g g g belong to e g we conjecture that if g is a profinite group in which every element admits a sink that is a procyclic subgroup then g is procyclic by locally nilpotent we prove the conjecture in two cases when g is a finite group or a soluble pro p group

finite groups and lie rings with a metacyclic frobenius group of automorphisms abstract suppose that a finite group g admits a frobenius group of automorphisms fh of coprime order with cyclic kernel f and complement h such that the fixed point subgroup c g h of the complement is nilpotent of class c it is proved that g has a nilpotent characteristic subgroup of index bounded in terms of c c g f and f whose nilpotency class is bounded in terms of c and h only this generalizes the previous theorem of the authors and p shumyatsky where for the case of c g f 1 the whole group was proved to be nilpotent of c h bounded class examples show that the condition of f being cyclic is essential results based on the classification provide reduction to soluble groups then representation theory arguments are used to bound the index of the fitting subgroup lie ring methods are used for nilpotent groups a similar theorem on lie rings with a metacyclic frobenius group of automorphisms fh is also proved

generalized fiducial inference for binary logistic item response models generalized fiducial inference gfi has been proposed as an alternative to likelihood based and bayesian inference in mainstream statistics confidence intervals cis can be constructed from a fiducial distribution on the parameter space in a fashion similar to those used with a bayesian posterior distribution however no prior distribution needs to be specified which renders gfi more suitable when no a priori information about model parameters is available in the current paper we apply gfi to a family of binary logistic item response theory models which includes the two parameter logistic 2pl bifactor and exploratory item factor models as special cases asymptotic properties of the resulting fiducial distribution are discussed random draws from the fiducial distribution can be obtained by the proposed markov chain monte carlo sampling algorithm we investigate the finite sample performance of our fiducial percentile ci and two commonly used wald type cis associated with maximum likelihood ml estimation via monte carlo simulation the use of gfi in high dimensional exploratory item factor analysis was illustrated by the analysis of a set of the eysenck personality questionnaire data

optimal scaling of discrete approximations to langevin diffusions we consider the optimal scaling problem for proposal distributions in hastings metropolis algorithms derived from langevin diffusions we prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterized by its overall acceptance rate independently of the target distribution the asymptotically optimal acceptance rate is 0 574 we show that as a function of dimension n the complexity of the algorithm is o n1 3 which compares favourably with the o n complexity of random walk metropolis algorithms we illustrate this comparison with some example simulations

symplectic integration of constrained hamiltonian systems a hamiltonian system in potential form h q p ptmp 2 f q subject to smooth constraints on q can be viewed as a hamiltonian system on a manifold but numerical computations must be performed in rn in this paper methods which reduce hamiltonian differential algebraic equations to odes in euclidean space are examined the authors study the construction of canonical parametrizations or local charts as well as methods based on the construction of ode systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an invariant manifold in each case a hamiltonian system of ordinary differential equations is produced the stability of the constraint invariants and the behavior of the original hamiltonian along solutions are investigated both numerically and analytically

bayesian inference for the common location parameter of several shifted exponential populations abstract consider k random samples which are independently drawn from k shifted exponential distributions with respective scale parameters 1 2 k and common location parameter on the basis of the given samples and in a bayesian framework we address the problem of point and interval estimation of the location parameter under the conjugate priors which are usually proper priors moreover we also address the problem of testing the equality of the location parameters we propose bayesian hypothesis testing procedures for the equality of the location parameters under the noninformative prior the noninformative prior is usually improper which yields a calibration problem that makes the bayes factor to be defined up to a multiplicative constant so we propose the default bayesian hypothesis testing procedures based on the fractional bayes factor and the intrinsic bayes factors under the reference priors our proposed bayesian procedures are compared and contrasted via a comparison study a simulation study and a real world data analysis to the existing classical exact procedures proposed by tippett tippett s method tippett 1931 fisher fisher s method fisher 1932 stouffer inverse normal method stouffer et al 1949 and george logit method george 1977 and to the generalized variable procedures proposed by tsui and weerahandi generalized p value method tsui and weerahandi 1989

a bayesian solution to the multivariate behrens fisher problem abstract we consider the problem of finding the posterior probabilities of ellipsoids for the difference between two multivariate normal means we do not require the two population covariance matrices to be equal therefore our results pertain to the multivariate behrens fisher problem a hotelling t 2 like quantity is defined and its cdf is expressed as a linear combination of the cdf s of some f distributions this representation enables us to compute desired probabilities exactly using only one dimensional numerical integrations the calculation can easily be done with natural conjugate priors as well as with diffuse priors our main theoretical result concerning convolutions of multivariate t distributions is of some general interest for the univariate case we suggest a much simpler proof than that of ruben 1960 we also give some bounds and approximations for the posterior probabilities of ellipsoids the computation of these approximations requires much less computer time than the computatio

efficient molecular dynamics using geodesic integration and solvent solute splitting we present an approach to langevin dynamics in the presence of holonomic constraints based on decomposition of the system into components representing geodesic flow constrained impulse and constrained diffusion we show that a particular ordering of the components results in an integrator that is an order of magnitude more accurate for configurational averages than existing alternatives moreover by combining the geodesic integration method with a solvent solute force splitting we demonstrate that stepsizes of at least 8 fs can be used for solvated biomolecules with high sampling accuracy and without substantially altering diffusion rates approximately increasing by a factor of two the efficiency of molecular dynamics sampling for such systems the methods described in this article are easily implemented using the standard apparatus of modern simulation codes

fitting height of a finite group with a frobenius group of automorphisms abstract suppose that a finite group g admits a frobenius group of automorphisms fh with kernel f and complement h such that f acts without nontrivial fixed points that is such that c g f 1 it is proved that the fitting height of g is equal to the fitting height of the fixed point subgroup c g h and the fitting series of c g h coincides with the intersections of c g h with the fitting series of g as a corollary it is also proved that for any set of primes the length of g is equal to the length of c g h

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

confidence intervals for p y1 y2 with normal outcomes in linear models recently there is an emerging interest in the inference of p y1 y2 where y1 and y2 stand for two independent continuous random variables so far most of the research in this field focuses on simply comparing two outcomes without adjusting for covariates this paper mainly presents a large sample approach based on a noncentral t distribution for the confidence interval estimation of p y1 y2 with normal outcomes in linear models furthermore the performance of the proposed large sample approach is compared with that of a generalized variable approach and a bootstrap approach simulation studies demonstrate that for small to medium sample sizes both the large sample approach and the generalized variable approach provide confidence intervals with satisfying coverage probabilities whereas the bootstrap approach can be slightly liberal for certain scenarios the proposed approaches are applied to three real life data sets copyright 2008 john wiley sons ltd

testing regression equality with unequal variances on obtient un test exact similaire a celui de chow 1960 qui comporte une simple integration unidimensionnelle

generalized fiducial inference a review and new results abstractr a fisher the father of modern statistics proposed the idea of fiducial inference during the first half of the 20th century while his proposal led to interesting methods for quantifying uncertainty other prominent statisticians of the time did not accept fisher s approach as it became apparent that some of fisher s bold claims about the properties of fiducial distribution did not hold up for multi parameter problems beginning around the year 2000 the authors and collaborators started to reinvestigate the idea of fiducial inference and discovered that fisher s approach when properly generalized would open doors to solve many important and difficult inference problems they termed their generalization of fisher s idea as generalized fiducial inference gfi the main idea of gfi is to carefully transfer randomness from the data to the parameter space using an inverse of a data generating equation without the use of bayes theorem the resulting generalized fiducial distribution gfd can

on p groups of maximal class as groups of automorphisms abstract let p be a p group of maximal class and m be a maximal subgroup of p let be an element in p m such that c p p 2 and assume that p suppose that p acts on a finite group g in such a manner that c g m 1 we show that if c g is nilpotent then the fitting height of g is at most two and c g is contained in the fitting subgroup of g for p 2 without assuming that c g is nilpotent we prove that the fitting height h g of g is at most h c g 1 and the fitting series of c g coincides with the intersection of c g with the fitting series of g it is also proved that if c g x is of exponent dividing e for all elements x p m then the exponent of g is bounded solely in terms of e and p these results are in parallel with known results on action of frobenius and dihedral groups

testing variance components in mixed models with generalized p values abstract a procedure for testing one sided hypotheses on variance components in a balanced random effects model is developed the testing is performed on the basis of a generalized p value and involves a one dimensional numerical integration in the special case for which the conventional methods provide an exact test this test is equivalent to the usual f test the test is also generalized bayes in the sense that under a certain diffuse prior the p value is numerically the same as the posterior probability of the null hypothesis

one and two sided tolerance intervals for general balanced mixed models and unbalanced one way random models in this article we develop procedures for one and two sided tolerance intervals for normal general linear models in which there exists a set of independent scaled chi squared random variables the proposed procedures are based on the concept of generalized pivotal quantities and are applicable to general mixed models provided that balanced data are available however this study focuses on situations involving unbalanced data specific attention is given to the unbalanced one way random model it is shown that the use of generalized pivotal quantities allows the construction of the tolerance intervals of interest fairly straightforward some practical examples are given to illustrate the proposed procedures furthermore detailed statistical simulation studies are conducted to evaluate their performance showing that the proposed procedures can be recommended for practical use

geometric numerical integration of inequality constrained nonsmooth hamiltonian systems we consider the geometric numerical integration of hamiltonian systems subject to both equality and hard inequality constraints as in the standard geometric integration setting we target long term structure preservation additionally however we also consider invariant preservation over persistent simultaneous and or frequent boundary interactions appropriately formulating geometric methods for these cases has long remained challenging due the inherent nonsmoothness and one sided conditions that they impose to resolve these issues we thus focus both on symplectic momentum preserving behavior and the preservation of additional structures unique to the inequality constrained setting toward these goals we introduce for the first time a fully nonsmooth discrete hamilton s principle and obtain an associated framework for composing geometric numerical integration methods for inequality equality constrained systems applying this framework we formulate a new family of geometric numerical integra

fixed point free action with some regular orbits abstract let the finite group a be acting on a finite solvable group g and suppose that no non trivial element of g is fixed under the action of all the elements of a assume furthermore that a g 1 a long standing conjecture is that then the fitting height of g is bounded by the length of the longest chain of subgroups of a in 3 this was proved in the case where for every proper subgroup b of a and every b invariant elementary abelian section s of g there exists some v s such that c b v c b s we say that b has a regular orbit on s in the present paper we establish the conjecture assuming only that some of these sections have regular orbits

probabilistic measures of cost effectiveness several probability based measures are introduced in order to assess the cost effectiveness of a treatment the basic measure consists of the probability that one treatment is less costly and more effective compared with another several variants of this measure are suggested as flexible options for cost effectiveness analysis the proposed measures are invariant under monotone transformations of the cost and effectiveness measures interval estimation of the proposed measures are investigated under a parametric model assuming bivariate normality and also non parametrically the delta method and a generalized pivotal quantity approach are both investigated under the bivariate normal model a non parametric u statistics based approach is also investigated for computing confidence intervals numerical results show that under bivariate normality the solution based on generalized pivotal quantities exhibits accurate performance in terms of maintaining the coverage probability of the confidence interval the non parametric u statistics based solution is accurate for sample sizes that are at least moderately large the results are illustrated using data from a clinical trial for prostate cancer therapy copyright 2016 john wiley sons ltd

interval estimation and hypothesis testing of intraclass correlation coefficients the generalized variable approach in this paper we propose a novel approach using the concept of generalized variable gv for the confidence interval estimation of the difference of two intraclass correlation coefficients under unequal family sizes this approach can also easily provide p values for hypothesis testing simulation results show that the gv approach can provide confidence intervals with good coverage properties and perform hypothesis testing with satisfactory type i error control furthermore the confidence intervals and p values by gv approach can be easily obtained by simulation therefore the gv approach is a suitable candidate for making inference concerning two intraclass correlation coefficients

joint confidence region estimation for area under roc curve and youden index in the field of diagnostic studies the area under the roc curve auc serves as an overall measure of a biomarker diagnostic test s accuracy youden index defined as the overall correct classification rate minus one at the optimal cut off point is another popular index for continuous biomarkers of binary disease status although researchers mainly evaluate the diagnostic accuracy using auc for the purpose of making diagnosis youden index provides an important and direct measure of the diagnostic accuracy at the optimal threshold and hence should be taken into consideration in addition to auc furthermore auc and youden index are generally correlated in this paper we initiate the idea of evaluating diagnostic accuracy based on auc and youden index simultaneously as the first step toward this direction this paper only focuses on the confidence region estimation of auc and youden index for a single marker we present both parametric and non parametric approaches for estimating joint confidence region of auc and youden index we carry out extensive simulation study to evaluate the performance of the proposed methods in the end we apply the proposed methods to a real data set copyright 2013 john wiley sons ltd

riemann manifold langevin and hamiltonian monte carlo methods the paper proposes metropolis adjusted langevin and hamiltonian monte carlo sampling methods defined on the riemann manifold to resolve the shortcomings of existing monte carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations the methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for metropolis hastings or indeed hamiltonian monte carlo and metropolis adjusted langevin algorithms this allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the markov chain the methodology proposed exploits the riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold providing highly efficient convergence and exploration of the target density the performance of these riemann manifold monte carlo methods is rigorously assessed by performing inference on logistic regression models log gaussian cox point processes stochastic volatility models and bayesian estimation of dynamic systems described by non linear differential equations substantial improvements in the time normalized effective sample size are reported when compared with alternative sampling approaches matlab code that is available from http www ucl ac uk statistics research rmhmc allows replication of all the results reported

on fixed point free automorphisms abstract let r be a cyclic group of prime order which acts on the extraspecial group f in such a way that f f r suppose rf acts on a group g so that c g f 1 and r g 1 it is proved that f c g r f g as corollaries to this it is shown that the fitting series of c g r coincides with the intersections of c g r with the fitting series of g and that when r is not a fermat prime the fitting heights of c g r and g are equal

generalized confidence intervals abstract the definition of a confidence interval is generalized so that problems such as constructing exact confidence regions for the difference in two normal means can be tackled without the assumption of equal variances under certain conditions the extended definition is shown to preserve a repeated sampling property that a practitioner expects from exact confidence intervals the proposed procedure is also applied to the problem of constructing confidence intervals for the difference in two exponential means and for variance components in mixed models a repeated sampling property of generalized p values is also given with this characterization one can carry out fixed level tests of parameters of continuous distributions on the basis of generalized p values finally pratt s paradox is revisited and a procedure that resolves the paradox is given

one sided tolerance limits in balanced and unbalanced one way random models based on generalized confidence intervals we consider the problem of deriving one sided tolerance intervals in the one way random model with balanced as well as unbalanced data under the usual normality assumptions the problems investigated deal with the computation of such intervals for the observable random variable as well as the unobservable random effect in the one way random model the tolerance limits are derived using the concept of a generalized confidence interval some approximations are derived for the tolerance limits and their performance is investigated by simulation the simulation results show that the proposed tolerance limits are quite satisfactory for practical use

a systematic look at the gamma process capability indices abstract process capability indices pcis are widely used to measure whether an in control process conforms to manufacturing specifications the normal distribution is assumed in most traditional applications of pcis nevertheless it is not uncommon that some quality characteristics have skewed distributions in such cases the gamma distribution is an appropriate model and percentile based pcis for the gamma process have been studied in the literature in practical applications of pcis it is important to select an appropriate distribution between the normal and the gamma distributions based on historical data in this study we first construct a hypothesis test for model discrimination between the normal and the gamma distributions asymptotic distribution of the test statistic under the gamma process is derived we then consider statistical inference for the percentile based pcis under the gamma process the maximum likelihood method is used for point estimation and the method of generalized pivotal quantities is used for interval estimation we demonstrate the proposed methods by a practical example

pathwise accuracy and ergodicity of metropolized integrators for sdes metropolized integrators for ergodic stochastic differential equations sdes are proposed that 1 are ergodic with respect to the known equilibrium distribution of the sdes and 2 approximate pathwise the solutions of the sdes on finitetime intervals both these properties are demonstrated in the paper and precise strong error estimates are obtained it is also shown that the metropolized integrator retains these properties even in situations where the drift in the sde is nonglobally lipschitz and vanilla explicit integrators for sdes typically become unstable and fail to be ergodic 2009 wiley periodicals inc

groups of automorphisms with tni centralizers abstract a subgroup h of a finite group g is called a tni subgroup if n g h h g 1 for any g g n g h let a be a group acting on g by automorphisms where c g a is a tni subgroup of g we prove that g is solvable if and only if c g a is solvable and determine some bounds for the nilpotent length of g in terms of the nilpotent length of c g a under some additional assumptions we also study the action of a frobenius group fh of automorphisms on a group g if the set of fixed points c g f of the kernel f forms a tni subgroup and obtain a bound for the nilpotent length of g in terms of the nilpotent lengths of c g f and c g h

generalized fiducial inference for wavelet regression we apply fisher s fiducial idea to conduct statistical inference for wavelet regression we first develop a general methodology for handling model selection problems within the fiducial framework with this new methodology we then propose fiduical based methods for performing wavelet curve estimation as well as constructing both pointwise and curvewise confidence intervals it is shown that under some mild regularity conditions both the new fiducial based pointwise and curvewise confidence intervals have asymptotically correct coverage furthermore simulation results show that these new fiducial based methods especially for constructing pointwise confidence intervals also possess promising empirical properties to the best of our knowledge this is the first time that the fiducial idea has been applied to a nonparametric estimation problem

an ergodic sampling scheme for constrained hamiltonian systems with applications to molecular dynamics this article addresses the problem of computing the gibbs distribu tion of a hamiltonian system that is subject to holonomic constraints in doing so we extend recent ideas of cances et al m2an vol 41 no 2 pp 351 389 2007 who could prove a law of large numbers for unconstrained molecular systems with a separable hamiltonian em ploying a discrete version of hamilton s principle studying ergodicity for constrained hamiltonian systems we specifically focus on the numerical discretization error even if the continuous system is perfectly ergodic this property is typically not preserved by the numerical discretization the discretization error is taken care of by means of a hybrid monte carlo al gorithm that allows for sampling bias free expectation values with respect to the gibbs measure independently of the stable step size we give a demonstration of the sampling algorithm by calculating the free energy profile of a small peptide

rattle a velocity version of the shake algorithm for molecular dynamics calculations an algorithm called rattle for integrating the equations of motion in molecular dynamics calculations for molecular models with internal constraints is presented the algorithm is similar to shake which is one of the standard methods for performing such calculations rattle calculates the positions and velocities at the next time from the positions and velocities at the present time step without requiring information about the earlier history like shake it is based on the verlet algorithm and retains the simplicity of using cartesian coordinates for each of the atoms to describe the configuration of a molecule with internal constraints rattle guarantees that the coordinates and velocities of the atoms in a molecule satisfy the internal constraints at each time step rattle has two advantages over shake on computers of fixed precision it is of higher precision than shake since it deals directly with the velocities it is easier to modify rattle for use with the recently developed constant temperature and constant pressure molecular dynamics methods and with the nonequilibrium molecular dynamics methods that make use of rescaling of the atomic velocities

interval estimates for the ratio and difference of two lognormal means health research often gives rise to data that follow lognormal distributions in two sample situations researchers are likely to be interested in estimating the difference or ratio of the population means several methods have been proposed for providing confidence intervals for these parameters however it is not clear which techniques are most appropriate or how their performance might vary additionally methods for the difference of means have not been adequately explored we discuss in the present article five methods of analysis these include two methods based on the log likelihood ratio statistic and a generalized pivotal approach additionally we provide and discuss the results of a series of computer simulations finally the techniques are applied to a real example

the fitting length of finite soluble groups ii fixed point free automorphisms abstract let g be a finite soluble group and let h g be the fitting length of g if is a fixed point free automorphism of g that is c g 1 we denote by w the composition length of a long standing conjecture is that h g w and it is known that this bound is always true if the order of g is coprime to the order of in this paper we find some bounds to h g in function of w without assuming that g 1 in particular we prove the validity of the universal bound h g 7 w 2 this improves the exponential bound known earlier from a special case of a theorem of dade

some tests for variance components using generalized p values the concept of a generalized p value introduced by tsui and weerahandi is applied for testing hypotheses in two situations testing the significance of a variance component in a general balanced mixed model when an exact f test does not exist and comparing randomeffects variance components in two independent balanced mixed models extensions to the unbalanced cases are also indicated the proposed test is compared with the test based on the satterthwaite approximation through their simulated type i error probabilities the simulations indicate that the test based on the generalized p value hastype i error probabilities less than the chosen significance level most of the time whereas the type i error probabilities of the satterthwaite approximate test can be much larger than the significance level the results are illustrated using two examples