perfect simulation in stochastic geometry simulation plays an important role in stochastic geometry and related fields because all but the simplest random set models tend to be intractable to analysis many simulation algorithms deliver approximate samples of such random set models for example by simulating the equilibrium distribution of a markov chain such as a spatial birth and death process the samples usually fail to be exact because the algorithm simulates the markov chain for a long but finite time and thus convergence to equilibrium is only approximate the seminal work by propp and wilson made an important contribution to simulation by proposing a coupling method coupling from the past cftp which delivers perfect that is to say exact simulations of markov chains in this paper we introduce this new idea of perfect simulation and illustrate it using two common models in stochastic geometry the dead leaves model and a boolean model conditioned to cover a finite set of points

gibbs sampling for bayesian non conjugate and hierarchical models by using auxiliary variables summary we demonstrate the use of auxiliary or latent variables for sampling non standard densities which arise in the context of the bayesian analysis of non conjugate and hierarchical models by using a gibbs sampler their strategic use can result in a gibbs sampler having easily sampled full conditionals we propose such a procedure to simplify or speed up the markov chain monte carlo algorithm the strength of this approach lies in its generality and its ease of implementation the aim of the paper therefore is to provide an alternative sampling algorithm to rejection based methods and other sampling approaches such as the metropolis hastings algorithm

extensions of fill s algorithm for perfect simulation fill s algorithm for perfect simulation for attractive finite state space models unbiased for user impatience is presented in terms of stochastic recursive sequences and extended in two ways repulsive discrete markov random fields with two coding sets like the auto poisson distribution on a lattice with 4 neighbourhood can be treated as monotone systems if a particular partial ordering and quasi maximal and quasi minimal states are used fill s algorithm then applies directly combining fill s rejection sampling with sandwiching leads to a version of the algorithm which works for general discrete conditionally specified repulsive models extensions to other types of models are briefly discussed

functions analytic on the half plane as quantum mechanical states a transform between the state space of one dimensional quantum mechanical systems and a direct sum of two spaces of square integrable functions analytic on the open upper half plane is constructed it gives a representation of usual quantum mechanics on which the free evolution is trivial and the representation of canonical transformation very simple generalizations to higher dimensions are also discussed

a connection between quantum hilbert space and classical phase space operators we develop a general classicalization procedure that links hilbert space and phase space operators using weyl s operator then we transform the time dependent schrodinger equation into a phase space picture using free parameters they include position q and momentum p we expand the phase space hamiltonian in an taylor series and fix parameters with the condition that coefficients of 0 i1 q and i1 p vanish this condition results in generalized hamilton equations and a natural link between classical and quantum dynamics while the quantum motion equation remains exact in this picture the schrodinger equation reduces in the classical limit to a generalized liouville equation for the quantum mechanical system state we modify glauber s coherent states with a suitable phase factor s q p t and use them to obtain phase space representations of quantum dynamics and quantum mechanical quantities

markov chain monte carlo 10 years and still running although markov chain monte carlo mcmc techniques can be traced back to the early 1950s and are almost contemporary with independent monte carlo methods the use of these techniques has only really taken off in the past 10 years at least in mainstream statistics with the work of gelfand and smith 1990 and the rediscovery of metropolis s and hastings s papers the impact on the discipline is deep and durable because these methods have opened new horizons in the scale of the problems that one can deal with thus enhancing the position of statistics in most applied fields the mcmc revolution has in particular boosted bayesian statistics to new heights by providing a virtually universal tool for dealing with integration and optimization problems this can be seen in for instance the explosion of papers dealing with complex models hierarchical modelings nonparametric bayesian estimation and spatial statistics this trend has also created new synergies with mathematicians and probabilists as well as econometricians engineers ecologists astronomers and others for theoretical requests and practical implications of mcmc techniques it is impossible to provide here a complete perspective on mcmc methods and applications for this as well as for other references we refer the reader to the books by gilks richardson and spiegelhalter 1995 and robert and casella 1999 here we focus on four particular aspects of mcmc algorithms theoretical foundations practical implementation bayesian inference and prospects the web provides many relevant sites including the mcmc preprint server http www statslab cam ac uk r mcmc which offers a most useful window to the current research on mcmc wilson s site on perfect simulation http dimacs rutgers edu dbwilson exact h which keeps track of papers and applets on this topic and a site on convergence control techniques http www ensae fr crest statistique robert mcdiag even more recent developments allow for on line computations through applets like breyer s http www maths lancs ac uk breyer java html which impressively illustrates the behavior of different samplers for simple problems note also that the bugs and coda software are freely available at http www mrc bsu cam ac uk bu

quantization of a classical system on a coadjoint orbit of the poincare group in 1 1 dimensions the connection is investigated between quantization by means of coherent states and geometric quantization when the base manifold is a coadjoint orbit and hence a homogeneous space of the 1 1 dimensional poincare group coherent states of the poincare group stem from a representation that is square integrable modulo closed subgroup and so they depend on a measurable section on the given homogeneous space for each section that leads to a tight frame a geometric prequantization is constructed i e a hermitian line bundle with metric connection conditions are given under which the two forms associated to the connection and to the coadjoint orbit structure of the base manifold coincide

fuzzy normal subgroups and fuzzy cosets abstract we introduce here the notion of 1 i a fuzzy normal subgroup and 2 ii a fuzzy coset we prove that for a group g a fuzzy subgroup is fuzzy normal if and only if it is constant on the conjugate classes of g further we show that the level subgroups of a fuzzy normal subgroup are all normal we obtain several results which are analogs of some basic theorems of group theory in particular a fuzzy version of lagrange s theorem is established

a contribution to the theory of fuzzy subgroups abstract in this paper we continue our study in order to give a partial answer to the question suggested by asaad in 1991 what can be said about the structure of a group g when the information are known about the structure of a fuzzy subgroup a of g and viceversa

modular algebras in geometric quantization presented here is a discussion on the connection between geometric quantization and algebraic quantization the former procedure relies on a construction of unitary irreducible representations that starts from co adjoint orbits and uses polarizations while the latter depends on the purely algebraic characterization of unitary irreducible representations which is based on central decompositions of von neumann algebras in involutive duality and their decompositions in terms of maximal abelian subalgebras intermediate stages of these two quantization methods turn out to be complementary leading thus to a new characterization of the so called discrete series representations

perfect slice samplers perfect sampling allows the exact simulation of random variables from the stationary measure of a markov chain by exploiting monotonicity properties of the slice sampler we show that a perfect version of the algorithm can be easily implemented at least when the target distribution is bounded various extensions including perfect product slice samplers and examples of applications are discussed

transforms associated to square integrable group representations i general results let g be a locally compact group which need not be unimodular let x u x x g be an irreducible unitary representation of g in a hilbert space h u assume that u is square integrable i e that there exists in h u at least one nonzero vector g such that u x g g 2 dx we give here a reasonably self contained analysis of the correspondence associating to every vector f h u the function u x g f on g discussing its isometry characterization of the range inversion and simplest interpolation properties this correspondence underlies many properties of generalized coherent states

quantum and semiclassical representations over lagrangian submanifolds in su 2 so 4 and su 1 1 irreducible representations of three simplest lie algebras are realized over lagrangian submanifolds over closed curves tori and spheres in coadjoint orbits the intertwining operator is constructed which enables to pass from an abstract representation to a representation the integral kernel of the intertwining operator involves special coherent states the simple integral formulas are obtained for exact and semiclassical eigenvectors and for solutions of the cauchy problem over lie algebras mentioned in the title the hamiltonians considered are nonanalytic in general

convergence of slice sampler markov chains we analyse theoretical properties of the slice sampler we find that the algorithm has extremely robust geometric ergodicity properties for the case of just one auxiliary variable we demonstrate that the algorithm is stochastically monotone and we deduce analytic bounds on the total variation distance from stationarity of the method by using foster lyapunov drift condition methodology

quantum and classical mechanics on homogeneous riemannian manifolds starting from the axioms of quantum mechanics as formalized by the systems of imprimitivity for homogeneous riemannian manifolds the classical theory is derived as a consequence complete with its phase space realized as the space of pure classical states a generalized version of the wigner moyal correspondence rule the jordan and lie algebra structures of functions on the cotangent bundle given by point wise multiplication and poisson bracket and the momentum map a comparison is also given of the quantum and classical dynamics and equilibrium statistical mechanics of free particles on compact manifolds of constant negative curvature

groups and fuzzy subgroups ii abstract in 1991 asaad has suggested the following question what can be said about the structure of a group g when information is known about the structure of a fuzzy subgroup a of g and vice versa the purpose of this paper is to continue the investigation of the above mentioned question

likelihood subgradient densities we introduce likelihood subgradient densities and explore their basic properties using mixtures of likelihood subgradient densities we propose an approach for constructing tight enveloping functions in the bayesian context in the case of normal priors with normal data the area underneath the resulting enveloping function is bounded above by the approach is extended to k dimensional models where the corresponding bound is more generally our approach should also yield tight enveloping functions for other models in which the data are close to normal such models include generalized linear models e g bayesian poisson regression and the bayesian logit model simulations based on the approach are performed for two separate models using accept reject methods

perfect samplers for mixtures of distributions summary we consider the construction of perfect samplers for posterior distributions associated with mixtures of exponential families and conjugate priors starting with a perfect slice sampler in the spirit of mira and co workers the methods rely on a marginalization akin to rao blackwellization and illustrate the duality principle of diebolt and robert a first approximation embeds the finite support distribution on the latent variables within a continuous support distribution that is easier to simulate by slice sampling but we later demonstrate that the approximation can be very poor we conclude by showing that an alternative perfect sampler based on a single backward chain can be constructed this alternative can handle much larger sample sizes than the slice sampler first proposed

densities of covariant observables positive operator valued observables in a complex hilbert space h based on a topological homogeneous space g h and g covariant with respect to a strongly continuous unitary representation on h of a locally compact group g are investigated the goal is to determine whether they are the weak integrals of some positive operator valued densities relative to a g quasi invariant measure on g h to this end the notion of a kernel hilbert space is generalized to spaces of equivalence classes with respect to of mappings of g h into a complex hilbert space k

tight frames of compactly supported affine wavelets this paper extends the class of orthonormal bases of compactly supported wavelets recently constructed by daubechies commun pure appl math 41 909 1988 for each integer n 1 a family of wavelet functions having support 0 2n 1 is constructed such that jk x 2j 2 2jx k kj k z is a tight frame of l2 r i e for every f l2 r f c jk jk f jk for some c 0 this family is parametrized by an algebraic subset vn of r4n furthermore for n 2 a proper algebraic subset wn of vn is specified such that all points in vn outside of wn yield orthonormal bases the relationship between these tight frames and the theory of group representations and coherent states is discussed

geometric quantization modular reduction theory and coherent states the natural role played by coherent states in the geometric quantization program is brought out by studying the mathematical equivalence between two physical interpretations that have recently been proposed for this program these interpretations are based respectively on the modular algebra structure of prequantization and the reproducing kernel structure of phase space quantization the arguments are presented in this paper for the particular case where the phase space of the system considered is the cotangent bundle t m of a homogeneous manifold m and for didactic reasons the latter is taken to be a real vector space

fuzzy subgroups of nilpotent groups in 1991 asaad has suggested the following question what can be said about the structure of a group g when information is known about the structure of a fuzzy subgroup a of g and vice versa this question has been partially investigated in fuzzy sets and systems39 1991 323 328 the purpose of this paper is to continue more investigations for the above mentioned question

spatial statistics and bayesian computation on wednesday may 6th 1992 professor b w silverman in the chair summary markov chain monte carlo mcmc algorithms such as the gibbs sampler have provided a bayesian inference machine in image analysis and in other areas of spatial statistics for several years founded on the pioneering ideas of ulf grenander more recently the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a markov random field has opened the way to the use of mcmc in general bayesian computation in this paper we trace the early development of mcmc in bayesian inference review some recent computational progress in statistical physics based on the introduction of auxiliary variables and discuss its current and future relevance in bayesian applications we briefly describe a simple mcmc implementation for the bayesian analysis of agricultural field experiments with which we have some practical experience

coherent states over symplectic homogeneous spaces a generalization of the perelomov procedure for the construction of coherent states is proposed the new procedure is used to construct systems of coherent states in the carrier spaces of unitary irreducible representations of groups g s v where v is a vector space and s gl v the coherent states are shown to be labeled by the points in cotangent bundles t o of orbits o of s in v the dual of v it is proven that t o is a symplectic homogeneous space of g the generalized procedure for the construction of coherent states presented in this paper is shown to encompass as special cases the constructions known in the literature for the coherent states of the weyl heisenberg the ax b and the galilei and poincare groups moreover completely new sets of coherent states are constructed for the euclidean group e n where the perelomov construction fails

groups and fuzzy subgroups abstract the purpose of this paper is to deal with the following two problems 1 what can be said about the structure of a fuzzy subgroup a of a group g when information is known about the structure of g 2 what can be said about the structure of a group g when information is known about the structure of a fuzzy subgroup a of g