stone coalgebras we argue that the category of stone spaces forms an interesting base category for coalgebras in particular if one considers the vietoris functor as an analogue to the power set functor on the category of sets we prove that the so called descriptive general frames which play a fundamental role in the semantics of modal logics can be seen as stone coalgebras in a natural way this yields a duality between modal algebras and coalgebras for the vietoris functor building on this idea we introduce the notion of a vietoris polynomial functor over the category of stone spaces for each such functor t we provide an adjunction between t sorted boolean algebras with operators and the stone coalgebras for t we also identify the subcategory of algebras on which the adjunction restricts to an equivalence and show that the final t coalgebra is the dual of the initial t bao

a nonparametric multidimensional latent class irt model in a bayesian framework we propose a nonparametric item response theory model for dichotomously scored items in a bayesian framework the model is based on a latent class lc formulation and it is multidimensional with dimensions corresponding to a partition of the items in homogenous groups that are specified on the basis of inequality constraints among the conditional success probabilities given the latent class moreover an innovative system of prior distributions is proposed following the encompassing approach in which the largest model is the unconstrained lc model a reversible jump type algorithm is described for sampling from the joint posterior distribution of the model parameters of the encompassing model by suitably post processing its output we then make inference on the number of dimensions i e number of groups of items measuring the same latent trait and we cluster items according to the dimensions when unidimensionality is violated the approach is illustrated by two examples on simulated data and two applications based on educational and quality of life data

predictive updating methods with application to bayesian classification we propose algorithms based on random draws from predictive distributions of unknown quantities missing values for instance this procedure can either be iterative which is a special variation of the gibbs sampler or be sequential which is a variation of sequential imputation in the latter case one can update the posterior distribution with new observations easily the methods proposed have intuitive statistical implications and can be generalized to accommodate other bayesian like procedures we display some applications of the method in connection with the bayesian bootstrap classification hierarchical models and selection of variables in particular as an application of the method we present a unified treatment of switching regression models driven by a general binary process and we develop a bayesian testing procedure some simulations and a real example are used to illustrate the methods proposed

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

interpretation of af c algebras in łukasiewicz sentential calculus on donne un critere pour la non simplicite d une af c algebre 7b u en termes de proprietes de la theorie de la recursivite du groupe dimension k 0 7b u

a bayesian population model with hierarchical mixture priors applied to blood count data abstract population pharmacokinetic and pharmacodynamic studies require analyzing nonlinear growth curves fit to multiple measurements from study subjects we propose a class of nonlinear population models with nonparametric second stage priors for analyzing such data the proposed models apply a flexible class of mixtures to implement the nonparametric second stage the discussion is based on a pharmacodynamic study involving longitudinal data consisting of hematologic profiles i e blood counts measured over time of cancer patients undergoing chemotherapy we describe a full posterior analysis in a bayesian framework this includes prediction of future observations profiles and end points for new patients estimation of the mean response function for observed individuals and inference on population characteristics the mixture model is specified and given a hyperprior distribution by means of a dirichlet processes prior on the mixing measure estimation is implemented by a combination of various m

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

universal coalgebra a theory of systems in the semantics of programming finite data types such as finite lists have traditionally been modelled by initial algebras later final coalgebras were used in order to deal with infinite data types coalgebras which are the dual of algebras turned out to be suited moreover as models for certain types of automata and more generally for transition and dynamical systems an important property of initial algebras is that they satisfy the familiar principle of induction such a principle was missing for coalgebras until the work of aczel 1988 on a theory of non wellfounded sets in which he introduced a proof principle nowadays called coinduction it was formulated in terms of bisimulation a notion originally stemming from the world of concurrent programming languages milner 1980 park 1981 using the notion of coalgebra homomorphism the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras aczel and mendler 1989 thus the three basic notions of universal algebra algebra homomorphism of algebras and congruence turn out to correspond to coalgebra homomorphism of coalgebras and bisimulation respectively in this paper the latter are taken as the basic ingredients of a theory called universal coalgebra some standard results from universal algebra are reformulated using the afore mentioned correspondence and proved for a large class of coalgebras leading to a series of results on e g the lattices of subcoalgebras and bisimulations simple coalgebras and coinduction and a covariety theorem for coalgebras similar to birkhoff s variety theorem

from quantale algebroids to topological spaces fixed and variable basis approaches using the category of quantale algebroids the paper considers a generalization of the classical papert papert isbell adjunction between the categories of topological spaces and locales to partial algebraic structures it also provides a single framework in which to treat the concepts of quasi standard and stratified fuzzy topology

bayesian inference and state number determination for hidden markov models an application to the information content of the yield curve about inflation this paper is concerned with bayesian inference in hidden markov models focusing on switching regression models we propose a new methodology that delivers a joint estimation of the parameters and the number of regimes that have actually appeared in the studied sample the only prior information that is required on the latter quantity is an upper bound we implement a particle filter algorithm to compute the corresponding estimates applying this methodology to the information content of the yield curve regarding future inflation in four oecd countries we show that the predictive content for given country and combination of maturities is subject to regime switching

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

assessing a mixture model for clustering with the integrated completed likelihood we propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood for this purpose the observed data are assigned to unknown clusters using a maximum a posteriori operator then the integrated completed likelihood icl is approximated using the bayesian information criterion bic numerical experiments on simulated and real data of the resulting icl criterion show that it performs well both for choosing a mixture model and a relevant number of clusters in particular icl appears to be more robust than bic to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data

bayesian meta analysis for longitudinal data models using multivariate mixture priors summary we propose a class of longitudinal data models with random effects that generalizes currently used models in two important ways first the random effects model is a flexible mixture of multivariate normals accommodating population heterogeneity outliers and nonlinearity in the regression on subject specific covariates second the model includes a hierarchical extension to allow for meta analysis over related studies the random effects distributions are decomposed into one part that is common across all related studies common measure and one part that is specific to each study and that captures the variability intrinsic between patients within the same study both the common measure and the study specific measures are parameterized as mixture of normals models we carry out inference using reversible jump posterior simulation to allow a random number of terms in the mixtures the sampler takes advantage of the small number of entertained models the motivating application is the analysis of two studies carried out by the cancer and leukemia group b calgb in both studies we record for each patient white blood cell counts wbc over time to characterize the toxic effects of treatment the wbcs are modeled through a nonlinear hierarchical model that gathers the information from both studies

word problems in elliott monoids abstract algorithmic issues concerning elliott local semigroups are seldom considered in the literature although these combinatorial structures completely classify af algebras in general the addition operation of an elliott local semigroup is partial but for every af algebra b whose murray von neumann order of projections is a lattice this operation is uniquely extendible to the addition of an involutive monoid e b let m 1 be the farey af algebra introduced by the present author in 1988 and rediscovered by f boca in 2008 the freeness properties of the involutive monoid e m 1 yield a natural word problem for every af algebra b with singly generated e b because b is automatically a quotient of m 1 given two formulas and in the language of involutive monoids the problem asks to decide whether and code the same equivalence of projections of b this mimics the classical definition of the word problem of a group presented by generators and relations we show that the word problem of m 1 is solvable in polynomial time and so is the word problem of the behncke leptin algebras a n k and of the effros shen algebras f for 0 1 q a real algebraic number or 1 e we construct a quotient of m 1 having a godel incomplete word problem and show that no primitive quotient of m 1 is godel incomplete

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

bayesian model averaging for linear regression models abstract we consider the problem of accounting for model uncertainty in linear regression models conditioning on a single selected model ignores model uncertainty and thus leads to the underestimation of uncertainty when making inferences about quantities of interest a bayesian solution to this problem involves averaging over all possible models i e combinations of predictors when making inferences about quantities of interest this approach is often not practical in this article we offer two alternative approaches first we describe an ad hoc procedure occam s window which indicates a small set of models over which a model average can be computed second we describe a markov chain monte carlo approach that directly approximates the exact solution in the presence of model uncertainty both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected in the extreme case where there are many candidate predictors but

a method for combining inference across related nonparametric bayesian models summary we consider the problem of combining inference in related nonparametric bayes models analogous to parametric hierarchical models the hierarchical extension formalizes borrowing strength across the related submodels in the nonparametric context modelling is complicated by the fact that the random quantities over which we define the hierarchy are infinite dimensional we discuss a formal definition of such a hierarchical model the approach includes a regression at the level of the nonparametric model for the special case of dirichlet process mixtures we develop a markov chain monte carlo scheme to allow efficient implementation of full posterior inference in the given model

topological theories and closed objects abstract recent work of several authors shows that many categories of interest to topologists can be represented as categories of lax algebras in this paper we introduce the concept of a topological theory as a syntactical tool to deal with lax algebras and show the usefulness of our approach by applying it to the study of function spaces

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

the global cauchy problem for the non linear klein gordon equation on demontre l unicite de solutions faibles et l existence et l unicite de solutions globales fortement continues dans l espace energie

compensated compactness for differential forms in carnot groups and applications abstract in this paper we prove a compensated compactness theorem for differential forms of the intrinsic complex of a carnot group the proof relies on an l s hodge decomposition for these forms because of the lack of homogeneity of the intrinsic exterior differential hodge decomposition is proved using the parametrix of a suitable 0 order laplacian on forms

bayesian analysis of mixtures of factor analyzers for bayesian inference on the mixture of factor analyzers natural conjugate priors on the parameters are introduced and then a gibbs sampler that generates parameter samples following the posterior is constructed in addition a deterministic estimation algorithm is derived by taking modes instead of samples from the conditional posteriors used in the gibbs sampler this is regarded as a maximum a posteriori estimation algorithm with hyperparameter search the behaviors of the gibbs sampler and the deterministic algorithm are compared on a simulation experiment

a modal proof theory for final polynomial coalgebras an infinitary proof theory is developed for modal logics whose models are coalgebras of polynomial functors on the category of sets the canonical model method from modal logic is adapted to construct a final coalgebra for any polynomial functor the states of this final coalgebra are certain maximal sets of formulas that have natural syntactic closure properties the syntax of these logics extends that of previously developed modal languages for polynomial coalgebras by adding formulas that express the termination of certain functions induced by transition paths a completeness theorem is proven for the logic of functors which have the lindenbaum property that every consistent set of formulas has a maximal extension this property is shown to hold if the deducibility relation is generated by countably many inference rules a counter example to completeness is also given this is a polynomial functor that is not lindenbaum it has an uncountable set of formulas that is deductively consistent but has no maximal extension and is unsatisfiable even though all of its countable subsets are satisfiable

stochastic relations congruences bisimulations and the hennessy milner theorem the relationship between congruences and bisimulations is investigated for stochastic relations it is shown that stochastic relations are bisimilar provided they have congruences that generate each other from this is derived that relations that have isomorphic factor spaces are bisimilar stochastic kripke models are introduced for a modal logic and illustrated for some popular logics the criterion developed here permits proving for the general case that kripke models are bisimilar iff they accept exactly the same formulas

a maximum likelihood estimation method for random coefficient regression models summary a method for estimating the distribution of the parameters of a random coefficient regression model is proposed this distribution accounting for interindividual variability is assumed to lie in a wide class of probability distributions rather than in a given parametric class estimation is based on observations from a sample of individuals and likelihood is the estimation criterion experimental designs may be different among individuals allowing the method to apply to routinely collected data the problem has strong connections with the theory of optimum design of experiments conditions are given under which the problem has a unique solution which then corresponds to a discrete distribution a simple pharmacokinetic model involving two parameters is used as an example these parameters have a bimodal distribution as statistical specification moreover only one observation is available per individual thus the method applies even when the model is not identifiable

on a class of semilinear evolution equations for vector potentials associated with maxwell s equations in carnot groups abstract in this paper we prove existence and regularity results for a class of semilinear evolution equations that are satisfied by vector potentials associated with maxwell s equations in carnot groups connected simply connected stratified nilpotent lie groups the natural setting for these equations is provided by the so called rumin s complex of intrinsic differential forms

the nonlinear mixed effects model with a smooth random effects density summary the fixed parameters of the nonlinear mixed effects model and the density of the random effects are estimated jointly by maximum likelihood the density of the random effects is assumed to be smooth but is otherwise unrestricted the method uses a series expansion that follows from the smoothness assumption to represent the density and quadrature to compute the likelihood standard algorithms are used for optimization empirical bayes estimates of random coefficients are obtained by computing posterior modes the method is applied to data from pharmacokinetics and properties of the method are investigated by application to simulated data

a hierarchy of probabilistic system types we arrange various classes of probabilistic systems studied in the literature in an expressiveness hierarchy our expressiveness criterion is the existence of a system translation from the less expressive type into the more expressive type that preserves and reflects probabilistic bisimilarity we model the different system types as coalgebras of suitable behaviour functors and argue that the corresponding coalgebraic bisimilarity coincides with probabilistic bisimilarity for the classes for which the latter notion has been proposed in the literature the theory of coalgebras provides a unified framework for the presentation of the different classes and the system translations we needed to establish the hierarchy all these translations arise in a standard way from natural transformations between the two behaviour functors involved such a translation generally preserves coalgebraic bisimilarity we exploit a new result that under mild assumptions on the behaviour functors a system translation induced by a natural transformation with injective components also reflects bisimilarity

enriched stone type dualities abstract a common feature of many duality results is that the involved equivalence functors are liftings of hom functors into the two element space resp lattice due to this fact we can only expect dualities for categories cogenerated by the two element set with an appropriate structure a prime example of such a situation is stone s duality theorem for boolean algebras and boolean spaces the latter being precisely those compact hausdorff spaces which are cogenerated by the two element discrete space in this paper we aim for a systematic way of extending this duality theorem to categories including all compact hausdorff spaces to achieve this goal we combine duality theory and quantale enriched category theory our main idea is that when passing from the two element discrete space to a cogenerator of the category of compact hausdorff spaces all other involved structures should be substituted by corresponding enriched versions accordingly we work with the unit interval 0 1 and present duality theory for ordered and metric compact hausdorff spaces and suitably defined finitely cocomplete categories enriched in 0 1

the global cauchy problem for the critical non linear wave equation abstract we study the global cauchy problem for the non linear wave equation p 1 0 for the critical value p n 2 n 2 in space dimension n 3 we identify a weak space time integrability property stip of the solutions and prove that it is sufficient to ensure the uniqueness of weak solutions the global existence of finite energy solutions with the naturally associated stip and the global existence of regular solutions with some n dependent restrictions on the regularity for spherically symmetric solutions we prove that the previous crucial stip follows from the morawetz inequality actually in a much stronger form than necessary thereby proving that all the previous results hold in the spherically symmetric case

categorical foundations of variety based topology and topological systems the paper considers a new approach to fuzzy topology based on the concept of variety and developed in the framework of topological theories resembling those of rodabaugh as a result a categorical generalization of the notion of topological system of vickers is obtained and its theory unfolded which clarifies the relations between algebra and topology we also justify the use of semi quantales as the basic underlying structure for doing lattice valued topology as well as provide a categorical framework incorporating the theory of bitopological spaces

on bayesian analysis of mixtures with an unknown number of components discussion author s reply new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

markov chain monte carlo estimation of classical and dynamic switching and mixture models bayesian estimation of a very general model class where the distribution of the observations depends on a latent process taking values in a discrete state space is discussed in this article this model class covers finite mixture modeling markov switching autoregressive modeling and dynamic linear models with switching the consequences the unidentifiability of this type of model has on markov chain monte carlo mcmc estimation are explicitly dealt with joint bayesian estimation of all latent variables model parameters and parameters that determine the probability law of the latent process is carried out by a new mcmc method called permutation sampling the permutation sampler first samples from the unconstrained posterior which often can be done in a convenient multimove manner and then applies a permutation of the current labeling of the states of the latent process in a first run the random permutation sampler used selected the permutation randomly the mcmc output of the random permutation s

a bayesian approach to finite mixture models in bioassay via data augmentation and gibbs sampling and its application to insecticide resistance after continued treatment with an insecticide within the population of the susceptible insects resistant strains will occur it is important to know whether there are any resistant strains what the proportions are and what the median lethal doses are for the insecticide lwin and martin 1989 biometrics 45 721 732 propose a probit mixture model and use the em algorithm to obtain the maximum likelihood estimates for the parameters this approach has difficulties in estimating the confidence intervals and in testing the number of components we propose a bayesian approach to obtaining the credible intervals for the location and scale of the tolerances in each component and for the mixture proportions by using data augmentation and gibbs sampler we use bayes factor for model selection and determining the number of components we illustrate the method with data published in lwin and martin 1989

high frequency approximation of solutions to critical nonlinear wave equations this work is devoted to the description of bounded energy sequences of solutions to the equation 1 u u 4 0 in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i up to remainder terms small in energy norm and in every strichartz norm the proof relies on scattering theory for 1 and on a structure theorem for bounded energy sequences of solutions to the linear wave equation in particular we infer the existence of an a priori estimate of strichartz norms of solutions to 1 in terms of their energy

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

computational and inferential difficulties with mixture posterior distributions abstract this article deals with both exploration and interpretation problems related to posterior distributions for mixture models the specification of mixture posterior distributions means that the presence of k modes is known immediately standard markov chain monte carlo mcmc techniques usually have difficulties with well separated modes such as occur here the mcmc sampler stays within a neighborhood of a local mode and fails to visit other equally important modes we show that exploration of these modes can be imposed using tempered transitions however if the prior distribution does not distinguish between the different components then the posterior mixture distribution is symmetric and standard estimators such as posterior means cannot be used we propose alternatives for bayesian inference for permutation invariant posteriors including a clustering device and alternative appropriate loss functions

practical bayesian density estimation using mixtures of normals abstract mixtures of normals provide a flexible model for estimating densities in a bayesian framework there are some difficulties with this model however first standard reference priors yield improper posteriors second the posterior for the number of components in the mixture is not well defined if the reference prior is used third posterior simulation does not provide a direct estimate of the posterior for the number of components we present some practical methods for coping with these problems finally we give some results on the consistency of the method when the maximum number of components is allowed to grow with the sample size

drug drug interaction prediction a bayesian meta analysis approach in drug drug interaction ddi research a two drug interaction is usually predicted by individual drug pharmacokinetics pk although subject specific drug concentration data from clinical pk studies on inhibitor inducer or substrate s pk are not usually published sample mean plasma drug concentrations and their standard deviations have been routinely reported in this paper an innovative ddi prediction method based on a three level hierarchical bayesian meta analysis model is developed the first level model is a study specific sample mean model the second level model is a random effect model connecting different pk studies and all priors of pk parameters are specified in the third level model a monte carlo markov chain mcmc pk parameter estimation procedure is developed and ddi prediction for a future study is conducted based on the pk models of two drugs and posterior distributions of the pk parameters the performance of bayesian meta analysis in ddi prediction is demonstrated through a ketoconazole midazolam example the biases of ddi prediction are evaluated through statistical simulation studies the ddi marker ratio of area under the concentration curves is predicted with little bias less than 5 per cent and its 90 per cent credible interval coverage rate is close to the nominal level sensitivity analysis is conducted to justify prior distribution selections copyright 2007 john wiley sons ltd

a semi parametric bayesian approach to average bioequivalence bioequivalence assessment is an issue of great interest development of statistical methods for assessing bioequivalence is an important area of research for statisticians bioequivalence is usually determined based on the normal distribution we relax this assumption and develop a semi parametric mixed model for bioequivalence data the proposed method is quite flexible and practically meaningful our proposed method is based on a mixture normal distribution and a non parametric bayesian approach using a dirichlet process mixture prior a numerical example illustrates the use of our procedure

a smooth nonparametric estimate of a mixing distribution using mixtures of gaussians abstract we propose a method of estimating mixing distributions using maximum likelihood over the class of arbitrary mixtures of gaussians subject to the constraint that the component variances be greater than or equal to some minimum value h this approach can lead to estimates of many shapes with smoothness controlled by parameter h we show that the resulting estimate will always be a finite mixture of gaussians each having variance h the nonparametric maximum likelihood estimate can be viewed as a special case with h 0 the method can be extended to estimate multivariate mixing distributions examples and the results of a simulation study are presented

measuring the effect of observations on bayes factors summary in this paper we consider a measure of the effect of single observations on a logarithmic bayes factor defined via the difference in the logarithms of the bayes factors conditional first on all the data and then omitting an observation the measure is related to the conditional predictive ordinate the form of the measure and examples of its use are presented for a variety of situations normal samples linear models log linear models and the checking of distributional assumptions

coalgebraic semantics of modal logics coalgebras can be seen as a natural abstraction of kripke frames in the same sense coalgebraic logics are generalised modal logics in this paper we give an overview of the basic tools techniques and results that connect coalgebras and modal logic we argue that coalgebras unify the semantics of a large range of different modal logics such as probabilistic graded relational conditional and discuss unifying approaches to reasoning at this level of generality we review languages defined in terms of the so called cover modality languages induced by predicate liftings as well as their common categorical abstraction and present abstract results on completeness expressiveness and complexity in these settings both for basic languages as well as a number of extensions such as hybrid languages and fixpoints

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

stone duality above dimension zero axiomatising the algebraic theory of c x abstract it has been known since the work of duskin and pelletier four decades ago that k op the opposite of the category of compact hausdorff spaces and continuous maps is monadic over the category of sets it follows that k op is equivalent to a possibly infinitary variety of algebras in the sense of slominski and linton isbell showed in 1982 that the lawvere linton algebraic theory of can be generated using a finite number of finitary operations together with a single operation of countably infinite arity in 1983 banaschewski and rosick independently proved a conjecture of bankston establishing a strong negative result on the axiomatisability of k op in particular is not a finitary variety isbell s result is best possible the problem of axiomatising by equations has remained open using the theory of chang s mv algebras as a key tool along with isbell s fundamental insight on the semantic nature of the infinitary operation we provide a finite axiomatisation of

a coalgebraic view on positive modal logic positive modal logic is the restriction of the modal local consequence relation defined by the class of all kripke models to the propositional negation free modal language the class of positive modal algebras is the one canonically associated with pml according to the theory of the algebrization of logics lecture notes in logic springer berlin 1996 a priestley style duality is established between the category of positive modal algebras and the category of k spaces in j igpl 7 6 1999 683 in this paper we establish a categorical equivalence between the category k of k spaces and the category coalg v of coalgebras of a suitable endofunctor v on the category of priestley spaces

sharp a priori estimates for div curl systems in heisenberg groups abstract in this paper we prove a family of inequalities for differential forms in heisenberg groups h 1 and h 2 that are the natural counterpart of a class of div curl inequalities in de rham s complex proved by lanzani stein and bourgain brezis

categorically algebraic topology versus universal topology this paper continues to develop the theory of categorically algebraic catalg topology introduced as a common framework for the majority of the existing many valued topological settings to provide convenient means of interaction between different approaches motivated by the results of universal topology of h herrlich we show that a concrete category is fibre small and topological if and only if it is concretely isomorphic to a subcategory of a category of catalg topological structures which is definable by topological co axioms

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

bayesian analysis of cross section and clustered data treatment models this paper is concerned with the problem of determining the effect of a categorical treatment variable on a response given that the treatment is non randomly assigned and the response on any given subject is observed for one setting of the treatment we consider classes of models that are designed for such problems these models are subjected to a fully bayesian analysis based on markov chain monte carlo methods the analysis of the treatment effect is then based on amongst other things the posterior distribution of the potential outcomes counter factuals at the subject level which is obtained as a by product of the mcmc simulation procedure the analysis is extended to models with categorical treatments and binary and clustered outcomes the problem of model comparisons is also considered different aspects of the methodology are illustrated through two data examples

final coalgebras for functors on measurable spaces we prove that every functor on the category meas of measurable spaces built from the identity and constant functors using products coproducts and the probability measure functor d has a final coalgebra our work builds on the construction of the universal harsanyi type spaces by heifetz and samet and papers by rosziger and jacobs on coalgebraic modal logic we construct logical languages probabilistic logics of transition systems and interpret them on coalgebras the final coalgebra is carried by the set of descriptions of all points in all coalgebras for the category set we work with the functor d of discrete probability measures we prove that every functor on set built from d and the expected functors has a final coalgebra the work for set differs from the work for meas negation in needed for final coalgebras on set but not for meas

estimation of finite mixture distributions through bayesian sampling summary a formal bayesian analysis of a mixture model usually leads to intractable calculations since the posterior distribution takes into account all the partitions of the sample we present approximation methods which evaluate the posterior distribution and bayes estimators by gibbs sampling relying on the missing data structure of the mixture model the data augmentation method is shown to converge geometrically since a duality principle transfers properties from the discrete missing data chain to the parameters the fully conditional gibbs alternative is shown to be ergodic and geometric convergence is established in the normal case we also consider non informative approximations associated with improper priors assuming that the sample corresponds exactly to a k component mixture

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

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea